The flux qubit revisited to enhance coherence and reproducibility

Nanowires: Exponential speedup in quantum computing

This review paper examines the crucial role of nanowires in the field of quantum computing, highlighting their importance as versatile platforms for qubits and vital building blocks for creating fault-tolerant and scalable quantum information processing systems. Researchers are studying many categories of nanowires, including semiconductor, superconducting, and topological nanowires, to explore their distinct quantum features that play a role in creating various qubit designs. The paper explores the interdisciplinary character of quantum computing, combining the fields of quantum physics and materials science. This text highlights the significance of quantum gate operations in manipulating qubits for computation, thus creating the toolbox of quantum algorithms. The paper emphasizes the key research areas in quantum technology, such as entanglement engineering, quantum error correction, and a wide range of applications spanning from encryption to climate change modeling. The research highlights the importance of tackling difficulties related to decoding mitigation, error correction, and hardware scalability to fully utilize the transformative potential of quantum computing in scientific, technical, and computational fields.

Coexistence of Nonequilibrium Density and Equilibrium Energy Distribution of Quasiparticles in a Superconducting Qubit

The density of quasiparticles typically observed in superconducting qubits exceeds the value expected in equilibrium by many orders of magnitude. Can this out-of-equilibrium quasiparticle density still possess an energy distribution in equilibrium with the phonon bath? Here, we answer this question affirmatively by measuring the thermal activation of charge-parity switching in a transmon qubit with a difference in superconducting gap on the two sides of the Josephson junction. We then demonstrate how the gap asymmetry of the device can be exploited to manipulate its parity.

Measurement of Small Photon Numbers in Circuit QED Resonators

Off-resonant interaction of fluctuating photons in a resonator with a qubit increases the qubit dephasing rate. We use this effect to measure a small average number of intracavity photons that are coherently or thermally driven. For spectral resolution, we do this by subjecting the qubit to a Carr-Purcell-Meiboom-Gill sequence and record the qubit dephasing rate for various periods between qubit π pulses. The recorded data is then analyzed with formulas for the photon-induced dephasing rate derived for the non-Gaussian noise regime with an arbitrary ratio of the resonator dispersive shift to decay rate. We show that the presented Carr-Purcell-Meiboom-Gill dephasing rate formulas agree well with experimental results and demonstrate measurement of thermal and coherent photon populations at the level of a few 10^{-4}.

Mechanically induced correlated errors on superconducting qubits with relaxation times exceeding 0.4 ms

Superconducting qubits are among the most advanced candidates for achieving fault-tolerant quantum computing. Despite recent significant advancements in the qubit lifetimes, the origin of the loss mechanism for state-of-the-art qubits is still subject to investigation. Furthermore, the successful implementation of quantum error correction requires negligible correlated errors between qubits. Here, we realize long-lived superconducting transmon qubits that exhibit fluctuating lifetimes, averaging 0.2 ms and exceeding 0.4 ms - corresponding to quality factors above 5 million and 10 million, respectively. We then investigate their dominant error mechanism. By introducing novel time-resolved error measurements that are synchronized with the operation of the pulse tube cooler in a dilution refrigerator, we find that mechanical vibrations from the pulse tube induce nonequilibrium dynamics in highly coherent qubits, leading to their correlated bit-flip errors. Our findings not only deepen our understanding of the qubit error mechanisms but also provide valuable insights into potential error-mitigation strategies for achieving fault tolerance by decoupling superconducting qubits from their mechanical environments.

Fast joint parity measurement via collective interactions induced by stimulated emission

Parity detection is essential in quantum error correction. Error syndromes coded in parity are detected routinely by sequential CNOT gates. Here, different from the standard CNOT-gate based scheme, we propose a reliable joint parity measurement (JPM) scheme inspired by stimulated emission. By controlling the collective behavior between data qubits and syndrome qubit, we realize the parity detection and experimentally implement the weight-2 and weight-4 JPM scheme in a tunable coupling superconducting circuit, which shows comparable performance to the CNOT scheme. Moreover, with the aid of the coupling tunability in quantum system, this scheme can be further utilized for specific joint entangling state preparation (JEP) with high fidelity, such as multiqubit entangled state preparation for non-adjacent qubits. This strategy, combined with the superconducting qubit system with tunable couplers, reveals tremendous potential and applications in the surface code architecture without adding extra circuit elements. Besides, the method we develop here can readily be applied in large-scale quantum computation and quantum simulation.

Geometric Phase of a Transmon in a Dissipative Quantum Circuit

Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, we study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. We do so both for the case in which the evolution is unitary and when it is subjected to dissipative effects. These models offer a comprehensive quantum description of an anharmonic system interacting with a single mode of the electromagnetic field within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment.

