Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts

We compare the classification as entangled or separable of Bell diagonal bipartite qudits with positive partial transposition (PPT) and their properties for different dimensions. For dimension [Formula: see text], a form of entanglement exists that is hard to detect and called bound entanglement due to the fact that such entangled states cannot be used for entanglement distillation. Up to this date, no efficient solution is known to differentiate bound entangled from separable states. We address and compare this problem named separability problem for a family of bipartite Bell diagonal qudits with special algebraic and geometric structures and applications in quantum information processing tasks in different dimensions. Extending analytical and numerical methods and results for Bell diagonal qutrits ([Formula: see text]), we successfully classify more than [Formula: see text] of representative Bell diagonal PPT states for [Formula: see text]. Via those representative states we are able to estimate the volumes of separable and bound entangled states among PPT ququarts ([Formula: see text]). We find that at least [Formula: see text] of all PPT states are separable, [Formula: see text] bound entangled and for [Formula: see text] it remains unclear whether they are separable or bound entangled. Comparing the structure of bound entangled states and their detectors, we find considerable differences in the detection capabilities for different dimensions and relate those to differences of the Euclidean geometry for qutrits ([Formula: see text]) and ququarts ([Formula: see text]). Finally, using a detailed visual analysis of the set of separable and bound entangled Bell diagonal states in both dimensions, qualitative observations are made that allow to better distinguish bound entangled from separable states.

Exploring finite temperature properties of materials with quantum computers

Thermal properties of nanomaterials are crucial to not only improving our fundamental understanding of condensed matter systems, but also to developing novel materials for applications spanning research and industry. Since quantum effects arise at the nano-scale, these systems are difficult to simulate on classical computers. Quantum computers can efficiently simulate quantum many-body systems, yet current quantum algorithms for calculating thermal properties of these systems incur significant computational costs in that they either prepare the full thermal state on the quantum computer, or they must sample a number of pure states from a distribution that grows with system size. Canonical thermal pure quantum (TPQ) states provide a promising path to estimating thermal properties of quantum materials as they neither require preparation of the full thermal state nor require a growing number of samples with system size. Here, we present an algorithm for preparing canonical TPQ states on quantum computers. We compare three different circuit implementations for the algorithm and demonstrate their capabilities in estimating thermal properties of quantum materials. Due to its increasing accuracy with system size and flexibility in implementation, we anticipate that this method will enable finite temperature explorations of relevant quantum materials on near-term quantum computers.

Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines

Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that variational quantum classifiers and support vector machines with quantum kernels can solve a classification problem based on the k-FORRELATION problem, which is known to be PROMISEBQP-complete. Because the PROMISEBQP complexity class includes all Bounded-Error Quantum Polynomial-Time (BQP) decision problems, our results imply that there exists a feature map and a quantum kernel that make variational quantum classifiers and quantum kernel support vector machines efficient solvers for any BQP problem. Hence, this work implies that their feature map and quantum kernel, respectively, can be designed to have a quantum advantage for any classification problem that cannot be classically solved in polynomial time but contrariwise by a quantum computer.

Suppressing quantum errors by scaling a surface code logical qubit

Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction^1,2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10^-6 logical error per cycle floor set by a single high-energy event (1.6 × 10^-7 excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.

Quantum machine learning beyond kernel methods

Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and studied extensively. Yet, our understanding of how these models compare, both mutually and to classical models, remains limited. In this work, we identify a constructive framework that captures all standard models based on parametrized quantum circuits: that of linear quantum models. In particular, we show using tools from quantum information theory how data re-uploading circuits, an apparent outlier of this framework, can be efficiently mapped into the simpler picture of linear models in quantum Hilbert spaces. Furthermore, we analyze the experimentally-relevant resource requirements of these models in terms of qubit number and amount of data needed to learn. Based on recent results from classical machine learning, we prove that linear quantum models must utilize exponentially more qubits than data re-uploading models in order to solve certain learning tasks, while kernel methods additionally require exponentially more data points. Our results provide a more comprehensive view of quantum machine learning models as well as insights on the compatibility of different models with NISQ constraints.

Entanglement detection with artificial neural networks

Quantum entanglement is one of the essential resources involved in quantum information processing tasks. However, its detection for usage remains a challenge. The Bell-type inequality for relative entropy of coherence serves as an entanglement witness for pure entangled states. However, it does not perform reliably for mixed entangled states. This paper constructs a classifier by employing the relationship between coherence and entanglement for supervised machine learning methods. This method encodes multiple Bell-type inequalities for the relative entropy of coherence into an artificial neural network to detect the entangled and separable states in a quantum dataset.

A new entropic quantum correlation measure for adversarial systems

Quantum correlation often refers to correlations exhibited by two or more local subsystems under a suitable measurement. These correlations are beyond the framework of classical statistics and the associated classical probability distribution. Quantum entanglement is the most well-known of such correlations and plays an important role in quantum information theory. However, there exist non-entangled states that still possess quantum correlations which cannot be described by classical statistics. One such measure that captures these non-classical correlations is discord. Here we introduce a new measure of quantum correlations which we call entropic accord that fits between entanglement and discord. It is defined as the optimised minimax mutual information of the outcome of the projective measurements between two parties. We show a strict hierarchy exists between entanglement, entropic accord and discord for two-qubit states. We study two-qubit states which shows the relationship between the three entropic quantities. In addition to revealing a class of correlations that are distinct from discord and entanglement, the entropic accord measure can be inherently more intuitive in certain contexts.

