Practical quantum advantage in quantum simulation

LDPC-cat codes for low-overhead quantum computing in 2D

The main obstacle to large scale quantum computing are the errors present in every physical qubit realization. Correcting these errors requires a large number of additional qubits. Two main avenues to reduce this overhead are (i) low-density parity check (LDPC) codes requiring very few additional qubits to correct errors (ii) cat qubits where bit-flip errors are exponentially suppressed by design. In this work, we combine both approaches to obtain an extremely low overhead architecture. Assuming a physical phase-flip error probability ϵ ≈ 0.1% per qubit and operation, one hundred logical qubits can be implemented on a 758 cat qubit chip, with a total logical error probability per cycle and per logical qubit ϵL ≤ 10-8. Our architecture also features two major advantages. First, the hardware implementation of the code can be realised with short-range qubit interactions in 2D and low-weight stabilizers, under constraints similar to those of the popular surface code architecture. Second, we demonstrate how to implement a fault-tolerant universal set of logical gates with an additional layer of routing cat qubits stacked on top of the LDPC layer, while maintaining the local connectivity. Furthermore, our architecture benefits from a high capacity of parallelization for these logical gates.

Fast single atom imaging for optical lattice arrays

High-resolution fluorescence imaging of ultracold atoms and molecules is paramount to performing quantum simulation and computation in optical lattices and tweezers. Imaging durations in these experiments typically range from a millisecond to a second, significantly limiting the cycle time. In this work, we present fast, 2.4 μs single-atom imaging in lattices, with 99.4% fidelity - pushing the readout duration of neutral atom quantum platforms to be close to that of superconducting qubit platforms. Additionally, we thoroughly study the performance of accordion lattices. We also demonstrate number-resolved imaging without parity projection, which will facilitate experiments such as the exploration of high-filling phases in the extended Bose-Hubbard models, multi-band or SU(N) Fermi-Hubbard models, and quantum link models.

Quantum and complex-valued hybrid networks for multi-principal element alloys phase prediction

This study introduces a hybrid network model for phase classification, integrating quantum networks and complex-valued neural networks. This architecture uses elemental composition as its only input, eliminating complex feature engineering. Parameterized quantum networks handle sparse elemental data and convert data from real to complex domains, increasing information dimensionality. Complex-valued neural networks process data in the complex domain, significantly reducing information loss during transitions. The experimental results show that the hybrid model achieves a phase classification accuracy of 94.93%, outperforming the best machine learning model by 2.27% and the quantum model by 8.67%. Precision, recall, and F1-score are also excellent at 0.9494, 0.9493, and 0.9500, respectively. Additional tests on phase transitions inAl x CoCrFeNi alloys confirm the model's robust generalization, identifying transition thresholds at 0.46 and 0.88, closely matching the 0.45 and 0.88 reported in related studies.

Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping

Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For instance, the measurement effort poses a critical bottleneck for variational quantum algorithms. We aim to find the optimal strategy with single-qubit measurements that yields the highest provable accuracy given a total measurement budget. As a central tool, we establish tail bounds for empirical estimators of the energy. They are helpful for identifying measurement settings that improve the energy estimate the most. This task constitutes an NP-hard problem. However, we are able to circumvent this bottleneck and use the tail bounds to develop a practical, efficient estimation strategy, which we call ShadowGrouping. As the name indicates, it combines shadow estimation methods with grouping strategies for Pauli strings. In numerical experiments, we demonstrate that ShadowGrouping improves upon state-of-the-art methods in estimating the electronic ground-state energies of various small molecules, both in provable and practical accuracy benchmarks. Hence, this work provides a promising way, e.g., to tackle the measurement bottleneck associated with quantum many-body Hamiltonians.

Interplay between disorder and topology in Thouless pumping on a superconducting quantum processor

Topological phases are robust against weak perturbations, but break down when disorder becomes sufficiently strong. However, moderate disorder can also induce topologically nontrivial phases. Thouless pumping, as a (1+1)D counterpart of the integer quantum Hall effect, is one of the simplest manifestations of topology. Here, we report experimental observations of the competition and interplay between Thouless pumping and disorder on a 41-qubit superconducting quantum processor. We improve a Floquet engineering technique to realize cycles of adiabatic pumping by simultaneously varying the on-site potentials and the hopping couplings. We demonstrate Thouless pumping in the presence of disorder and show its breakdown as the strength of disorder increases. Moreover, we observe two types of topological pumping that are induced by on-site potential disorder and hopping disorder, respectively. In particular, an intrinsic topological pump that is induced by quasi-periodic hopping disorder has never been experimentally realized before. Our highly controllable system provides a valuable quantum simulating platform for studying various aspects of topological physics in the presence of disorder.

