Estimating the features of noise is the first step in a chain of protocols that will someday lead to fault-tolerant quantum computers. The randomized benchmarking (RB) protocol is designed with this exact mindset, estimating the average strength of noise in a quantum processor with relative ease in practice. However, RB, along with most other benchmarking and characterization methods, is limited in scope because it assumes that the noise is temporally uncorrelated (Markovian), which is increasingly evident not to be the case. Here, we combine the RB protocol with a recent framework describing non-Markovian quantum phenomena to derive a general analytical expression of the average sequence fidelity (ASF) for non-Markovian RB with the Clifford group. We show that one can identify non-Markovian features of the noise directly from the ASF through its deviations from the Markovian case, proposing a set of methods to collectively estimate these deviations, non-Markovian memory time scales, and diagnose (in)coherence of non-Markovian noise in a RB experiment. Finally, we demonstrate the efficacy of our proposal by means of several proof-of-principle examples. Our methods are directly implementable and pave the way for a better understanding of correlated noise in quantum processors.

In cavity-based axion dark matter detectors, quantum noise remains a primary barrier to achieving the scan rate necessary for a comprehensive search of axion parameter space. Here, we introduce a method of scan rate enhancement in which an axion-sensitive cavity is coupled to an auxiliary resonant circuit through simultaneous two-mode squeezing (entangling) and state-swapping interactions. We show analytically that when combined, these interactions can amplify an axion signal before it becomes polluted by vacuum noise introduced by measurement. This internal amplification yields a wider bandwidth of axion sensitivity, increasing the rate at which the detector can search through frequency space. With interaction rates predicted by circuit simulations of this system, we show that this technique can increase the scan rate up to 15-fold relative to the scan rate of a detector limited by vacuum noise.

When is the quantum speed limit (QSL) really quantum? While vanishing QSL times often indicate emergent classical behavior, it is still not entirely understood what precise aspects of classicality are at the origin of this dynamical feature. Here, we show that vanishing QSL times (or, equivalently, diverging quantum speeds) can be traced back to reduced uncertainty in quantum observables and can thus be understood as a consequence of emerging classicality for these particular observables. We illustrate this mechanism by developing a QSL formalism for continuous-variable quantum systems undergoing general Gaussian dynamics. For these systems, we show that three typical scenarios leading to vanishing QSL times, namely large squeezing, small effective Planck’s constant, and large particle number, can be fundamentally connected to each other. In contrast, by studying the dynamics of open quantum systems and mixed states, we show that the classicality that emerges due to incoherent mixing of states from the addition of classical noise typically increases the QSL time.

Near-term quantum computers are limited by the decoherence of qubits to only being able to run low-depth quantum circuits with acceptable fidelity. This severely restricts what quantum algorithms can be compiled and implemented on such devices. One way to overcome these limitations is to expand the available gate set from single- and two-qubit gates to multiqubit gates, which entangle three or more qubits in a single step. Here, we show that such multiqubit gates can be realized by the simultaneous application of multiple two-qubit gates to a group of qubits where at least one qubit is involved in two or more of the two-qubit gates. Multiqubit gates implemented in this way are as fast as, or sometimes even faster than, the constituent two-qubit gates. Furthermore, these multiqubit gates do not require any modification of the quantum processor, but are ready to be used in current quantum-computing platforms. We demonstrate this idea for two specific cases: simultaneous controlled-$Z$ gates and simultaneous iswap gates. We show how the resulting multiqubit gates relate to other well-known multiqubit gates and demonstrate through numerical simulations that they would work well in available quantum hardware, reaching gate fidelities well above 99%. We also present schemes for using these simultaneous two-qubit gates to swiftly create large entangled states like Dicke and Greenberger-Horne-Zeilinger states.