High-dimensional quantum key distribution implemented with biphotons

We present a high-dimensional measurement device-independent (MDI) quantum key distribution (QKD) protocol employing biphotons to encode information. We exploit the biphotons as qutrits to improve the tolerance to error rate. Qutrits have a larger quantum system; hence they carry more bits of classical information and have improved robustness against eavesdropping compared to qubits. Notably, our proposed protocol is independent of measurement devices, thus eliminating the possibility of side-channel attacks. Also, we employ the finite key analysis approach to study the performance of our proposed protocol under realistic conditions where finite resources are used. Furthermore, we simulated the secret key rate for the proposed protocol in terms of the transmission distance for different fixed amounts of signals. The results prove that this protocol achieves a considerable secret key rate for a moderate transmission distance of 90 km by using [Formula: see text] signals. Moreover, the expected secret key rate was simulated to examine our protocol's performance at various intrinsic error rate values, [Formula: see text] caused by misalignment and instability due to the optical system. These results show that reasonable key rates are achieved with a minimum data size of about [Formula: see text] signals which are realizable with the current technology. Thus, implementing MDI-QKD using finite resources while allowing intrinsic errors due to the optical system makes a giant step forward toward realizing practical QKD implementations.

Provably-secure quantum randomness expansion with uncharacterised homodyne detection

Quantum random number generators (QRNGs) are able to generate numbers that are certifiably random, even to an agent who holds some side information. Such systems typically require that the elements being used are precisely calibrated and validly certified for a credible security analysis. However, this can be experimentally challenging and result in potential side-channels which could compromise the security of the QRNG. In this work, we propose, design and experimentally demonstrate a QRNG protocol that completely removes the calibration requirement for the measurement device. Moreover, our protocol is secure against quantum side information. We also take into account the finite-size effects and remove the independent and identically distributed requirement for the measurement side. More importantly, our QRNG scheme features a simple implementation which uses only standard optical components and are readily implementable on integrated-photonic platforms. To validate the feasibility and practicability of the protocol, we set up a fibre-optical experimental system with a home-made homodyne detector with an effective efficiency of 91.7% at 1550 nm. The system works at a rate of 2.5 MHz, and obtains a net randomness expansion rate of 4.98 kbits/s at 10¹⁰ rounds. Our results pave the way for an integrated QRNG with self-testing feature and provable security.

Long distance entanglement and high-dimensional quantum teleportation in the Fermi-Hubbard model

The long distance entanglement in finite size open Fermi-Hubbard chains, together with the end-to-end quantum teleportation are investigated. We show the peculiarity of the ground state of the Fermi-Hubbard model to support maximum long distance entanglement, which allows it to operate as a quantum resource for high fidelity long distance quantum teleportation. We determine the physical properties and conditions for creating scalable long distance entanglement and analyze its stability under the effect of the Coulomb interaction and the hopping amplitude. Furthermore, we show that the choice of the measurement basis in the protocol can drastically affect the fidelity of quantum teleportation and we argue that perfect information transfer can be attained by choosing an adequate basis reflecting the salient properties of the quantum channel, i.e. Hubbard projective measurements.

Programmable frequency-bin quantum states in a nano-engineered silicon device

Photonic qubits should be controllable on-chip and noise-tolerant when transmitted over optical networks for practical applications. Furthermore, qubit sources should be programmable and have high brightness to be useful for quantum algorithms and grant resilience to losses. However, widespread encoding schemes only combine at most two of these properties. Here, we overcome this hurdle by demonstrating a programmable silicon nano-photonic chip generating frequency-bin entangled photons, an encoding scheme compatible with long-range transmission over optical links. The emitted quantum states can be manipulated using existing telecommunication components, including active devices that can be integrated in silicon photonics. As a demonstration, we show our chip can be programmed to generate the four computational basis states, and the four maximally-entangled Bell states, of a two-qubits system. Our device combines all the key properties of on-chip state reconfigurability and dense integration, while ensuring high brightness, fidelity, and purity.

Suppressing Decoherence in Quantum State Transfer with Unitary Operations

Decoherence is the fundamental obstacle limiting the performance of quantum information processing devices. The problem of transmitting a quantum state (known or unknown) from one place to another is of great interest in this context. In this work, by following the recent theoretical proposal, we study an application of quantum state-dependent pre- and post-processing unitary operations for protecting the given (multi-qubit) quantum state against the effect of decoherence acting on all qubits. We observe the increase in the fidelity of the output quantum state both in a quantum emulation experiment, where all protecting unitaries are perfect, and in a real experiment with a cloud-accessible quantum processor, where protecting unitaries themselves are affected by the noise. We expect the considered approach to be useful for analyzing capabilities of quantum information processing devices in transmitting known quantum states. We also demonstrate the applicability of the developed approach for suppressing decoherence in the process of distributing a two-qubit state over remote physical qubits of a quantum processor.

Quantum-Solving Algorithm for d'Alembert Solutions of the Wave Equation

When faced with a quantum-solving problem for partial differential equations, people usually transform such problems into Hamiltonian simulation problems or quantum-solving problems for linear equation systems. In this paper, we propose a third approach to solving partial differential equations that differs from the two approaches. By using the duality quantum algorithm, we construct a quantum-solving algorithm for solving the first-order wave equation, which represents a typical class of partial differential equations. Numerical results of the quantum circuit have high precision consistency with the theoretical d'Alembert solution. Then the routine is applied to the wave equation with either a dissipation or dispersion term. As shown by complexity analysis for all these cases of the wave equation, our algorithm has a quadratic acceleration for each iteration compared to the classical algorithm.

