Probing entanglement in a 2D hard-core Bose-Hubbard lattice.

Entanglement and its propagation are central to understanding many physical properties of quantum systems1-3. Notably, within closed quantum many-body systems, entanglement is believed to yield emergent thermodynamic behaviour4-7. However, a universal understanding remains challenging owing to the non-integrability and computational intractability of most large-scale quantum systems. Quantum hardware platforms provide a means to study the formation and scaling of entanglement in interacting many-body systems8-14. Here we use a controllable 4 × 4 array of superconducting qubits to emulate a 2D hard-core Bose-Hubbard (HCBH) lattice. We generate superposition states by simultaneously driving all lattice sites and extract correlation lengths and entanglement entropy across its many-body energy spectrum. We observe volume-law entanglement scaling for states at the centre of the spectrum and a crossover to the onset of area-law scaling near its edges.

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.

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.

Improving qubit coherence using closed-loop feedback.

Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coherence time by 26% and reducing the single-qubit error rate from (8.5 ± 2.1) × 10-4 to (5.9 ± 0.7) × 10-4. Importantly, the resulting high-fidelity operation remains effective even away from the qubit flux-noise insensitive point, significantly increasing the frequency bandwidth over which the qubit can be operated with high fidelity. This approach is helpful in large qubit grids, where frequency crowding and parasitic interactions between the qubits limit their performance.

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.

Quantum-coherent nanoscience.

For the past three decades nanoscience has widely affected many areas in physics, chemistry and engineering, and has led to numerous fundamental discoveries, as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing, has not played an explicit role in much of nanoscience. This Review describes fundamental principles and practical applications of quantum coherence in nanoscale systems, a research area we call quantum-coherent nanoscience. We structure this Review according to specific degrees of freedom that can be quantum-coherently controlled in a given nanoscale system, such as charge, spin, mechanical motion and photons. We review the current state of the art and focus on outstanding challenges and opportunities unlocked by the merging of nanoscience and coherent quantum operations.

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.

Author Correction: Impact of ionizing radiation on superconducting qubit coherence.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Impact of ionizing radiation on superconducting qubit coherence.

Technologies that rely on quantum bits (qubits) require long coherence times and high-fidelity operations1. Superconducting qubits are one of the leading platforms for achieving these objectives2,3. However, the coherence of superconducting qubits is affected by the breaking of Cooper pairs of electrons4-6. The experimentally observed density of the broken Cooper pairs, referred to as quasiparticles, is orders of magnitude higher than the value predicted at equilibrium by the Bardeen-Cooper-Schrieffer theory of superconductivity7-9. Previous work10-12 has shown that infrared photons considerably increase the quasiparticle density, yet even in the best-isolated systems, it remains much higher10 than expected, suggesting that another generation mechanism exists13. Here we provide evidence that ionizing radiation from environmental radioactive materials and cosmic rays contributes to this observed difference. The effect of ionizing radiation leads to an elevated quasiparticle density, which we predict would ultimately limit the coherence times of superconducting qubits of the type measured here to milliseconds. We further demonstrate that radiation shielding reduces the flux of ionizing radiation and thereby increases the energy-relaxation time. Albeit a small effect for today's qubits, reducing or mitigating the impact of ionizing radiation will be critical for realizing fault-tolerant superconducting quantum computers.

Waveguide quantum electrodynamics with superconducting artificial giant atoms.

Models of light-matter interactions in quantum electrodynamics typically invoke the dipole approximation1,2, in which atoms are treated as point-like objects when compared to the wavelength of the electromagnetic modes with which they interact. However, when the ratio between the size of the atom and the mode wavelength is increased, the dipole approximation no longer holds and the atom is referred to as a 'giant atom'2,3. So far, experimental studies with solid-state devices in the giant-atom regime have been limited to superconducting qubits that couple to short-wavelength surface acoustic waves4-10, probing the properties of the atom at only a single frequency. Here we use an alternative architecture that realizes a giant atom by coupling small atoms to a waveguide at multiple, but well separated, discrete locations. This system enables tunable atom-waveguide couplings with large on-off ratios3 and a coupling spectrum that can be engineered by the design of the device. We also demonstrate decoherence-free interactions between multiple giant atoms that are mediated by the quasi-continuous spectrum of modes in the waveguide-an effect that is not achievable using small atoms11. These features allow qubits in this architecture to switch between protected and emissive configurations in situ while retaining qubit-qubit interactions, opening up possibilities for high-fidelity quantum simulations and non-classical itinerant photon generation12,13.