Microwave quantum diode

The fragile nature of quantum circuits is a major bottleneck to scalable quantum applications. Operating at cryogenic temperatures, quantum circuits are highly vulnerable to amplifier backaction and external noise. Non-reciprocal microwave devices such as circulators and isolators are used for this purpose. These devices have a considerable footprint in cryostats, limiting the scalability of quantum circuits. As a proof-of-concept, here we report a compact microwave diode architecture, which exploits the non-linearity of a superconducting flux qubit. At the qubit degeneracy point we experimentally demonstrate a significant difference between the power levels transmitted in opposite directions. The observations align with the proposed theoretical model. At - 99 dBm input power, and near the qubit-resonator avoided crossing region, we report the transmission rectification ratio exceeding 90% for a 50 MHz wide frequency range from 6.81 GHz to 6.86 GHz, and over 60% for the 250 MHz range from 6.67 GHz to 6.91 GHz. The presented architecture is compact, and easily scalable towards multiple readout channels, potentially opening up diverse opportunities in quantum information, microwave read-out and optomechanics.

Effective protocol for generating NOON states of resonator modes

We propose a protocol for the generation of NOON states of resonator modes. The physical model is composed of two Kerr-nonlinear resonators and a four-level qudit. Using the off-resonant couplings between the resonators and the qudit, qudit-level-dependent frequency shifts on the two resonators are induced. The frequency shifts allow us to drive different resonators to the N-photon state when the qudit is in different intermediate levels. Consequently, the generation of NOON states with arbitrary photon number N can be completed in only three steps, i.e., driving the qudit to a superposition state of the two intermediate levels, driving one of the resonators to its N-photon state, and driving the qudit back to its ground level. Numerical simulations show that, in the regime of strong Kerr nonlinearity and coupling strengths, the protocol can produce the NOON state with high fidelity in the cases of different photon numbers. In addition, it is possible for the protocol to produce acceptable fidelity in the presence of systematic errors and decoherence factors. Therefore, the protocol may provide some useful perspectives for effective generation of photonic NOON states.

Nonergodic Measurements of Qubit Frequency Noise

Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of the noise. The time needed for quantum measurements to display quasiergodic behavior can strongly depend on the measurement parameters.

Dynamics of Dispersive Measurements of Flux-Qubit States: Energy-Level Splitting Connected to Quantum Wave Mechanics

Superconducting flux qubits have many advantages as a storage of quantum information, such as broad range tunability of frequency, small-size fabricability, and high controllability. In the flux qubit-oscillator, qubits are connected to SQUID resonators for the purpose of performing dispersive non-destructive readouts of qubit signals with high fidelity. In this work, we propose a theoretical model for analyzing quantum characteristics of a flux qubit-oscillator on the basis of quantum solutions obtained using a unitary transformation approach. The energy levels of the combined system (qubit + resonator) are analyzed in detail. Equally spaced each energy level of the resonator splits into two parts depending on qubit states. Besides, coupling of the qubit to the resonator brings about an additional modification in the split energy levels. So long as the coupling strength and the tunnel splitting are not zero but finite values, the energy-level splitting of the resonator does not disappear. We conclude that quantum nondemolition dispersive measurements of the qubit states are possible by inducing bifurcation of the resonator states through the coupling.

Quantum computer-aided design for advanced superconducting qubit: Plasmonium

Complex quantum electronic circuits can be used to design noise-protected qubits, but their complexity may exceed the capabilities of classical simulation. In such cases, quantum computers are necessary for efficient simulation. In this work, we demonstrate the use of variational quantum computing on a transmon-based quantum processor to simulate a superconducting quantum electronic circuit and design a new type of qubit called "Plasmonium", which operates in the plasmon-transition regime. The fabricated Plasmonium qubits show a high two-qubit gate fidelity of 99.58(3)%, as well as a smaller physical size and larger anharmonicity compared to transmon qubits. These properties make Plasmonium a promising candidate for scaling up multi-qubit devices. Our results demonstrate the potential of using quantum computers to aid in the design of advanced quantum processors.

Probing the symmetry breaking of a light-matter system by an ancillary qubit

Hybrid quantum systems in the ultrastrong, and even more in the deep-strong, coupling regimes can exhibit exotic physical phenomena and promise new applications in quantum technologies. In these nonperturbative regimes, a qubit-resonator system has an entangled quantum vacuum with a nonzero average photon number in the resonator, where the photons are virtual and cannot be directly detected. The vacuum field, however, is able to induce the symmetry breaking of a dispersively coupled probe qubit. We experimentally observe the parity symmetry breaking of an ancillary Xmon artificial atom induced by the field of a lumped-element superconducting resonator deep-strongly coupled with a flux qubit. This result opens a way to experimentally explore the novel quantum-vacuum effects emerging in the deep-strong coupling regime.