Quantum brachistochrone

Quantum brachistochrone (QB) is a quantum analogue of classical brachistochrone (shortest path). It is a solution to the following problem: How can we perform a desired quantum operation (or obtain a desired final quantum state) most quickly, by a time-dependent Hamiltonian subject to given constraints? Finding QB is a fundamental problem in quantum mechanics in its own right. Moreover, it will be useful in the study of quantum information and quantum engineering, such as quantum speed limits and implementations of quantum computers. A general framework for finding QBs, called QB formalism, has been developed. It is based on Pontryagin's maximum principle. We review the basics of the QB formalism, give simple examples, and briefly discuss some related studies. This article is part of the theme issue 'Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives'.

Entanglement-assisted quantum communication with simple measurements

Dense coding is the seminal example of how entanglement can boost qubit communication, from sending one bit to sending two bits. This is made possible by projecting separate particles onto a maximally entangled basis. We investigate more general communication tasks, in both theory and experiment, and show that simpler measurements enable strong and sometimes even optimal entanglement-assisted qubit communication protocols. Using only partial Bell state analysers for two qubits, we demonstrate quantum correlations that cannot be simulated with two bits of classical communication. Then, we show that there exists an established and operationally meaningful task for which product measurements are sufficient for the strongest possible quantum predictions based on a maximally entangled two-qubit state. Our results reveal that there are scenarios in which the power of entanglement in enhancing quantum communication can be harvested in simple and scalable optical experiments.

Enhancing photon generation rate with broadband room-temperature quantum memory

Photons with high generation rate is one of the essential resources for quantum communication, quantum computing and quantum metrology. Due to the naturally memory-built-in feature, the memory-based photon source is a promising route towards large-scale quantum information processing. However, such photon sources are mostly implemented in extremely low-temperature ensembles or isolated systems, limiting its physical scalability. Here we realize a single-photon source based on a far off-resonance Duan-Lukin-Cirac-Zoller quantum memory at broadband and room-temperature regime. By harnessing high-speed feedback control and repeat-until-success write process, the photon generation rate obtains considerable enhancement up to tenfold. Such a memory-enhanced single-photon source, based on the broadband room-temperature quantum memory, suggests a promising way for establishing large-scale quantum memory-enabled network at ambient condition.

SiGe quantum wells with oscillating Ge concentrations for quantum dot qubits

Large-scale arrays of quantum-dot spin qubits in Si/SiGe quantum wells require large or tunable energy splittings of the valley states associated with degenerate conduction band minima. Existing proposals to deterministically enhance the valley splitting rely on sharp interfaces or modifications in the quantum well barriers that can be difficult to grow. Here, we propose and demonstrate a new heterostructure, the "Wiggle Well", whose key feature is Ge concentration oscillations inside the quantum well. Experimentally, we show that placing Ge in the quantum well does not significantly impact our ability to form and manipulate single-electron quantum dots. We further observe large and widely tunable valley splittings, from 54 to 239 μeV. Tight-binding calculations, and the tunability of the valley splitting, indicate that these results can mainly be attributed to random concentration fluctuations that are amplified by the presence of Ge alloy in the heterostructure, as opposed to a deterministic enhancement due to the concentration oscillations. Quantitative predictions for several other heterostructures point to the Wiggle Well as a robust method for reliably enhancing the valley splitting in future qubit devices.

Quantum variational algorithms are swamped with traps

One of the most important properties of classical neural networks is how surprisingly trainable they are, though their training algorithms typically rely on optimizing complicated, nonconvex loss functions. Previous results have shown that unlike the case in classical neural networks, variational quantum models are often not trainable. The most studied phenomenon is the onset of barren plateaus in the training landscape of these quantum models, typically when the models are very deep. This focus on barren plateaus has made the phenomenon almost synonymous with the trainability of quantum models. Here, we show that barren plateaus are only a part of the story. We prove that a wide class of variational quantum models-which are shallow, and exhibit no barren plateaus-have only a superpolynomially small fraction of local minima within any constant energy from the global minimum, rendering these models untrainable if no good initial guess of the optimal parameters is known. We also study the trainability of variational quantum algorithms from a statistical query framework, and show that noisy optimization of a wide variety of quantum models is impossible with a sub-exponential number of queries. Finally, we numerically confirm our results on a variety of problem instances. Though we exclude a wide variety of quantum algorithms here, we give reason for optimism for certain classes of variational algorithms and discuss potential ways forward in showing the practical utility of such algorithms.

Arbitrary entanglement of three qubits via linear optics

We present a linear-optical scheme for generating an arbitrary state of three qubits. It requires only three independent particles in the input and post-selection of the coincidence type at the output. The success probability of the protocol is equal for any desired state. Furthermore, the optical design remains insensitive to particle statistics (bosons, fermions or anyons). This approach builds upon the no-touching paradigm, which demonstrates the utility of particle indistinguishability as a resource of entanglement for practical applications.