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.

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.

Coherent control of a hybrid superconducting circuit made with graphene-based van der Waals heterostructures.

Quantum coherence and control is foundational to the science and engineering of quantum systems1,2. In van der Waals materials, the collective coherent behaviour of carriers has been probed successfully by transport measurements3-6. However, temporal coherence and control, as exemplified by manipulating a single quantum degree of freedom, remains to be verified. Here we demonstrate such coherence and control of a superconducting circuit incorporating graphene-based Josephson junctions. Furthermore, we show that this device can be operated as a voltage-tunable transmon qubit7-9, whose spectrum reflects the electronic properties of massless Dirac fermions travelling ballistically4,5. In addition to the potential for advancing extensible quantum computing technology, our results represent a new approach to studying van der Waals materials using microwave photons in coherent quantum circuits.

Distinguishing Coherent and Thermal Photon Noise in a Circuit Quantum Electrodynamical System.

In the cavity-QED architecture, photon number fluctuations from residual cavity photons cause qubit dephasing due to the ac Stark effect. These unwanted photons originate from a variety of sources, such as thermal radiation, leftover measurement photons, and cross talk. Using a capacitively shunted flux qubit coupled to a transmission line cavity, we demonstrate a method that identifies and distinguishes coherent and thermal photons based on noise-spectral reconstruction from time-domain spin-locking relaxometry. Using these measurements, we attribute the limiting dephasing source in our system to thermal photons rather than coherent photons. By improving the cryogenic attenuation on lines leading to the cavity, we successfully suppress residual thermal photons and achieve T_{1}-limited spin-echo decay time. The spin-locking noise-spectroscopy technique allows broad frequency access and readily applies to other qubit modalities for identifying general asymmetric nonclassical noise spectra.

Suppressing relaxation in superconducting qubits by quasiparticle pumping.

Dynamical error suppression techniques are commonly used to improve coherence in quantum systems. They reduce dephasing errors by applying control pulses designed to reverse erroneous coherent evolution driven by environmental noise. However, such methods cannot correct for irreversible processes such as energy relaxation. We investigate a complementary, stochastic approach to reducing errors: Instead of deterministically reversing the unwanted qubit evolution, we use control pulses to shape the noise environment dynamically. In the context of superconducting qubits, we implement a pumping sequence to reduce the number of unpaired electrons (quasiparticles) in close proximity to the device. A 70% reduction in the quasiparticle density results in a threefold enhancement in qubit relaxation times and a comparable reduction in coherence variability.

The flux qubit revisited to enhance coherence and reproducibility.

The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad-frequency tunability, strong anharmonicity, high reproducibility and relaxation times in excess of 40 µs at its flux-insensitive point. Qubit relaxation times T1 across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise and 1/f-flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal-photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in T2≈85 µs, approximately the 2T1 limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting T2 in contemporary qubits based on transverse qubit-resonator interaction.

Single microwave-photon detector using an artificial Λ-type three-level system.

Single-photon detection is a requisite technique in quantum-optics experiments in both the optical and the microwave domains. However, the energy of microwave quanta are four to five orders of magnitude less than their optical counterpart, making the efficient detection of single microwave photons extremely challenging. Here we demonstrate the detection of a single microwave photon propagating through a waveguide. The detector is implemented with an impedance-matched artificial Λ system comprising the dressed states of a driven superconducting qubit coupled to a microwave resonator. Each signal photon deterministically induces a Raman transition in the Λ system and excites the qubit. The subsequent dispersive readout of the qubit produces a discrete 'click'. We attain a high single-photon-detection efficiency of 0.66±0.06 with a low dark-count probability of 0.014±0.001 and a reset time of ∼400 ns. This detector can be exploited for various applications in quantum sensing, quantum communication and quantum information processing.

Heisenberg-Limited Qubit Read-Out with Two-Mode Squeezed Light.

We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, it is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circuit quantum electrodynamics.