Cryogenic III-V and Nb electronics integrated on silicon for large-scale quantum computing platforms

Quantum computers now encounter the significant challenge of scalability, similar to the issue that classical computing faced previously. Recent results in high-fidelity spin qubits manufactured with a Si CMOS technology, along with demonstrations that cryogenic CMOS-based control/readout electronics can be integrated into the same chip or die, opens up an opportunity to break out the challenges of qubit size, I/O, and integrability. However, the power consumption of cryogenic CMOS-based control/readout electronics cannot support thousands or millions of qubits. Here, we show that III-V two-dimensional electron gas and Nb superconductor-based cryogenic electronics can be integrated with Si and operate at extremely low power levels, enabling the control and readout for millions of qubits. Our devices offer a unity gain cutoff frequency of 601 GHz, a unity power gain cutoff frequency of 593 GHz, and a low noise indication factorI D g m - 1 of 0.21 Vmm S - 1 at 4 K using more than 10 times less power consumption than CMOS.

Transpiling Quantum Assembly Language Circuits to a Qudit Form

In this paper, we introduce the workflow for converting qubit circuits represented by Open Quantum Assembly format (OpenQASM, also known as QASM) into the qudit form for execution on qudit hardware and provide a method for translating qudit experiment results back into qubit results. We present the comparison of several qudit transpilation regimes, which differ in decomposition of multicontrolled gates: qubit as ordinary qubit transpilation and execution, qutrit with d=3 levels and single qubit in qudit, and ququart with d=4 levels and 2 qubits per ququart. We provide several examples of transpiling circuits for trapped ion qudit processors, which demonstrate potential advantages of qudits.

Trapped-ion quantum simulation of electron transfer models with tunable dissipation

Electron transfer is at the heart of many fundamental physical, chemical, and biochemical processes essential for life. The exact simulation of these reactions is often hindered by the large number of degrees of freedom and by the essential role of quantum effects. Here, we experimentally simulate a paradigmatic model of molecular electron transfer using a multispecies trapped-ion crystal, where the donor-acceptor gap, the electronic and vibronic couplings, and the bath relaxation dynamics can all be controlled independently. By manipulating both the ground-state and optical qubits, we observe the real-time dynamics of the spin excitation, measuring the transfer rate in several regimes of adiabaticity and relaxation dynamics. Our results provide a testing ground for increasingly rich models of molecular excitation transfer processes that are relevant for molecular electronics and light-harvesting systems.

Probing decoherence in molecular 4f qubits

We probe herein the fundamental factors that induce decoherence in ensembles of molecular magnetic materials. This is done by pulse Electron Paramagnetic Resonance measurements at X-band (∼9.6 GHz) on single crystals of Gd@Y(trensal) at 0.5, 10-1, 10-2 and 10-3% doping levels, using Hahn echo, partial refocusing and CPMG sequences. The phase memory time, T m, obtained by the Hahn echo sequence at X-band is compared to the one previously determined at higher frequency/magnetic field (∼240 GHz). The combined information from these experiments allows to gain insight into the contributions to decoherence originating from various relaxation mechanisms such as spin-lattice relaxation, electron and nuclear spin diffusion and instantaneous diffusion. We show that while at high magnetic fields T m is limited by spin-lattice relaxation seemingly attributed to a direct process, at lower fields the limiting factor is spectral diffusion. At X-band, for Gd@Y(trensal) we determine a T m in the range 1-12 μs, at 5 K, depending on the magnetic field and concentration of Gd(trensal) in the isostructural diamagnetic host Y(trensal). Importantly, Gd@Y(trensal) displays measurable coherence at temperatures above liquid nitrogen ones, with 125 K being the upper limit. At the lowest dilution level of 10-3% and under dynamic decoupling conditions, the ratio of T m versus the time it takes to implement a quantum gate, T G, reaches the order of 104, in the example of a single qubit π-rotation, which corresponds to an upper limit of gate fidelity of the order of 99.99%, reaching thus the lower limit of qubit figure of merit required for implementations in quantum information technologies.

Simulating Non-Markovian Dynamics in Multidimensional Electronic Spectroscopy via Quantum Algorithm

Including the effect of the molecular environment in the numerical modeling of time-resolved electronic spectroscopy remains an important challenge in computational spectroscopy. In this contribution, we present a general approach for the simulation of the optical response of multichromophore systems in a structured environment and its implementation as a quantum algorithm. A key step of the procedure is the pseudomode embedding of the system-environment problem resulting in a finite set of quantum states evolving according to a Markovian quantum master equation. This formulation is then solved by a collision model integrated into a quantum algorithm designed to simulate linear and nonlinear response functions. The workflow is validated by simulating spectra for the prototypical excitonic dimer interacting with fast (memoryless) and finite-memory environments. The results demonstrate, on the one hand, the potential of the pseudomode embedding for simulating the dynamical features of nonlinear spectroscopy, including lineshape, spectral diffusion, and relaxations along delay times. On the other hand, the explicit synthesis of quantum circuits provides a fully quantum simulation protocol of nonlinear spectroscopy harnessing the efficient quantum simulation of many-body dynamics promised by the future generation of fault-tolerant quantum computers.