Ultra-low loss quantum photonic circuits integrated with single quantum emitters

The scaling of many photonic quantum information processing systems is ultimately limited by the flux of quantum light throughout an integrated photonic circuit. Source brightness and waveguide loss set basic limits on the on-chip photon flux. While substantial progress has been made, separately, towards ultra-low loss chip-scale photonic circuits and high brightness single-photon sources, integration of these technologies has remained elusive. Here, we report the integration of a quantum emitter single-photon source with a wafer-scale, ultra-low loss silicon nitride photonic circuit. We demonstrate triggered and pure single-photon emission into a Si₃N₄ photonic circuit with ≈ 1 dB/m propagation loss at a wavelength of ≈ 930 nm. We also observe resonance fluorescence in the strong drive regime, showing promise towards coherent control of quantum emitters. These results are a step forward towards scaled chip-integrated photonic quantum information systems in which storing, time-demultiplexing or buffering of deterministically generated single-photons is critical.

Information theoretical limits for quantum optimal control solutions: error scaling of noisy control channels

Accurate manipulations of an open quantum system require a deep knowledge of its controllability properties and the information content of the implemented control fields. By using tools of information and quantum optimal control theory, we provide analytical bounds (information-time bounds) to characterize our capability to control the system when subject to arbitrary sources of noise. Moreover, since the presence of an external noise field induces open quantum system dynamics, we also show that the results provided by the information-time bounds are in very good agreement with the Kofman-Kurizki universal formula describing decoherence processes. Finally, we numerically test the scaling of the control accuracy as a function of the noise parameters, by means of the dressed chopped random basis (dCRAB) algorithm for quantum optimal control.

Distribution of controlled unitary quantum gates towards factoring large numbers on today's small-register devices

Factoring a 2048-bit number using Shor's algorithm, when accounting for error correction, reportedly requires 400,000 qubits. However, it is well known that there is yet much time before we will have this many qubits in the same local system. This is why we propose a protocol for distributed quantum computation applicable to small register devices, specifically for the distribution of controlled unitary gates, the key element in the construction of every quantum computation algorithm. We leverage quantum sharing of partial results to obtain a parallel processing scheme, allowing for the first time the quantum distribution of very large gates with thousands of inputs using only small register devices with tens of qubits. In this way, we improve all previous controlled unitary gate distribution approaches, obtaining surprising results. The impact is quantified for recent milestone hardware realizations of quantum processors.

Uncomputably complex renormalisation group flows

Renormalisation group methods are among the most important techniques for analysing the physics of many-body systems: by iterating a renormalisation group map, which coarse-grains the description of a system and generates a flow in the parameter space, physical properties of interest can be extracted. However, recent work has shown that important physical features, such as the spectral gap and phase diagram, may be impossible to determine, even in principle. Following these insights, we construct a rigorous renormalisation group map for the original undecidable many-body system that appeared in the literature, which reveals a renormalisation group flow so complex that it cannot be predicted. We prove that each step of this map is computable, and that it converges to the correct fixed points, yet the resulting flow is uncomputable. This extreme form of unpredictability for renormalisation group flows had not been shown before and goes beyond the chaotic behaviour seen previously.

Time inhomogeneous quantum dynamical maps

We discuss a wide class of time inhomogeneous quantum evolution which is represented by two-parameter family of completely positive trace-preserving maps. These dynamical maps are constructed as infinite series of jump processes. It is shown that such dynamical maps satisfy time inhomogeneous memory kernel master equation which provides a generalization of the master equation involving the standard convolution. Time-local (time convolution-less) approach is discussed as well. Finally, the comparative analysis of traditional time homogeneous versus time inhomogeneous scenario is provided.

Computing Shor's algorithmic steps with interference patterns of classical light

When considered as orthogonal bases in distinct vector spaces, the unit vectors of polarization directions and the Laguerre-Gaussian modes of polarization amplitude are inseparable, constituting a so-called classical entangled light beam. Equating this classical entanglement to quantum entanglement necessary for computing purpose, we show that the parallelism featured in Shor's factoring algorithm is equivalent to the concurrent light-path propagation of an entangled beam or pulse train. A gedanken experiment is proposed for executing the key algorithmic steps of modular exponentiation and Fourier transform on a target integer N using only classical manipulations on the amplitudes and polarization directions. The multiplicative order associated with the sought-after integer factors is identified through a four-hole diffraction interference from sources obtained from the entangled beam profile. The unique mapping from the fringe patterns to the computed order is demonstrated through simulations for the case [Formula: see text].

Coherent interaction-free detection of microwave pulses with a superconducting circuit

The interaction-free measurement is a fundamental quantum effect whereby the presence of a photosensitive object is determined without irreversible photon absorption. Here we propose the concept of coherent interaction-free detection and demonstrate it experimentally using a three-level superconducting transmon circuit. In contrast to standard interaction-free measurement setups, where the dynamics involves a series of projection operations, our protocol employs a fully coherent evolution that results, surprisingly, in a higher probability of success. We show that it is possible to ascertain the presence of a microwave pulse resonant with the second transition of the transmon, while at the same time avoid exciting the device onto the third level. Experimentally, this is done by using a series of Ramsey microwave pulses coupled into the first transition and monitoring the ground-state population.