Inductively shunted transmons exhibit noise insensitive plasmon states and a fluxon decay exceeding 3 hours

Currently available quantum processors are dominated by noise, which severely limits their applicability and motivates the search for new physical qubit encodings. In this work, we introduce the inductively shunted transmon, a weakly flux-tunable superconducting qubit that offers charge offset protection for all levels and a 20-fold reduction in flux dispersion compared to the state-of-the-art resulting in a constant coherence over a full flux quantum. The parabolic confinement provided by the inductive shunt as well as the linearity of the geometric superinductor facilitates a high-power readout that resolves quantum jumps with a fidelity and QND-ness of >90% and without the need for a Josephson parametric amplifier. Moreover, the device reveals quantum tunneling physics between the two prepared fluxon ground states with a measured average decay time of up to 3.5 h. In the future, fast time-domain control of the transition matrix elements could offer a new path forward to also achieve full qubit control in the decay-protected fluxon basis.

Millisecond Coherence in a Superconducting Qubit

Improving control over physical qubits is a crucial component of quantum computing research. Here we report a superconducting fluxonium qubit with uncorrected coherence time T_{2}^{*}=1.48±0.13  ms, exceeding the state of the art for transmons by an order of magnitude. The average gate fidelity was benchmarked at 0.99991(1). Notably, even in the millisecond range, the coherence time is limited by material absorption and could be further improved with a more rigorous fabrication. Our demonstration may be useful for suppressing errors in the next generation quantum processors.

Evolution of 1/f Flux Noise in Superconducting Qubits with Weak Magnetic Fields

The microscopic description of 1/f magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here, we apply weak in-plane magnetic fields to a capacitively shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent 1/f noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure-dephasing time in fields up to B=100  G. With direct noise spectroscopy, we further observe a transition from a 1/f to approximately Lorentzian frequency dependence below 10 Hz and a reduction of the noise above 1 MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of 1/f flux noise in superconducting circuits.

Quantum heat diode versus light emission in circuit quantum electrodynamical system

Precisely controlling heat transfer in a quantum mechanical system is particularly significant for designing quantum thermodynamical devices. With the technology of experiment advances, circuit quantum electrodynamics (circuit QED) has become a promising system due to controllable light-matter interactions as well as flexible coupling strengths. In this paper, we design a thermal diode in terms of the two-photon Rabi model of the circuit QED system. We find that the thermal diode can not only be realized in the resonant coupling but also achieve better performance, especially for the detuned qubit-photon ultrastrong coupling. We also study the photonic detection rates and their nonreciprocity, which indicate similar behaviors with the nonreciprocal heat transport. This provides the potential to understand thermal diode behavior from the quantum optical perspective and could shed new insight into the relevant research on thermodynamical devices.

Material-Inherent Noise Sources in Quantum Information Architecture

NISQ is a representative keyword at present as an acronym for "noisy intermediate-scale quantum", which identifies the current era of quantum information processing (QIP) technologies. QIP science and technologies aim to accomplish unprecedented performance in computation, communications, simulations, and sensing by exploiting the infinite capacity of parallelism, coherence, and entanglement as governing quantum mechanical principles. For the last several decades, quantum computing has reached to the technology readiness level 5, where components are integrated to build mid-sized commercial products. While this is a celebrated and triumphant achievement, we are still a great distance away from quantum-superior, fault-tolerant architecture. To reach this goal, we need to harness technologies that recognize undesirable factors to lower fidelity and induce errors from various sources of noise with controllable correction capabilities. This review surveys noisy processes arising from materials upon which several quantum architectures have been constructed, and it summarizes leading research activities in searching for origins of noise and noise reduction methods to build advanced, large-scale quantum technologies in the near future.

Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits

We present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems, including those described by originally unbounded Hamiltonians that are made finite-dimensional by a cutoff. Our bound is geared towards the qubit approximation of superconducting circuits and presents a sufficient condition for remaining within the [Formula: see text]-dimensional qubit subspace of a circuit model of [Formula: see text] qubits. The novelty of this adiabatic theorem is that, unlike previous rigorous results, it does not contain [Formula: see text] as a factor in the adiabatic timescale, and it allows one to obtain an expression for the adiabatic timescale independent of the cutoff of the infinite-dimensional Hilbert space of the circuit Hamiltonian. As an application, we present an explicit dependence of this timescale on circuit parameters for a superconducting flux qubit and demonstrate that leakage out of the qubit subspace is inevitable as the tunnelling barrier is raised towards the end of a quantum anneal. We also discuss a method of obtaining a [Formula: see text] effective Hamiltonian that best approximates the true dynamics induced by slowly changing circuit control parameters. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

Error-Mitigated Quantum Metrology via Virtual Purification

Quantum metrology with entangled resources aims to achieve sensitivity beyond the standard quantum limit by harnessing quantum effects even in the presence of environmental noise. So far, sensitivity has been mainly discussed from the viewpoint of reducing statistical errors under the assumption of perfect knowledge of a noise model. However, we cannot always obtain complete information about a noise model due to coherence time fluctuations, which are frequently observed in experiments. Such unknown fluctuating noise leads to systematic errors and nullifies the quantum advantages. Here, we propose an error-mitigated quantum metrology that can filter out unknown fluctuating noise with the aid of purification-based quantum error mitigation. We demonstrate that our protocol mitigates systematic errors and recovers superclassical scaling in a practical situation with time-inhomogeneous bias-inducing noise. Our result is the first demonstration to reveal the usefulness of purification-based error mitigation for unknown fluctuating noise, thus paving the way not only for practical quantum metrology but also for quantum computation affected by such noise.