Quantum Simulation of Partial Differential Equations via Schrödingerization

We present a novel new way-called Schrödingerization-to simulate general (quantum and nonquantum) systems of linear ordinary and partial differential equations (PDEs) via quantum simulation. We introduce a new transform, referred to as the warped phase transformation, where any linear-including nonautonamous-system of ordinary or partial differential equation can be recast into a system of Schrödinger's equations, in real time, in a straightforward way. This approach is not only applicable to PDEs for classical problems but is also useful for quantum problems, including the preparation of quantum ground states and Gibbs thermal states, the simulation of quantum states in random media in the semiclassical limit, simulation of Schrödinger's equation in a bounded domain with artificial boundary conditions, and other non-Hermitian physics. This formulation is versatile enough to be applicable in a simple way to both digital quantum simulation as well as to analog quantum simulation, and using either qubits or continuous-variable quantum systems (qumodes).

Fermi Polaron in Atom-Ion Hybrid Systems

Atom-ion hybrid systems are promising platforms for the quantum simulation of polaron physics in certain quantum materials. Here, we investigate the ionic Fermi polaron, a charged impurity in a polarized Fermi bath, at zero temperature using quantum Monte Carlo techniques. We compute the energy spectrum, residue, effective mass, and structural properties. Significant deviations from field-theory prediction occur in the strong coupling regime due to large density inhomogeneities around the ion. We observe a smooth polaron-molecule transition in contrast with the neutral case. This study provides insights into solid-state systems like Fermi exciton polarons in thin semiconductors and quantum technologies based on atom-ion platforms.

Hybrid Hamiltonian Simulation for Excitation Dynamics

Hamiltonian simulation is one of the most anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation is commonly time dependent using Trotter-Suzuki product formulas so that long time quantum dynamic simulations (QDSs) become impratical for near-term quantum processors. Hamiltonian simulation based on Cartan decomposition (CD) provides an appealing scheme for QDSs with fixed-depth circuits, while it is limited to a time-independent Hamiltonian. In this work, we generalize this CD-based Hamiltonian simulation algorithm for studying time-dependent systems by combining it with variational quantum algorithms. The time-dependent and time-independent parts of the Hamiltonian are treated by using variational and CD-based Hamiltonian simulation algorithms, respectively. As such, this hybrid Hamiltonian simulation requires only fixed-depth quantum circuits to handle time-dependent cases while maintaining a high accuracy. We apply this new algorithm to study the response of spin and molecular systems to δ-kick electric fields and obtain accurate spectra for these excitation processes.

Simulating the Landau-Zener sweep in deeply sub-Ohmic environments

With the goal to study dissipative Landau-Zener (LZ) sweeps in realistic solid-state qubits, we utilize novel methods from non-Markovian open quantum system dynamics that enable reliable long-time simulations for sub-Ohmic environments. In particular, we combine a novel representation of the dynamical propagator, the uniform time evolving matrix product operator method, with a stochastic realization of finite temperature fluctuations. The latter greatly reduces the computational cost for the matrix product operator approach, enabling convergence in the experimentally relevant deeply sub-Ohmic regime. Our method allows the exact simulation of dynamical protocols with long operation times, such as the LZ sweep, in challenging parameter regimes that are realized in current experimental platforms.

Quantum algorithms for scientific computing

Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in real world applications. Areas that are likely to have the greatest impact on high performance computing (HPC) include simulation of quantum systems, optimization, and machine learning. We draw our examples from electronic structure calculations and computational fluid dynamics which account for a large fraction of current scientific and engineering use of HPC. Potential challenges include encoding and decoding classical data for quantum devices, and mismatched clock speeds between classical and quantum processors. Even a modest quantum enhancement to current classical techniques would have far-reaching impacts in areas such as weather forecasting, aerospace engineering, and the design of 'green' materials for sustainable development. This requires significant effort from the computational science, engineering and quantum computing communities working together.

Subspace-Search Quantum Imaginary Time Evolution for Excited State Computations

Quantum systems in excited states are attracting significant interest with the advent of noisy intermediate-scale quantum (NISQ) devices. While ground states of small molecular systems are typically explored using hybrid variational algorithms like the variational quantum eigensolver (VQE), the study of excited states has received much less attention, partly due to the absence of efficient algorithms. In this work, we introduce the subspace search quantum imaginary time evolution (SSQITE) method, which calculates excited states using quantum devices by integrating key elements of the subspace search variational quantum eigensolver (SSVQE) and the variational quantum imaginary time evolution (VarQITE) method. The effectiveness of SSQITE is demonstrated through calculations of low-lying excited states of benchmark model systems including H2 and LiH molecules. A toy Hamiltonian is also employed to demonstrate that the robustness of VarQITE in avoiding local minima extends to its use in excited state algorithms. With this robustness in avoiding local minima, SSQITE shows promise for advancing quantum computations of excited states across a wide range of applications.