Spin-defect qubits in two-dimensional transition metal dichalcogenides operating at telecom wavelengths

Solid state quantum defects are promising candidates for scalable quantum information systems which can be seamlessly integrated with the conventional semiconductor electronic devices within the 3D monolithically integrated hybrid classical-quantum devices. Diamond nitrogen-vacancy (NV) center defects are the representative examples, but the controlled positioning of an NV center within bulk diamond is an outstanding challenge. Furthermore, quantum defect properties may not be easily tuned for bulk crystalline quantum defects. In comparison, 2D semiconductors, such as transition metal dichalcogenides (TMDs), are promising solid platform to host a quantum defect with tunable properties and a possibility of position control. Here, we computationally discover a promising defect family for spin qubit realization in 2D TMDs. The defects consist of transition metal atoms substituted at chalcogen sites with desirable spin-triplet ground state, zero-field splitting in the tens of GHz, and strong zero-phonon coupling to optical transitions in the highly desirable telecom band.

Anti-Zeno purification of spin baths by quantum probe measurements

The quantum Zeno and anti-Zeno paradigms have thus far addressed the evolution control of a quantum system coupled to an immutable bath via non-selective measurements performed at appropriate intervals. We fundamentally modify these paradigms by introducing, theoretically and experimentally, the concept of controlling the bath state via selective measurements of the system (a qubit). We show that at intervals corresponding to the anti-Zeno regime of the system-bath exchange, a sequence of measurements has strongly correlated outcomes. These correlations can dramatically enhance the bath-state purity and yield a low-entropy steady state of the bath. The purified bath state persists long after the measurements are completed. Such purification enables the exploitation of spin baths as long-lived quantum memories or as quantum-enhanced sensors. The experiment involved a repeatedly probed defect center dephased by a nuclear spin bath in a diamond at low-temperature.

High-fidelity qutrit entangling gates for superconducting circuits

Ternary quantum information processing in superconducting devices poses a promising alternative to its more popular binary counterpart through larger, more connected computational spaces and proposed advantages in quantum simulation and error correction. Although generally operated as qubits, transmons have readily addressable higher levels, making them natural candidates for operation as quantum three-level systems (qutrits). Recent works in transmon devices have realized high fidelity single qutrit operation. Nonetheless, effectively engineering a high-fidelity two-qutrit entanglement remains a central challenge for realizing qutrit processing in a transmon device. In this work, we apply the differential AC Stark shift to implement a flexible, microwave-activated, and dynamic cross-Kerr entanglement between two fixed-frequency transmon qutrits, expanding on work performed for the ZZ interaction with transmon qubits. We then use this interaction to engineer efficient, high-fidelity qutrit CZ^† and CZ gates, with estimated process fidelities of 97.3(1)% and 95.2(3)% respectively, a significant step forward for operating qutrits on a multi-transmon device.

Formation of robust bound states of interacting microwave photons

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2-9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

Encryption chain based on measurement result and its applications on semi-quantum key distribution protocol

This study proposes a new encoding method, also known as an encryption chain based on the measurement result. Then, using the encryption chain to propose a unitary-operation-based semi-quantum key distribution protocol (SQKD) protocol. In the existing SQKD protocols, semi-quantum environments adopt a round-trip transmission strategy. In round-trip transmission, the classical participant must resend the received photons to the quantum participant after implementing local operations. Therefore, round-trip transmissions are vulnerable to Trojan horse attacks. Hence, the classical participant must be equipped with a photon number splitter and an optical wavelength filter device against Trojan horse attacks. This is illogical for semi-quantum environments because the burden on the classical participant is significantly increased as it involves the prevention of Trojan horse attacks. The proposed SQKD protocol is congenitally immune to Trojan horse attacks and involves no extra hardware because it is designed based on a one-way transmission as opposed to a round-trip transmission. When compared to the existing SQKD protocols, the proposed SQKD protocol provides the best qubit efficiency, and classical participants only require two quantum capabilities, which enhance its practicability. Moreover, the proposed SQKD protocol is free from collective attacks, Trojan horse attacks, and intercept-resend attacks. Thus, the proposed scheme is more efficient and practical than the existing SQKD protocols.

Non-Hermitian Generalization of Rényi Entropy

From their conception to present times, different concepts and definitions of entropy take key roles in a variety of areas from thermodynamics to information science, and they can be applied to both classical and quantum systems. Among them is the Rényi entropy. It is able to characterize various properties of classical information with a unified concise form. We focus on the quantum counterpart, which unifies the von Neumann entropy, max- and min-entropy, collision entropy, etc. It can only be directly applied to Hermitian systems because it usually requires that the density matrices is normalized. For a non-Hermitian system, the evolved density matrix may not be normalized; i.e., the trace can be larger or less than one as the time evolution. However, it is not well-defined for the Rényi entropy with a non-normalized probability distribution relevant to the density matrix of a non-Hermitian system, especially when the trace of the non-normalized density matrix is larger than one. In this work, we investigate how to describe the Rényi entropy for non-Hermitian systems more appropriately. We obtain a concisely and generalized form of α-Rényi entropy, which we extend the unified order-α from finite positive real numbers to zero and infinity. Our generalized α-Rényi entropy can be directly calculated using both of the normalized and non-normalized density matrices so that it is able to describe non-Hermitian entropy dynamics. We illustrate the necessity of our generalization by showing the differences between ours and the conventional Rényi entropy for non-Hermitian detuning two-level systems.