Magnetic impurities in $s$-wave superconductors lead to spin-polarized Yu-Shiba-Rusinov (YSR) in-gap states. Chains of magnetic impurities offer one of the most viable routes for the realization of Majorana bound states, which hold promise for topological quantum computing. However, this ambitious goal looks distant, since no quantum coherent degrees of freedom have yet been identified in these systems. To fill this gap, we propose an effective two-level system, a YSR qubit, stemming from two nearby impurities. Using a time-dependent wave-function approach, we derive an effective Hamiltonian describing the YSR-qubit evolution as a function of the distance between the impurity spins, their relative orientations, and their dynamics. We show that the YSR qubit can be controlled and read out using state-of-the-art experimental techniques for manipulation of the spins. Finally, we address the effect of spin noise on the coherence properties of the YSR qubit and show robust behavior for a wide range of experimentally relevant parameters. Looking forward, the YSR qubit could facilitate the implementation of a universal set of quantum gates in hybrid systems where they are coupled to topological Majorana qubits.

Viewing a quantum thermal machine as a non-Hermitian quantum system, we characterize in full generality its analytical time-dependent dynamics by deriving the spectrum of its non-Hermitian Liouvillian for an arbitrary initial state. We show that the thermal machine features a number of Liouvillian exceptional points (EPs) for experimentally realistic parameters, in particular, a third-order exceptional point that leaves signatures both in short- and long-time regimes. Remarkably, we demonstrate that this EP corresponds to a regime of critical decay for the quantum thermal machine towards its steady state, bearing a striking resemblance with a critically damped harmonic oscillator. These results open up exciting possibilities for the precise dynamical control of quantum thermal machines exploiting exceptional points from non-Hermitian physics and are amenable to state-of-the-art solid-state platforms such as semiconducting and superconducting devices.

Quantum algorithms offer significant speed-ups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms have recently been tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW’19 paper on the QSVT [Gilyén et al., ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which the QSVT naturally emerges. Paralleling GSLW’19, we then employ the QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how the QSVT is a single framework comprising the three major quantum algorithms, suggesting a grand unification of quantum algorithms.

With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge overhead imposed by quantum error correction itself. We propose a fault-tolerant quantum computing scheme that can nonetheless be assembled from a small number of experimental components, potentially dramatically reducing the engineering challenges associated with building a large-scale fault-tolerant quantum computer. Our scheme has a threshold of $0.39\mathrm{\%}$ for depolarizing noise, assuming that memory errors are negligible. In the presence of memory errors, the logical error rate decays exponentially with $\sqrt{T/\tau }$, where $T$ is the memory coherence time and $\tau$ is the timescale for elementary gates. Our approach is based on a novel procedure for fault-tolerantly preparing three-dimensional cluster states using a single actively controlled qubit and a pair of delay lines. Although a circuit-level error may propagate to a high-weight error, the effect of this error on the prepared state is always equivalent to that of a constant-weight error. We describe how the requisite gates can be implemented using existing technologies in quantum photonic and phononic systems. With continued improvements in only a few components, we expect these systems to be promising candidates for demonstrating fault-tolerant quantum computation with a comparatively modest experimental effort.

A quantum network consisting of magnonic and mechanical nodes connected by light is proposed. Recent years have witnessed a significant development in cavity magnonics based on collective spin excitations in ferrimagnetic crystals, such as yttrium iron garnet (YIG). Magnonic systems are considered to be a promising building block for a future quantum network. However, a major limitation of the system is that the coherence time of the magnon excitations is limited by their intrinsic loss (typically in the order of $1\mu \mathrm{s}$ for YIG). Here, we show that by coupling the magnonic system to a mechanical system using optical pulses, an arbitrary magnonic state (either classical or quantum) can be transferred to and stored in a distant long-lived mechanical resonator. The fidelity depends on the pulse parameters and the transmission loss. We further show that the magnonic and mechanical nodes can be prepared in a macroscopic entangled state. These demonstrate the quantum state transfer and entanglement distribution in such a novel quantum network of magnonic and mechanical nodes. Our work shows the possibility to connect two separate fields of optomagnonics and optomechanics, and to build a long-distance quantum network based on magnonic and mechanical systems.