Variational benchmarks for quantum many-body problems

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.

Adaptive Variational Quantum Computing Approaches for Green's Functions and Nonlinear Susceptibilities

We present and benchmark quantum computing approaches for calculating real-time single-particle Green's functions and nonlinear susceptibilities of Hamiltonian systems. The approaches leverage adaptive variational quantum algorithms for state preparation and propagation. Using automatically generated compact circuits, the dynamical evolution is performed over sufficiently long times to achieve adequate frequency resolution of the response functions. We showcase accurate Green's function calculations using a statevector simulator on classical hardware for Fermi-Hubbard chains of 4 and 6 sites, with maximal ansatz circuit depths of 65 and 424 layers, respectively, and for the molecule LiH with a maximal ansatz circuit depth of 81 layers. Additionally, we consider an antiferromagnetic quantum spin-1 model that incorporates the Dzyaloshinskii-Moriya interaction to illustrate calculations of the third-order nonlinear susceptibilities, which can be measured in two-dimensional coherent spectroscopy experiments. These results demonstrate that real-time approaches using adaptive parametrized circuits to evaluate linear and nonlinear response functions can be feasible with near-term quantum processors.

Combinatorial summation of Feynman diagrams

Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a universal framework for efficient summation of connected or skeleton Feynman diagrams for generic quantum many-body systems. It is based on an explicit combinatorial construction of the sum of the integrands by dynamic programming, at a computational cost that can be made only exponential in the diagram order on a classical computer and potentially polynomial on a quantum computer. We illustrate the technique by an unbiased diagrammatic Monte Carlo calculation of the equation of state of the 2D SU(N) Hubbard model in an experimentally relevant regime, which has remained challenging for state-of-the-art numerical methods.

Future Potential of Quantum Computing and Simulations in Biological Science

The review article presents the recent progress in quantum computing and simulation within the field of biological sciences. The article is designed mainly into two portions: quantum computing and quantum simulation. In the first part, significant aspects of quantum computing was illustrated, such as quantum hardware, quantum RAM and big data, modern quantum processors, qubit, superposition effect in quantum computation, quantum interference, quantum entanglement, and quantum logic gates. Simultaneously, in the second part, vital features of the quantum simulation was illustrated, such as the quantum simulator, algorithms used in quantum simulations, and the use of quantum simulation in biological science. Finally, the review provides exceptional views to future researchers about different aspects of quantum simulation in biological science.

Microwave signal processing using an analog quantum reservoir computer

Quantum reservoir computing (QRC) has been proposed as a paradigm for performing machine learning with quantum processors where the training takes place in the classical domain, avoiding the issue of barren plateaus in parameterized-circuit quantum neural networks. It is natural to consider using a quantum processor based on microwave superconducting circuits to classify microwave signals that are analog-continuous in time. However, while there have been theoretical proposals of analog QRC, to date QRC has been implemented using the circuit model-imposing a discretization of the incoming signal in time. In this paper we show how a quantum superconducting circuit comprising an oscillator coupled to a qubit can be used as an analog quantum reservoir for a variety of classification tasks, achieving high accuracy on all of them. Our work demonstrates processing of ultra-low-power microwave signals within our superconducting circuit, a step towards achieving a quantum sensing-computational advantage on impinging microwave signals.

Quantum neural network approach to Markovian dissipative dynamics of many-body open quantum systems

Numerous variational methods have been proposed for solving quantum many-body systems, but they often face exponentially increasing computational complexity as the Hilbert space dimension grows. To address this, we introduce a novel approach using quantum neural networks to simulate the dissipative dynamics of many-body open quantum systems. This method combines neural-network quantum state representation with the time-dependent variational principle, both implemented via quantum algorithms. This results in accurate open quantum dynamics described by the Lindblad quantum master equation, exemplified by the spin-boson and transverse field Ising models. Our approach avoids the computational expense of classical algorithms and demonstrates the potential advantages of quantum computing for many-body simulations. To reduce measurement errors, we introduce a projection reset procedure, which could benefit other quantum simulations. In addition, our approach can be extended to simulate non-Markovian quantum dynamics.