Demonstration of Tunable Three-Body Interactions between Superconducting Qubits

Nonpairwise multiqubit interactions present a useful resource for quantum information processors. Their implementation would facilitate more efficient quantum simulations of molecules and combinatorial optimization problems, and they could simplify error suppression and error correction schemes. Here, we present a superconducting circuit architecture in which a coupling module mediates two-local and three-local interactions between three flux qubits by design. The system Hamiltonian is estimated via multiqubit pulse sequences that implement Ramsey-type interferometry between all neighboring excitation manifolds in the system. The three-local interaction is coherently tunable over several MHz via the coupler flux biases and can be turned off, which is important for applications in quantum annealing, analog quantum simulation, and gate-model quantum computation.

A Pair of Coupled Waveguides as a Classical Analogue for a Solid-State Qubit

We have determined conditions when a pair of coupled waveguides, a common element for integrated room-temperature photonics, can act as a qubit based on a system with a double-well potential. Moreover, we have used slow-varying amplitude approximation (SVA) for the "classical" wave equation to study the propagation of electromagnetic beams in a couple of dielectric waveguides both analytically and numerically. As a part of an extension of the optical-mechanical analogy, we have considered examples of "quantum operations" on the electromagnetic wave state in a pair of waveguides. Furthermore, we have provided examples of "quantum-mechanical" calculations of nonlinear transfer functions for the implementation of the considered element in optical neural networks.

Complete Physical Characterization of Quantum Nondemolition Measurements via Tomography

We introduce a self-consistent tomography for arbitrary quantum nondemolition (QND) detectors. Based on this, we build a complete physical characterization of the detector, including the measurement processes and a quantification of the fidelity, ideality, and backaction of the measurement. This framework is a diagnostic tool for the dynamics of QND detectors, allowing us to identify errors, and to improve their calibration and design. We illustrate this on a realistic Jaynes-Cummings simulation of a superconducting qubit readout. We characterize nondispersive errors, quantify the backaction introduced by the readout cavity, and calibrate the optimal measurement point.

Quantum-Enhanced Heat Engine Based on Superabsorption

We propose a quantum-enhanced heat engine with entanglement. The key feature of our scheme is superabsorption, which facilitates enhanced energy absorption by entangled qubits. Whereas a conventional engine with N separable qubits provides power with a scaling of P=Θ(N), our engine uses superabsorption to provide power with a quantum scaling of P=Θ(N^{2}). This quantum heat engine also exhibits a scaling advantage over classical ones composed of N-particle Langevin systems. Our work elucidates the quantum properties allowing for the enhancement of performance.

Weak spin-flip scattering in Pd89Ni11 interlayer of NbN-based ferromagnetic Josephson junctions

We studied niobium nitride (NbN)-based π-junctions with a diluted ferromagnetic Pd₈₉Ni₁₁ interlayer (NbN/PdNi/NbN junctions). In the NbN/PdNi/NbN junctions with various PdNi thicknesses, we observed a non-monotonic dependence of the critical currents on PdNi thickness, indicating the effects of the exchange interaction on the superconducting order parameter. From theoretical fitting of the experimental data, we found that the NbN/PdNi/NbN junctions showed a significantly smaller degree of spin-flip scattering in the PdNi interlayer than in the CuNi interlayer of NbN/CuNi/NbN junctions reported previously. The weak spin-flip scattering leads to a longer decay length of the Josephson critical current, so the critical currents were observed over a wide range of PdNi thicknesses (10–40 nm). We also fabricated superconducting quantum interference devices (SQUIDs) including the NbN/PdNi/NbN junction, using a PdNi thickness in which the π-state was expected. A half-flux-quantum shift, as evidence of the π-state, was observed in the magnetic field-dependent critical currents of the SQUIDs. This result represents an important step towards the practical application of NbN-based π-Josephson junctions.