Entanglement and quantum correlations in the XX spin-1/2 honeycomb lattice

The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model in presence of a transverse magnetic field (TF) is known. With the absence of the magnetic field, two quantum phases, namely, the Néel and the dimerized phases have been identified. Moreover, canted Néel and the paramagnetic (PM) phases also emerge by applying the magnetic field. In this paper, using two powerful numerical exact techniques, Lanczos exact diagonalization, and Density matrix renormalization group (DMRG) methods, we study this model by focusing on the quantum correlations, the concurrence, and the quantum discord (QD) among nearest-neighbor spins. We show that the quantum correlations can capture the position of the quantum critical points in the whole range of the ground state phase diagram consistent with previous results. Although the concurrence and the QD are short-range, informative about long-ranged critical correlations. In addition, we address a ”magnetic-entanglement” behavior that starts from an entangled field around the saturation field.

Flexible learning of quantum states with generative query neural networks

Deep neural networks are a powerful tool for characterizing quantum states. Existing networks are typically trained with experimental data gathered from the quantum state that needs to be characterized. But is it possible to train a neural network offline, on a different set of states? Here we introduce a network that can be trained with classically simulated data from a fiducial set of states and measurements, and can later be used to characterize quantum states that share structural similarities with the fiducial states. With little guidance of quantum physics, the network builds its own data-driven representation of a quantum state, and then uses it to predict the outcome statistics of quantum measurements that have not been performed yet. The state representations produced by the network can also be used for tasks beyond the prediction of outcome statistics, including clustering of quantum states and identification of different phases of matter.

Preparation and Analysis of Two-Dimensional Four-Qubit Entangled States with Photon Polarization and Spatial Path

Entanglement states serve as the central resource for a number of important applications in quantum information science, including quantum key distribution, quantum precision measurement, and quantum computing. In pursuit of more promising applications, efforts have been made to generate entangled states with more qubits. However, the efficient creation of a high-fidelity multiparticle entanglement remains an outstanding challenge due to the difficulty that increases exponentially with the number of particles. We design an interferometer that is capable of coupling the polarization and spatial paths of photons and prepare 2-D four-qubit GHZ entanglement states. Using quantum state tomography, entanglement witness, and the violation of Ardehali inequality against local realism, the properties of the prepared 2-D four-qubit entangled state are analyzed. The experimental results show that the prepared four-photon system is an entangled state with high fidelity.

High-fidelity quantum information transmission using a room-temperature nonrefrigerated lossy microwave waveguide

Quantum microwave transmission is key to realizing modular superconducting quantum computers and distributed quantum networks. A large number of incoherent photons are thermally generated within the microwave frequency spectrum. The closeness of the transmitted quantum state to the source-generated quantum state at the input of the transmission link (measured by the transmission fidelity) degrades due to the presence of the incoherent photons. Hence, high-fidelity quantum microwave transmission has long been considered to be infeasible without refrigeration. In this study, we propose a novel method for high-fidelity quantum microwave transmission using a room-temperature lossy waveguide. The proposed scheme consists of connecting two cryogenic nodes (i.e., a transmitter and a receiver) by the room-temperature lossy microwave waveguide. First, cryogenic preamplification is implemented prior to transmission. Second, at the receiver side, a cryogenic loop antenna is placed inside the output port of the waveguide and coupled to an LC harmonic oscillator located outside the waveguide. The loop antenna converts quantum microwave fields to a quantum voltage across the coupled LC harmonic oscillator. Noise photons are induced across the LC oscillator including the source generated noise, the preamplification noise, the thermal occupation of the waveguide, and the fluctuation-dissipation noise. The loop antenna detector at the receiver is designed to extensively suppress the induced photons across the LC oscillator. The signal transmittance is maintained intact by providing significant preamplification gain. Our calculations show that high-fidelity quantum transmission (i.e., more than [Formula: see text]) is realized based on the proposed scheme for transmission distances reaching 100 m.

Universal control of a six-qubit quantum processor in silicon

Future quantum computers capable of solving relevant problems will require a large number of qubits that can be operated reliably1. However, the requirements of having a large qubit count and operating with high fidelity are typically conflicting. Spins in semiconductor quantum dots show long-term promise2,3 but demonstrations so far use between one and four qubits and typically optimize the fidelity of either single- or two-qubit operations, or initialization and readout4-11. Here, we increase the number of qubits and simultaneously achieve respectable fidelities for universal operation, state preparation and measurement. We design, fabricate and operate a six-qubit processor with a focus on careful Hamiltonian engineering, on a high level of abstraction to program the quantum circuits, and on efficient background calibration, all of which are essential to achieve high fidelities on this extended system. State preparation combines initialization by measurement and real-time feedback with quantum-non-demolition measurements. These advances will enable testing of increasingly meaningful quantum protocols and constitute a major stepping stone towards large-scale quantum computers.

Generalization in quantum machine learning from few training data

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as [Formula: see text]. When only K ≪ T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to [Formula: see text]. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

Quantum error correction with silicon spin qubits

Future large-scale quantum computers will rely on quantum error correction (QEC) to protect the fragile quantum information during computation1,2. Among the possible candidate platforms for realizing quantum computing devices, the compatibility with mature nanofabrication technologies of silicon-based spin qubits offers promise to overcome the challenges in scaling up device sizes from the prototypes of today to large-scale computers3-5. Recent advances in silicon-based qubits have enabled the implementations of high-quality one-qubit and two-qubit systems6-8. However, the demonstration of QEC, which requires three or more coupled qubits1, and involves a three-qubit gate9-11 or measurement-based feedback, remains an open challenge. Here we demonstrate a three-qubit phase-correcting code in silicon, in which an encoded three-qubit state is protected against any phase-flip error on one of the three qubits. The correction to this encoded state is performed by a three-qubit conditional rotation, which we implement by an efficient single-step resonantly driven iToffoli gate. As expected, the error correction mitigates the errors owing to one-qubit phase-flip, as well as the intrinsic dephasing mainly owing to quasi-static phase noise. These results show successful implementation of QEC and the potential of a silicon-based platform for large-scale quantum computing.