Construction of Antisymmetric Variational Quantum States with Real Space Representation

Electronic state calculations using quantum computers are mostly based on the second quantized formulation, which is suitable for qubit representation. Another way to describe electronic states on a quantum computer is based on the first quantized formulation, which is expected to achieve smaller scaling with respect to the number of basis functions than the second quantized formulation. Among basis functions, a real space basis is an attractive option for quantum dynamics simulations in the fault-tolerant quantum computation (FTQC) era. A major difficulty in the first quantized algorithm with a real space basis is state preparation for many-body electronic systems. This difficulty stems from the antisymmetry of electrons, and it is not straightforward to construct antisymmetric quantum states on a quantum circuit. In this study, we provide a design principle for constructing variational quantum circuits to prepare an antisymmetric quantum state. The proposed circuit generates the superposition of exponentially many Slater determinants, that is, multiconfiguration state, which provides a systematic approach to approximating the exact ground state. We performed the variational quantum eigensolver (VQE) to obtain the ground state of a one-dimensional hydrogen molecular system. As a result, the proposed circuit well reproduced the exact antisymmetric ground state and its energy, whereas the conventional variational circuit yielded neither the antisymmetric nor the symmetric state. Furthermore, we analyzed the many-body wave functions based on the quantum information theory, which illustrated the relation between the electron correlation and the quantum entanglement.

Local Readout and Control of Current and Kinetic Energy Operators in Optical Lattices

Quantum gas microscopes have revolutionized quantum simulations with ultracold atoms, allowing one to measure local observables and snapshots of quantum states. However, measurements so far were mostly carried out in the occupation basis. Here, we demonstrate how all kinetic operators, such as kinetic energy or current operators, can be measured and manipulated with single-bond resolution. Beyond simple expectation values of these observables, the single-shot measurements allow one to access full counting statistics and complex correlation functions. Our work paves the way for the implementation of efficient quantum state tomography and hybrid quantum computing protocols for itinerant particles on a lattice. In addition, we demonstrate how site-resolved programmable potentials enable a spatially selective, parallel readout in different bases as well as the engineering of arbitrary initial states.

Probing Site-Resolved Current in Strongly Interacting Superconducting Circuit Lattices

Transport measurements are fundamental for understanding condensed matter phenomena, from superconductivity to the fractional quantum Hall effect. Analogously, they can be powerful tools for probing synthetic quantum matter in quantum simulators. Here we demonstrate the measurement of in situ particle current in a superconducting circuit lattice and apply it to study transport in both coherent and bath-coupled lattices. Our method utilizes controlled tunneling in a double-well potential to map current to on-site density, revealing site-resolved current and current statistics. We prepare a strongly interacting Bose-Hubbard lattice at different lattice fillings, and observe the change in current statistics as the many-body states transition from superfluid to Mott insulator. Furthermore, we explore nonequilibrium current dynamics by coupling the lattice to engineered driven-dissipative baths that serve as tunable particle source and drain. We observe steady-state current in discrete conduction channels and interaction-assisted transport. These results establish a versatile platform to investigate microscopic quantum transport in superconducting circuits.

Quantum advantage and stability to errors in analogue quantum simulators

Several quantum hardware platforms, while being unable to perform fully fault-tolerant quantum computation, can still be operated as analogue quantum simulators for addressing many-body problems. However, due to the presence of errors, it is not clear to what extent those devices can provide us with an advantage with respect to classical computers. In this work, we make progress on this problem for noisy analogue quantum simulators computing physically relevant properties of many-body systems both in equilibrium and undergoing dynamics. We first formulate a system-size independent notion of stability against extensive errors, which we prove for Gaussian fermion models, as well as for a restricted class of spin systems. Remarkably, for the Gaussian fermion models, our analysis shows the stability of critical models which have long-range correlations. Furthermore, we analyze how this stability may lead to a quantum advantage, for the problem of computing the thermodynamic limit of many-body models, in the presence of a constant error rate and without any explicit error correction.

A primer for quantum computing and its applications to healthcare and biomedical research

OBJECTIVES

To introduce quantum computing technologies as a tool for biomedical research and highlight future applications within healthcare, focusing on its capabilities, benefits, and limitations.

TARGET AUDIENCE

Investigators seeking to explore quantum computing and create quantum-based applications for healthcare and biomedical research.

SCOPE

Quantum computing requires specialized hardware, known as quantum processing units, that use quantum bits (qubits) instead of classical bits to perform computations. This article will cover (1) proposed applications where quantum computing offers advantages to classical computing in biomedicine; (2) an introduction to how quantum computers operate, tailored for biomedical researchers; (3) recent progress that has expanded access to quantum computing; and (4) challenges, opportunities, and proposed solutions to integrate quantum computing in biomedical applications.

One-way optomechanical interaction between nanoparticles

Within a closed system, physical interactions are reciprocal. However, the effective interaction between two entities of an open system may not obey reciprocity. Here, we describe a non-reciprocal interaction between nanoparticles which is one-way, almost insensitive to the interparticle distance, and scalable to many particles. The interaction we propose is based on the non-conservative optical forces between two nanoparticles with highly directional scattering patterns. However, we elucidate that scattering patterns can in general be very misleading about the interparticle forces. We introduce zeroth- and first-order non-reciprocity factors to precisely quantify the merits of any optomechanical interaction between nanoparticles. Our proposed one-way interaction could constitute an important step in the realization of mesoscopic heat pumps and refrigerators, the study of non-equilibrium systems, and the simulation of non-Hermitian quantum models.