Hexagonal boron nitride as a low-loss dielectric for superconducting quantum circuits and qubits

Dielectrics with low loss at microwave frequencies are imperative for high-coherence solid-state quantum computing platforms. Here we study the dielectric loss of hexagonal boron nitride (hBN) thin films in the microwave regime by measuring the quality factor of parallel-plate capacitors (PPCs) made of NbSe₂-hBN-NbSe₂ heterostructures integrated into superconducting circuits. The extracted microwave loss tangent of hBN is bounded to be at most in the mid-10^-6 range in the low-temperature, single-photon regime. We integrate hBN PPCs with aluminium Josephson junctions to realize transmon qubits with coherence times reaching 25 μs, consistent with the hBN loss tangent inferred from resonator measurements. The hBN PPC reduces the qubit feature size by approximately two orders of magnitude compared with conventional all-aluminium coplanar transmons. Our results establish hBN as a promising dielectric for building high-coherence quantum circuits with substantially reduced footprint and with a high energy participation that helps to reduce unwanted qubit cross-talk.

Intrinsic and induced quantum quenches for enhancing qubit-based quantum noise spectroscopy

Quantum sensing protocols that exploit the dephasing of a probe qubit are powerful and ubiquitous methods for interrogating an unknown environment. They have a variety of applications, ranging from noise mitigation in quantum processors, to the study of correlated electron states. Here, we discuss a simple strategy for enhancing these methods, based on the fact that they often give rise to an inadvertent quench of the probed system: there is an effective sudden change in the environmental Hamiltonian at the start of the sensing protocol. These quenches are extremely sensitive to the initial environmental state, and lead to observable changes in the sensor qubit evolution. We show how these new features give access to environmental response properties. This enables methods for direct measurement of bath temperature, and for detecting non-thermal equilibrium states. We also discuss how to deliberately control and modulate this quench physics, which enables reconstruction of the bath spectral function. Extensions to non-Gaussian quantum baths are also discussed, as is the application of our ideas to a range of sensing platforms (e.g., nitrogen-vacancy (NV) centers in diamond, semiconductor quantum dots, and superconducting circuits).

Stability of superconducting resonators: Motional narrowing and the role of Landau-Zener driving of two-level defects

Frequency instability of superconducting resonators and qubits leads to dephasing and time-varying energy loss and hinders quantum processor tune-up. Its main source is dielectric noise originating in surface oxides. Thorough noise studies are needed to develop a comprehensive understanding and mitigation strategy of these fluctuations. We use a frequency-locked loop to track the resonant frequency jitter of three different resonator types—one niobium nitride superinductor, one aluminum coplanar waveguide, and one aluminum cavity—and we observe notably similar random telegraph signal fluctuations. At low microwave drive power, the resonators exhibit multiple, unstable frequency positions, which, for increasing power, coalesce into one frequency due to motional narrowing caused by sympathetic driving of two-level system defects by the resonator. In all three devices, we identify a dominant fluctuator whose switching amplitude (separation between states) saturates with increasing drive power, but whose characteristic switching rate follows the power law dependence of quasi-classical Landau-Zener transitions.

Superconducting Quantum Interference in Twisted van der Waals Heterostructures

We demonstrate the formation of both Josephson junctions and superconducting quantum interference devices (SQUIDs) using a dry transfer technique to stack and deterministically misalign mechanically exfoliated flakes of NbSe₂. The current-voltage characteristics of the resulting twisted NbSe₂-NbSe₂ junctions are found to be sensitive to the misalignment angle of the crystallographic axes, opening up a new control parameter for optimization of the device performance, which is not available in thin-film-deposited junctions. A single lithographic process has then been implemented to shape Josephson junctions into SQUID geometries with typical loop areas of ∼25 μm² and weak links ∼600 nm wide. At T = 3.75 K in an applied magnetic field, these devices display large stable current and voltage modulation depths of up to ΔI_c ∼ 75% and ΔV ∼ 1.4 mV, respectively.

Enhanced Coherence in Superconducting Circuits via Band Engineering

In superconducting circuits interrupted by Josephson junctions, the dependence of the energy spectrum on offset charges on different islands is 2e periodic through the Aharonov-Casher effect and resembles a crystal band structure that reflects the symmetries of the Josephson potential. We show that higher-harmonic Josephson elements described by a cos(2φ) energy-phase relation provide an increased freedom to tailor the shape of the Josephson potential and design spectra featuring multiplets of flat bands and Dirac points in the charge Brillouin zone. Flat bands provide noise-insensitive energy levels, and consequently, engineering band pairs with flat spectral gaps can help improve the coherence of the system. We discuss a modified version of a flux qubit that achieves, in principle, no decoherence from charge noise and introduce a flux qutrit that shows a spin-1 Dirac spectrum and is simultaneously quite robust to both charge and flux noise.

Quantum Microwave Radiometry with a Superconducting Qubit

The interaction of photons and coherent quantum systems can be employed to detect electromagnetic radiation with remarkable sensitivity. We introduce a quantum radiometer based on the photon-induced dephasing process of a superconducting qubit for sensing microwave radiation at the subunit photon level. Using this radiometer, we demonstrate the radiative cooling of a 1 K microwave resonator and measure its mode temperature with an uncertainty ∼0.01  K. We thus develop a precise tool for studying the thermodynamics of quantum microwave circuits, which provides new solutions for calibrating hybrid quantum systems and detecting candidate particles for dark matter.