Triplet-pair spin signatures from macroscopically aligned heteroacenes in an oriented single crystal

The photo-driven process of singlet fission generates coupled triplet pairs (TT) with fundamentally intriguing and potentially useful properties. The quintet ⁵TT₀ sublevel is particularly interesting for quantum information because it is highly entangled, is addressable with microwave pulses, and could be detected using optical techniques. Previous theoretical work on a model Hamiltonian and nonadiabatic transition theory, called the JDE model, has determined that this sublevel can be selectively populated if certain conditions are met. Among the most challenging, the molecules within the dimer undergoing singlet fission must have their principal magnetic axes parallel to one another and to an applied Zeeman field. Here, we present time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy of a single crystal sample of a tetracenethiophene compound featuring arrays of dimers aligned in this manner, which were mounted so that the orientation of the field relative to the molecular axes could be controlled. The observed spin sublevel populations in the paired TT and unpaired (T+T) triplets are consistent with predictions from the JDE model, including preferential ⁵TT₀ formation at z ‖ B₀, with one caveat-two ⁵TT spin sublevels have little to no population. This may be due to crossings between the ⁵TT and ³TT manifolds in the field range investigated by TR-EPR, consistent with the intertriplet exchange energy determined by monitoring photoluminescence at varying magnetic fields.

Quantum annealing with special drivers for circuit fault diagnostics

We present a very general construction for quantum annealing protocols to solve Combinational Circuit Fault Diagnosis problems that restricts the evolution to the space of valid diagnoses. This is accomplished by using special local drivers that induce a transition graph on the space of feasible configurations that is regular and instance independent for each given circuit topology. Analysis of small instances shows that the energy gap has a generic form, and that the minimum gap occurs in the last third of the evolution. We used these features to construct an improved annealing schedule and benchmarked its performance through closed system simulations. We found that degeneracy can help the performance of quantum annealing, especially for instances with a higher number of faults in their minimum fault diagnosis. This contrasts with the performance of classical approaches based on brute force search that are used in industry for large scale circuits.

Entangling single atoms over 33 km telecom fibre

Quantum networks promise to provide the infrastructure for many disruptive applications, such as efficient long-distance quantum communication and distributed quantum computing1,2. Central to these networks is the ability to distribute entanglement between distant nodes using photonic channels. Initially developed for quantum teleportation3,4 and loophole-free tests of Bell's inequality5,6, recently, entanglement distribution has also been achieved over telecom fibres and analysed retrospectively7,8. Yet, to fully use entanglement over long-distance quantum network links it is mandatory to know it is available at the nodes before the entangled state decays. Here we demonstrate heralded entanglement between two independently trapped single rubidium atoms generated over fibre links with a length up to 33 km. For this, we generate atom-photon entanglement in two nodes located in buildings 400 m line-of-sight apart and to overcome high-attenuation losses in the fibres convert the photons to telecom wavelength using polarization-preserving quantum frequency conversion9. The long fibres guide the photons to a Bell-state measurement setup in which a successful photonic projection measurement heralds the entanglement of the atoms10. Our results show the feasibility of entanglement distribution over telecom fibre links useful, for example, for device-independent quantum key distribution11-13 and quantum repeater protocols. The presented work represents an important step towards the realization of large-scale quantum network links.

One decade of quantum optimal control in the chopped random basis

The chopped random basis (CRAB) ansatz for quantum optimal control has been proven to be a versatile tool to enable quantum technology applications such as quantum computing, quantum simulation, quantum sensing, and quantum communication. Its capability to encompass experimental constraints-while maintaining an access to the usually trap-free control landscape-and to switch from open-loop to closed-loop optimization (including with remote access-or RedCRAB) is contributing to the development of quantum technology on many different physical platforms. In this review article we present the development, the theoretical basis and the toolbox for this optimization algorithm, as well as an overview of the broad range of different theoretical and experimental applications that exploit this powerful technique.

Verification of Information Thermodynamics in a Trapped Ion System

Information thermodynamics has developed rapidly over past years, and the trapped ions, as a controllable quantum system, have demonstrated feasibility to experimentally verify the theoretical predictions in the information thermodynamics. Here, we address some representative theories of information thermodynamics, such as the quantum Landauer principle, information equality based on the two-point measurement, information-theoretical bound of irreversibility, and speed limit restrained by the entropy production of system, and review their experimental demonstration in the trapped ion system. In these schemes, the typical physical processes, such as the entropy flow, energy transfer, and information flow, build the connection between thermodynamic processes and information variation. We then elucidate the concrete quantum control strategies to simulate these processes by using quantum operators and the decay paths in the trapped-ion system. Based on them, some significantly dynamical processes in the trapped ion system to realize the newly proposed information-thermodynamic models is reviewed. Although only some latest experimental results of information thermodynamics with a single trapped-ion quantum system are reviewed here, we expect to find more exploration in the future with more ions involved in the experimental systems.