A cryogenic on-chip microwave pulse generator for large-scale superconducting quantum computing

For superconducting quantum processors, microwave signals are delivered to each qubit from room-temperature electronics to the cryogenic environment through coaxial cables. Limited by the heat load of cabling and the massive cost of electronics, such an architecture is not viable for millions of qubits required for fault-tolerant quantum computing. Monolithic integration of the control electronics and the qubits provides a promising solution, which, however, requires a coherent cryogenic microwave pulse generator that is compatible with superconducting quantum circuits. Here, we report such a signal source driven by digital-like signals, generating pulsed microwave emission with well-controlled phase, intensity, and frequency directly at millikelvin temperatures. We showcase high-fidelity readout of superconducting qubits with the microwave pulse generator. The device demonstrated here has a small footprint, negligible heat load, great flexibility to operate, and is fully compatible with today's superconducting quantum circuits, thus providing an enabling technology for large-scale superconducting quantum computers.

Observing the Quantum Mpemba Effect in Quantum Simulations

The nonequilibrium physics of many-body quantum systems harbors various unconventional phenomena. In this Letter, we experimentally investigate one of the most puzzling of these phenomena-the quantum Mpemba effect, where a tilted ferromagnet restores its symmetry more rapidly when it is farther from the symmetric state compared to when it is closer. We present the first experimental evidence of the occurrence of this effect in a trapped-ion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and postprocessed using the classical shadows technique. Our findings are further substantiated by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, offering direct evidence of subsystem thermalization.

Enhancing a Many-Body Dipolar Rydberg Tweezer Array with Arbitrary Local Controls

We implement and characterize a protocol that enables arbitrary local controls in a dipolar atom array, where the degree of freedom is encoded in a pair of Rydberg states. Our approach relies on a combination of local addressing beams and global microwave fields. Using this method, we directly prepare two different types of three-atom entangled states, including a W state and a state exhibiting finite chirality. We verify the nature of the underlying entanglement by performing quantum state tomography. Finally, leveraging our ability to measure multibasis, multibody observables, we explore the adiabatic preparation of low-energy states in a frustrated geometry consisting of a pair of triangular plaquettes. By using local addressing to tune the symmetry of the initial state, we demonstrate the ability to prepare correlated states distinguished only by correlations of their chirality (a fundamentally six-body observable). Our protocol is generic, allowing for rotations on arbitrary sub-groups of atoms within the array at arbitrary times during the experiment; this extends the scope of capabilities for quantum simulations of the dipolar XY model.

Measurement-Based Infused Circuits for Variational Quantum Eigensolvers

Variational quantum eigensolvers (VQEs) are successful algorithms for studying physical systems on quantum computers. Recently, they were extended to the measurement-based model of quantum computing, bringing resource graph states and their advantages into the realm of quantum simulation. In this Letter, we incorporate such ideas into traditional VQE circuits. This enables novel problem-informed designs and versatile implementations of many-body Hamiltonians. We showcase our approach on real superconducting quantum computers by performing VQE simulations of testbed systems including the perturbed planar code, Z_{2} lattice gauge theory, 1D quantum chromodynamics, and the LiH molecule.

Non-equilibrium quantum domain reconfiguration dynamics in a two-dimensional electronic crystal and a quantum annealer

Relaxation dynamics of complex many-body quantum systems trapped into metastable states is a very active field of research from both the theoretical and experimental point of view with implications in a wide array of topics from macroscopic quantum tunnelling and nucleosynthesis to non-equilibrium superconductivity and energy-efficient memory devices. In this work, we investigate quantum domain reconfiguration dynamics in the electronic superlattice of a quantum material using time-resolved scanning tunneling microscopy and unveil a crossover from temperature to noisy quantum fluctuation dominated dynamics. The process is modeled using a programmable superconducting quantum annealer in which qubit interconnections correspond directly to the microscopic interactions between electrons in the quantum material. Crucially, the dynamics of both the experiment and quantum simulation is driven by spectrally similar pink noise. We find that the simulations reproduce the emergent time evolution and temperature dependence of the experimentally observed electronic domain dynamics.

Quantitative Analogue Simulation of Planar Molecules

Synthetic quantum systems provide a pathway for exploring the physics of complex quantum matter in a programmable fashion. This approach becomes particularly advantageous when it comes to systems that are thermodynamically unfavorable. By sculpting the potential landscape of Cu(111) surfaces with carbon monoxide quantum corrals in a cryogenic scanning tunneling microscope, we created analogue simulators of planar organic molecules, including antiaromatic and non-Kekulé species that are generally reactive or unstable. Spectroscopic imaging of such synthetic molecules reveals close replications of molecular orbitals obtained from ab initio calculations of the organic molecules. We further illustrate the quantitative nature of such analogue simulators by faithful extraction of bond orders and global aromaticity indices, which are otherwise technically daunting using real molecules. Our approach therefore sets the stage for new research frontiers pertaining to the quantum physics and chemistry of designer nanostructures.