Materials challenges and opportunities for quantum computing hardware

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

Efficient and Low-Backaction Quantum Measurement Using a Chip-Scale Detector

Superconducting qubits are a leading platform for scalable quantum computing and quantum error correction. One feature of this platform is the ability to perform projective measurements orders of magnitude more quickly than qubit decoherence times. Such measurements are enabled by the use of quantum-limited parametric amplifiers in conjunction with ferrite circulators-magnetic devices which provide isolation from noise and decoherence due to amplifier backaction. Because these nonreciprocal elements have limited performance and are not easily integrated on chip, it has been a long-standing goal to replace them with a scalable alternative. Here, we demonstrate a solution to this problem by using a superconducting switch to control the coupling between a qubit and amplifier. Doing so, we measure a transmon qubit using a single, chip-scale device to provide both parametric amplification and isolation from the bulk of amplifier backaction. This measurement is also fast, high fidelity, and has 70% efficiency, comparable to the best that has been reported in any superconducting qubit measurement. As such, this work constitutes a high-quality platform for the scalable measurement of superconducting qubits.

Multi-level quantum noise spectroscopy

System noise identification is crucial to the engineering of robust quantum systems. Although existing quantum noise spectroscopy (QNS) protocols measure an aggregate amount of noise affecting a quantum system, they generally cannot distinguish between the underlying processes that contribute to it. Here, we propose and experimentally validate a spin-locking-based QNS protocol that exploits the multi-level energy structure of a superconducting qubit to achieve two notable advances. First, our protocol extends the spectral range of weakly anharmonic qubit spectrometers beyond the present limitations set by their lack of strong anharmonicity. Second, the additional information gained from probing the higher-excited levels enables us to identify and distinguish contributions from different underlying noise mechanisms.

Magnetic flux noise in superconducting qubits and the gap states continuum

In the present study we investigate the selected local aspects of the metal-induced gap states (MIGSs) at the disordered metal-insulator interface, that were previously proposed to produce magnetic moments responsible for the magnetic flux noise in some of the superconducting qubit modalities. Our analysis attempts to supplement the available studies and provide new theoretical contribution toward their validation. In particular, we explicitly discuss the behavior of the MIGSs in the momentum space as a function of the onsite energy deviation, that mimics random potential disorder at the interface in the local approximation. It is found, that when the difference between the characteristic electronic potentials in the insulator increases, the corresponding MIGSs become more localized. This effect is associated with the increasing degree of the potential disorder that was earlier observed to produce highly localized MIGSs in the superconducting qubits. At the same time, the presented findings show that the disorder-induced localization of the MIGSs can be related directly to the decay characteristics of these states as well as to the bulk electronic properties of the insulator. As a result, our study reinforces plausibility of the previous corresponding investigations on the origin of the flux noise, but also allows to draw future directions toward their better verification.

Two-level systems in superconducting quantum devices due to trapped quasiparticles

A major issue for the implementation of large-scale superconducting quantum circuits is the interaction with interfacial two-level system (TLS) defects that lead to qubit parameter fluctuations and relaxation. Another major challenge comes from nonequilibrium quasiparticles (QPs) that result in qubit relaxation and dephasing. Here, we reveal a previously unexplored decoherence mechanism in the form of a new type of TLS originating from trapped QPs, which can induce qubit relaxation. Using spectral, temporal, thermal, and magnetic field mapping of TLS-induced fluctuations in frequency tunable resonators, we identify a highly coherent subset of the general TLS population with a low reconfiguration temperature ∼300 mK and a nonuniform density of states. These properties can be understood if the TLS are formed by QPs trapped in shallow subgap states formed by spatial fluctutations of the superconducting order parameter. This implies that even very rare QP bursts will affect coherence over exponentially long time scales.

Efficient scheme for creating a W-type optical entangled coherent state

W-type optical entangled coherent states have important applications in quantum communication. Previous works require performing measurement in the preparation of such W states. We here propose an efficient scheme for creating a W-type optical entangled coherent state without measurement. This scheme employs a setup composed of three microwave cavities and a superconducting flux coupler qutrit. Because no measurement is required, the W state can be generated deterministically. In addition, the system complexity is greatly reduced because of using only one qutrit to couple the three cavities. Numerical analysis shows that within current experimental technology, the W state can be prepared with high fidelity. This scheme is universal and can be extended to create the W-type optical entangled coherent state, by using three microwave or optical cavities coupled via a three-level natural or artificial atom.