Comparison of Lumped Oscillator Model and Energy Participation Ratio Methods in Designing Two-Dimensional Superconducting Quantum Chips

Over the past two decades, superconducting quantum circuits have become one of the essential platforms for realizing quantum computers. The Hamiltonian of a superconducting quantum circuit system is the key to describing the dynamic evolution of the system. For this reason, various methods for analyzing the Hamiltonian of a superconducting quantum circuit system have been proposed, among which the LOM (Lumped Oscillator Model) and the EPR (Energy Participation Ratio) methods are the most popular ones. To analyze and improve the design methods of superconducting quantum chips, this paper compares the similarities and differences of the LOM and the EPR quantification methods. We verify the applicability of these two theoretical approaches to the design of 2D transmon quantum chips. By comparing the theoretically simulated results and the experimentally measured data at extremely low temperature, the errors between the theoretical calculation and observed measurement values of the two methods were summarized. Results show that the LOM method has more parameter outputs in data diversity and the qubit frequency calculation in LOM is more accurate. The reason is that in LOM more coupling between different systems are taken into consideration. These analyses would have reference significance for the design of superconducting quantum chips.

Variational quantum support vector machine based on [Formula: see text] matrix expansion and variational universal-quantum-state generator

We analyze a binary classification problem by using a support vector machine based on variational quantum-circuit model. We propose to solve a linear equation of the support vector machine by using a [Formula: see text] matrix expansion. In addition, it is shown that an arbitrary quantum state is prepared by optimizing a universal quantum circuit representing an arbitrary [Formula: see text] based on the steepest descent method. It may be a quantum generalization of Field-Programmable-Gate Array (FPGA).

A Chirality-Based Quantum Leap

There is increasing interest in the study of chiral degrees of freedom occurring in matter and in electromagnetic fields. Opportunities in quantum sciences will likely exploit two main areas that are the focus of this Review: (1) recent observations of the chiral-induced spin selectivity (CISS) effect in chiral molecules and engineered nanomaterials and (2) rapidly evolving nanophotonic strategies designed to amplify chiral light-matter interactions. On the one hand, the CISS effect underpins the observation that charge transport through nanoscopic chiral structures favors a particular electronic spin orientation, resulting in large room-temperature spin polarizations. Observations of the CISS effect suggest opportunities for spin control and for the design and fabrication of room-temperature quantum devices from the bottom up, with atomic-scale precision and molecular modularity. On the other hand, chiral-optical effects that depend on both spin- and orbital-angular momentum of photons could offer key advantages in all-optical and quantum information technologies. In particular, amplification of these chiral light-matter interactions using rationally designed plasmonic and dielectric nanomaterials provide approaches to manipulate light intensity, polarization, and phase in confined nanoscale geometries. Any technology that relies on optimal charge transport, or optical control and readout, including quantum devices for logic, sensing, and storage, may benefit from chiral quantum properties. These properties can be theoretically and experimentally investigated from a quantum information perspective, which has not yet been fully developed. There are uncharted implications for the quantum sciences once chiral couplings can be engineered to control the storage, transduction, and manipulation of quantum information. This forward-looking Review provides a survey of the experimental and theoretical fundamentals of chiral-influenced quantum effects and presents a vision for their possible future roles in enabling room-temperature quantum technologies.

Generalized scaling of spin qubit coherence in over 12,000 host materials

Atomic defects in solid-state materials are promising candidates as quantum bits, or qubits. New materials are actively being investigated as hosts for new defect qubits; however, there are no unifying guidelines that can quantitatively predict qubit performance in a new material. One of the most critical property of qubits is their quantum coherence. While cluster correlation expansion (CCE) techniques are useful to simulate the coherence of electron spins in defects, they are computationally expensive to investigate broad classes of stable materials. Using CCE simulations, we reveal a general scaling relation between the electron spin coherence time and the properties of qubit host materials that enables rapid and quantitative exploration of new materials hosting spin defects.

Spin defect centers with long quantum coherence times (T₂) are key solid-state platforms for a variety of quantum applications. Cluster correlation expansion (CCE) techniques have emerged as a powerful tool to simulate the T₂ of defect electron spins in these solid-state systems with good accuracy. Here, based on CCE, we uncover an algebraic expression for T₂ generalized for host compounds with dilute nuclear spin baths under a magnetic field that enables a quantitative and comprehensive materials exploration with a near instantaneous estimate of the coherence time. We investigated more than 12,000 host compounds at natural isotopic abundance and found that silicon carbide (SiC), a prominent widegap semiconductor for quantum applications, possesses the longest coherence times among widegap nonchalcogenides. In addition, more than 700 chalcogenides are shown to possess a longer T₂ than SiC. We suggest potential host compounds with promisingly long T₂ up to 47 ms and pave the way to explore unprecedented functional materials for quantum applications.

Nanomaterials for Quantum Information Science and Engineering

Quantum information science and engineering (QISE)-which entails the use of quantum mechanical states for information processing, communications, and sensing-and the area of nanoscience and nanotechnology have dominated condensed matter physics and materials science research in the 21st century. Solid-state devices for QISE have, to this point, predominantly been designed with bulk materials as their constituents. This review considers how nanomaterials (i.e., materials with intrinsic quantum confinement) may offer inherent advantages over conventional materials for QISE. The materials challenges for specific types of qubits, along with how emerging nanomaterials may overcome these challenges, are identified. Challenges for and progress toward nanomaterials-based quantum devices are condidered. The overall aim of the review is to help close the gap between the nanotechnology and quantum information communities and inspire research that will lead to next-generation quantum devices for scalable and practical quantum applications.