A Vision for the Future of Multiscale Modeling

The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.

Haplotype-resolved assembly of diploid and polyploid genomes using quantum computing

Precision medicine's emphasis on individual genetic variants highlights the importance of haplotype-resolved assembly, a computational challenge in bioinformatics given its combinatorial nature. While classical algorithms have made strides in addressing this issue, the potential of quantum computing remains largely untapped. Here, we present the vehicle routing problem (VRP) assembler: an approach that transforms this task into a vehicle routing problem, an optimization formulation solvable on a quantum computer. We demonstrate its potential and feasibility through a proof of concept on short synthetic diploid and triploid genomes using a D-Wave quantum annealer. To tackle larger-scale assembly problems, we integrate the VRP assembler with Google's OR-Tools, achieving a haplotype-resolved local assembly across the human major histocompatibility complex (MHC) region. Our results show encouraging performance compared to Hifiasm with phasing accuracy approaching the theoretical limit, underscoring the promising future of quantum computing in bioinformatics.

A Perspective on Protein Structure Prediction Using Quantum Computers

Despite the recent advancements by deep learning methods such as AlphaFold2, in silico protein structure prediction remains a challenging problem in biomedical research. With the rapid evolution of quantum computing, it is natural to ask whether quantum computers can offer some meaningful benefits for approaching this problem. Yet, identifying specific problem instances amenable to quantum advantage and estimating the quantum resources required are equally challenging tasks. Here, we share our perspective on how to create a framework for systematically selecting protein structure prediction problems that are amenable for quantum advantage, and estimate quantum resources for such problems on a utility-scale quantum computer. As a proof-of-concept, we validate our problem selection framework by accurately predicting the structure of a catalytic loop of the Zika Virus NS3 Helicase, on quantum hardware.

Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics

Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier. Part of a series of Essays which concisely present author visions for the future of their field.

Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics

Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.

Vibrational ADAPT-VQE: Critical points lead to problematic convergence

Quantum chemistry is one of the most promising applications for which quantum computing is expected to have a significant impact. Despite considerable research in the field of electronic structure, calculating the vibrational properties of molecules on quantum computers remains a relatively unexplored field. In this work, we develop a vibrational Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (vADAPT-VQE) formalism based on an infinite product representation (IPR) of anti-Hermitian excitation operators of the Full Vibrational Configuration Interaction (FVCI) wavefunction, which allows for preparing eigenstates of vibrational Hamiltonians on quantum computers. In order to establish the vADAPT-VQE algorithm using the IPR, we study the exactness of disentangled Unitary Vibrational Coupled Cluster (dUVCC) theory and show that dUVCC can formally represent the FVCI wavefunction in an infinite expansion. To investigate the performance of the vADAPT-VQE algorithm, we numerically study whether the vADAPT-VQE algorithm generates a sequence of operators that may represent the FVCI wavefunction. Our numerical results indicate frequent appearance of critical points in the wavefunction preparation using vADAPT-VQE. These results imply that one may encounter diminishing usefulness when preparing vibrational wavefunctions on quantum computers using vADAPT-VQE and that additional studies are required to find methods that can circumvent this behavior.

Quantum simulation of the bosonic Kitaev chain

Superconducting quantum circuits are a natural platform for quantum simulations of a wide variety of important lattice models describing topological phenomena, spanning condensed matter and high-energy physics. One such model is the bosonic analog of the well-known fermionic Kitaev chain, a 1D tight-binding model with both nearest-neighbor hopping and pairing terms. Despite being fully Hermitian, the bosonic Kitaev chain exhibits a number of striking features associated with non-Hermitian systems, including chiral transport and a dramatic sensitivity to boundary conditions known as the non-Hermitian skin effect. Here, using a multimode superconducting parametric cavity, we implement the bosonic Kitaev chain in synthetic dimensions. The lattice sites are mapped to frequency modes of the cavity, and the in situ tunable complex hopping and pairing terms are created by parametric pumping at the mode-difference and mode-sum frequencies, respectively. We experimentally demonstrate important precursors of nontrivial topology and the non-Hermitian skin effect in the bosonic Kitaev chain, including chiral transport, quadrature wavefunction localization, and sensitivity to boundary conditions. Our experiment is an important first step towards exploring genuine many-body non-Hermitian quantum dynamics.

Spontaneously Sliding Multipole Spin Density Waves in Cold Atoms

We report on the observation of spontaneously drifting coupled spin and quadrupolar density waves in the ground state of laser driven Rubidium atoms. These laser-cooled atomic ensembles exhibit spontaneous magnetism via light mediated interactions when submitted to optical feedback by a retroreflecting mirror. Drift direction and chirality of the waves arise from spontaneous symmetry breaking. The observations demonstrate a novel transport process in out-of-equilibrium magnetic systems.