Suppression of Unwanted ZZ Interactions in a Hybrid Two-Qubit System

Mitigating crosstalk errors, whether classical or quantum mechanical, is critically important for achieving high-fidelity entangling gates in multiqubit circuits. For weakly anharmonic superconducting qubits, unwanted ZZ interactions can be suppressed by combining qubits with opposite anharmonicity. We present experimental measurements and theoretical modeling of two-qubit gate error for gates based on the cross resonance interaction between a capacitively shunted flux qubit and a transmon, and demonstrate the elimination of the ZZ interaction.

High-Contrast ZZ Interaction Using Superconducting Qubits with Opposite-Sign Anharmonicity

For building a scalable quantum processor with superconducting qubits, ZZ interaction is of great concern because its residual has a crucial impact to two-qubit gate fidelity. Two-qubit gates with fidelity meeting the criterion of fault-tolerant quantum computation have been demonstrated using ZZ interaction. However, as the performance of quantum processors improves, the residual static ZZ can become a performance-limiting factor for quantum gate operation and quantum error correction. Here, we introduce a superconducting architecture using qubits with opposite-sign anharmonicity, a transmon qubit, and a C-shunt flux qubit, to address this issue. We theoretically demonstrate that by coupling the two types of qubits, the high-contrast ZZ interaction can be realized. Thus, we can control the interaction with a high on-off ratio to implement two-qubit controlled-Z gates, or suppress it during two-qubit gate operation using XY interaction (e.g., an iSWAP gate). The proposed architecture can also be scaled up to multiqubit cases. In a fixed coupled system, ZZ crosstalk related to neighboring spectator qubits could also be heavily suppressed.

Implementation of a Walsh-Hadamard Gate in a Superconducting Qutrit

We have implemented a Walsh-Hadamard gate, which performs a quantum Fourier transform, in a superconducting qutrit. The qutrit is encoded in the lowest three energy levels of a capacitively shunted flux device, operated at the optimal flux-symmetry point. We use an efficient decomposition of the Walsh-Hadamard gate into two unitaries, generated by off-diagonal and diagonal Hamiltonians, respectively. The gate implementation utilizes simultaneous driving of all three transitions between the three pairs of energy levels of the qutrit, one of which is implemented with a two-photon process. The gate has a duration of 35 ns and an average fidelity over a representative set of states, including preparation and tomography errors, of 99.2%, characterized with quantum-state tomography. Compensation of ac-Stark and Bloch-Siegert shifts is essential for reaching high gate fidelities.

π phase shifter based on NbN-based ferromagnetic Josephson junction on a silicon substrate

In the field of superconducting electronics, a π phase shifter based on a ferromagnetic Josephson junction is expected to provide various advantages to classical and quantum superconducting devices. Here we report niobium nitride (NbN)-based ferromagnetic π junctions on a silicon (Si) substrate with a titanium nitride (TiN) buffer layer, which have applications to flux-bias-free flux quantum bits (qubits) and classical digital logic elements. We fabricated and characterized NbN/aluminum nitride (AlN)/NbN Josephson junctions, NbN/copper nickel (CuNi)/NbN ferromagnetic Josephson junctions, and superconducting quantum interference devices (SQUIDs) consisting of these junctions on the Si substrate. The fabricated NbN/AlN/NbN junctions showed a high junction quality suitable for qubit applications. Furthermore, the magnetic field dependence of the SQUID's critical current indicated that the NbN/CuNi/NbN junction worked as a π phase shifter on the Si substrate.

Parity-Protected Superconductor-Semiconductor Qubit

Coherence of superconducting qubits can be improved by implementing designs that protect the parity of Cooper pairs on superconducting islands. Here, we introduce a parity-protected qubit based on voltage-controlled semiconductor nanowire Josephson junctions, taking advantage of the higher harmonic content in the energy-phase relation of few-channel junctions. A symmetric interferometer formed by two such junctions, gate-tuned into balance and frustrated by a half-quantum of applied flux, yields a cos(2φ) Josephson element, reflecting coherent transport of pairs of Cooper pairs. We demonstrate that relaxation of the qubit can be suppressed tenfold by tuning into the protected regime.

Perspectives of quantum annealing: methods and implementations

Quantum annealing is a computing paradigm that has the ambitious goal of efficiently solving large-scale combinatorial optimization problems of practical importance. However, many challenges have yet to be overcome before this goal can be reached. This perspectives article first gives a brief introduction to the concept of quantum annealing, and then highlights new pathways that may clear the way towards feasible and large scale quantum annealing. Moreover, since this field of research is to a strong degree driven by a synergy between experiment and theory, we discuss both in this work. An important focus in this article is on future perspectives, which complements other review articles, and which we hope will motivate further research.

Projecting an ultra-strongly-coupled system in a non-energy-eigenbasis with a driven nonlinear resonator

We explore the problem of projecting the ground-state of an ultra-strong-coupled circuit-QED system into a non-energy-eigenstate. As a measurement apparatus we consider a nonlinear driven resonator. We find that the post-measurement state of the nonlinear resonator exhibits a large correlation with the post-measurement state of the ultra-strongly coupled system even when the coupling between measurement device and system is much smaller than the energy scales of the system itself. While the projection is imperfect, we argue that because of the strong nonlinear response of the resonator it works in a practical regime where a linear measurement apparatus would fail.

Efficient Quantum Error Correction of Dephasing Induced by a Common Fluctuator

Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new family of special-purpose quantum error-correcting codes that offer an exponential reduction in overhead compared to the usual repetition code. They are tailored for a common and important source of decoherence in current experiments, whereby a register of qubits is subject to phase noise through coupling to a common fluctuator, such as a resonator or a spin defect. The smallest instance encodes one logical qubit into two physical qubits, and corrects decoherence to leading-order using a constant number of one- and two-qubit operations. More generally, while the repetition code on n qubits corrects errors to order t^{O(n)}, with t the time between recoveries, our codes correct to order t^{O(2^{n})}. Moreover, they are robust to model imperfections in small- and intermediate-scale devices, where they already provide substantial gains in error suppression. As a result, these hardware-efficient codes open a potential avenue for useful quantum error correction in near-term, pre-fault tolerant devices.

Quantum supremacy using a programmable superconducting processor

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor¹. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits^2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2⁵³ (about 10¹⁶). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy^8-14 for this specific computational task, heralding a much-anticipated computing paradigm.

Creation of superposition of arbitrary states encoded in two high-Q cavities

The principle of superposition is a key ingredient for quantum mechanics. A recent work [Phys. Rev. Lett.116, 110403 (2016)10.1103/PhysRevLett.116.110403] has shown that a quantum adder that deterministically generates a superposition of two unknown states is forbidden. Here we consider the implementation of the probabilistic quantum adder in the 3D cavity-transmon system. Our implementation is based on a three-level superconducting transmon qubit dispersively coupled to two cavities. Numerical simulations show that high-fidelity generation of the superposition of two coherent states is feasible with current circuit QED technology. Our method also works for other physical systems such as two optical cavities coupled to a three-level atom or two nitrogen-vacancy center ensembles interacted with one three-level superconducting flux qubit.

Non-Gaussian noise spectroscopy with a superconducting qubit sensor

Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices.

Field-Effect Controllable Metallic Josephson Interferometer

Gate-tunable Josephson junctions (JJs) are the backbone of superconducting classical and quantum computation. Typically, these systems exploit low-charge-concentration materials and present technological difficulties limiting their scalability. Surprisingly, electric field modulation of a supercurrent in metallic wires and JJs has been recently demonstrated. Here, we report the realization of titanium-based monolithic interferometers which allow tuning both JJs independently via voltage bias applied to capacitively coupled electrodes. Our experiments demonstrate full control of the amplitude of the switching current (I_s) and of the superconducting phase across the single JJ in a wide range of temperatures. Astoundingly, by gate-biasing a single junction, the maximum achievable total I_s is suppressed down to values much lower than the critical current of a single JJ. A theoretical model including gate-induced phase fluctuations on a single junction accounts for our experimental findings. This class of quantum interferometers could represent a breakthrough for several applications such as digital electronics, quantum computing, sensitive magnetometry, and single-photon detection.

Photon-Assisted Charge-Parity Jumps in a Superconducting Qubit

We evaluate the rates of energy and phase relaxation of a superconducting qubit caused by stray photons with energy exceeding the threshold for breaking a Cooper pair. All channels of relaxation within this mechanism are associated with the change in the charge parity of the qubit, enabling the separation of the photon-assisted processes from other contributions to the relaxation rates. Among the signatures of the new mechanism is the same order of rates of the transitions in which a qubit loses or gains energy, which is in agreement with recent experiments. Our theory offers the possibility to characterize the electromagnetic environment of superconducting devices at the single-photon level for frequencies above the superconducting gap.

Granular aluminium as a superconducting material for high-impedance quantum circuits

Superconducting quantum information processing machines are predominantly based on microwave circuits with relatively low characteristic impedance, about 100 Ω, and small anharmonicity, which can limit their coherence and logic gate fidelity^1,2. A promising alternative is circuits based on so-called superinductors^3-6, with characteristic impedances exceeding the resistance quantum R_Q = 6.4 kΩ. However, previous implementations of superinductors, consisting of mesoscopic Josephson junction arrays^7,8, can introduce unintended nonlinearity or parasitic resonant modes in the qubit vicinity, degrading its coherence. Here, we present a fluxonium qubit design based on a granular aluminium superinductor strip^9-11. We show that granular aluminium can form an effective junction array with high kinetic inductance and be in situ integrated with standard aluminium circuit processing. The measured qubit coherence time [Formula: see text] illustrates the potential of granular aluminium for applications ranging from protected qubit designs to quantum-limited amplifiers and detectors.