Variational Quantum Simulation of Lindblad Dynamics via Quantum State Diffusion

Quantum simulation of dynamics in open quantum systems is crucial but poses a significant challenge due to the non-Hermitian nature leading to nonunitary evolution and the limited quantum resources on current quantum computers. Here we introduce a variational hybrid quantum-classical algorithm designed for simulating the time evolution governed by the Lindblad master equation. Our approach involves on a stochastic unveiling of the density matrix, transforming the Lindblad equation into a wave function-based quantum state diffusion (QSD) method with the aim of reducing qubit requirements. We then apply variational quantum simulation (VQS) to efficiently capture the nonunitary evolution in QSD. We demonstrate our QSD-VQS algorithm by investigating the quantum dynamics in a two-level system subjected to an amplitude damping channel and a four-level transverse field Ising model within a dissipative environment including time-independent and periodic Hamiltonian cases. The results reveal its promising utility with upcoming hardware in the near future.

Controlling NMR spin systems for quantum computation

Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.

Benchmarking highly entangled states on a 60-atom analogue quantum simulator

Quantum systems have entered a competitive regime in which classical computers must make approximations to represent highly entangled quantum states1,2. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices2-5, and it remains unsolved how to estimate the actual entanglement content of experiments6. Here, we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analogue Rydberg quantum simulator, reaching a high-entanglement entropy regime in which exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement6, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution2-5. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we use. Our results enable a new model for evaluating the ability of both analogue and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

Post-quantum cryptography and the quantum future of cybersecurity

We review the current status of efforts to develop and deploy post-quantum cryptography on the Internet. Then we suggest specific ways in which quantum technologies might be used to enhance cybersecurity in the near future and beyond. We focus on two goals: protecting the secret keys that are used in classical cryptography, and ensuring the trustworthiness of quantum computations. These goals may soon be within reach, thanks to recent progress in both theory and experiment. This progress includes interactive protocols for testing quantumness as well as for performing uncloneable cryptographic computations; and experimental demonstrations of device-independent random number generators, device-independent quantum key distribution, quantum memories, and analog quantum simulators.

Photonic Source of Heralded Greenberger-Horne-Zeilinger States

Generating large multiphoton entangled states is of main interest due to enabling universal photonic quantum computing and all-optical quantum repeater nodes. These applications exploit measurement-based quantum computation using cluster states. Remarkably, it was shown that photonic cluster states of arbitrary size can be generated by using feasible heralded linear optics fusion gates that act on heralded three-photon Greenberger-Horne-Zeilinger (GHZ) states as the initial resource state. Thus, the capability of generating heralded GHZ states is of great importance for scaling up photonic quantum computing. Here, we experimentally demonstrate this required building block by reporting a polarisation-encoded heralded GHZ state of three photons, for which we build a high-rate six-photon source (547±2  Hz) from a solid-state quantum emitter and a stable polarization-based interferometer. The detection of three ancillary photons heralds the generation of three-photon GHZ states among the remaining particles with fidelities up to F=0.7278±0.0106. Our results initiate a path for scalable entangling operations using heralded linear-optics implementations.

Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges

Simulating quantum many-body systems is a key application for emerging quantum processors. While analog quantum simulation has already demonstrated quantum advantage, its digital counterpart has recently become the focus of intense research interest due to the availability of devices that aim to realize general-purpose quantum computers. In this perspective, we give a selective overview of the currently pursued approaches, review the advances in digital quantum simulation by comparing non-variational with variational approaches and identify hardware and algorithmic challenges. Based on this review, the question arises: What are the most promising problems that can be tackled with digital quantum simulation? We argue that problems of a qualitative nature are much more suitable for near-term devices then approaches aiming purely for a quantitative accuracy improvement.

Exact Non-Markovian Quantum Dynamics on the NISQ Device Using Kraus Operators

The theory of open quantum systems has many applications ranging from simulating quantum dynamics in condensed phases to better understanding quantum-enabled technologies. At the center of theoretical chemistry are the developments of methodologies and computational tools for simulating charge and excitation energy transfer in solutions, biomolecules, and molecular aggregates. As a variety of these processes display non-Markovian behavior, classical computer simulation can be challenging due to exponential scaling with existing methods. With quantum computers holding the promise of efficient quantum simulations, in this paper, we present a new quantum algorithm based on Kraus operators that capture the exact non-Markovian effect at a finite temperature. The implementation of the Kraus operators on the quantum machine uses a combination of singular value decomposition (SVD) and optimal Walsh operators that result in shallow circuits. We demonstrate the feasibility of the algorithm by simulating the spin-boson dynamics and the exciton transfer in the Fenna-Matthews-Olson (FMO) complex. The NISQ results show very good agreement with the exact ones.