Today’s quantum computers are composed of tens of qubits interacting with each other and the environment in increasingly complex networks. To achieve the best possible performance when operating such systems, it is necessary to have accurate knowledge of all parameters in the quantum computer Hamiltonian. In this paper, we demonstrate theoretically and experimentally a method to efficiently learn the parameters of resonant interactions for quantum computers consisting of frequency-tunable superconducting qubits. Such interactions include, for example, those with other qubits, resonators, two-level systems, or other wanted or unwanted modes. Our method is based on a significantly improved swap spectroscopy calibration and consists of an offline data collection algorithm, followed by an online Bayesian learning algorithm. The purpose of the offline algorithm is to detect and coarsely estimate resonant interactions from a state of zero knowledge. It produces a quadratic speedup in the scaling of the number of measurements. The online algorithm subsequently refines the estimate of the parameters to accuracy comparable with that of traditional swap spectroscopy calibration but in constant time. We perform an experiment implementing our technique with a superconducting qubit. By combining both algorithms, we observe a reduction of the calibration time by 1 order of magnitude. Our method will improve present medium-scale superconducting quantum computers and will also scale up to larger systems. Finally, the two algorithms presented here can be readily adopted by communities working on different physical implementations of quantum computing architectures.

Many prominent quantum computing algorithms with applications in fields such as chemistry and materials science require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a novel approach to tackle this problem through an adaptive measurement scheme. We present an algorithm that optimizes informationally complete positive operator-valued measurements (POVMs) on the fly in order to minimize the statistical fluctuations in the estimation of relevant cost functions. We show its advantage by improving the efficiency of the variational quantum eigensolver in calculating ground-state energies of molecular Hamiltonians with extensive numerical simulations. Our results indicate that the proposed method is competitive with state-of-the-art measurement-reduction approaches in terms of efficiency. In addition, the informational completeness of the approach offers a crucial advantage, as the measurement data can be reused to infer other quantities of interest. We demonstrate the feasibility of this prospect by reusing ground-state energy-estimation data to perform high-fidelity reduced state tomography.

There are two elementary superconducting qubit types that derive directly from the quantum harmonic oscillator. In one, the inductor is replaced by a nonlinear Josephson junction to realize the widely used charge qubits with a compact phase variable and a discrete charge wave function. In the other, the junction is added in parallel, which gives rise to an extended phase variable, continuous wave functions, and a rich energy-level structure due to the loop topology. While the corresponding rf superconducting quantum interference device Hamiltonian was introduced as a quadratic quasi-one-dimensional potential approximation to describe the fluxonium qubit implemented with long Josephson-junction arrays, in this work we implement it directly using a linear superinductor formed by a single uninterrupted aluminum wire. We present a large variety of qubits, all stemming from the same circuit but with drastically different characteristic energy scales. This includes flux and fluxonium qubits but also the recently introduced quasicharge qubit with strongly enhanced zero-point phase fluctuations and a heavily suppressed flux dispersion. The use of a geometric inductor results in high reproducibility of the inductive energy as guaranteed by top-down lithography—a key ingredient for intrinsically protected superconducting qubits.

In this work, we study the distinguishability of random states drawn from the Wishart ensemble as well as black hole microstates. We compute the relative entropy and many generalizations, including the Petz Rényi relative entropy, sandwiched Rényi relative entropy, fidelities, and trace distances. These generalized quantities are able to teach us about new structures in the space of random states and black hole microstates where the von Neumann and relative entropies were insufficient. We further generalize to generic random tensor networks where new phenomena arise due to the locality in the networks. These phenomena sharpen the relationship between holographic states and random tensor networks. We discuss the implications of our results on the black hole information problem using replica wormholes, specifically the state dependence (hair) in Hawking radiation. Understanding the differences between Hawking radiation of distinct evaporating black holes is an important piece of the information problem that was not addressed by entropy calculations using the island formula. We interpret our results in the language of quantum hypothesis testing and the subsystem eigenstate thermalization hypothesis (ETH), deriving that chaotic (including holographic) systems obey subsystem ETH for all subsystems less than half the total system size.

Secret sharing is a multiparty cryptographic primitive that can be applied to a network of partially distrustful parties for encrypting data that is both sensitive (it must remain secure) and important (it must not be lost or destroyed). When sharing classical secrets (as opposed to quantum states), one can distinguish between protocols that leverage bipartite quantum key distribution (QKD) and those that exploit multipartite entanglement. The latter class are known to be vulnerable to so-called participant attacks and, while progress has been made recently, there is currently no analysis that quantifies their performance in the composable, finite-size regime, which has become the gold standard for QKD security. Given this—and the fact that distributing multipartite entanglement is typically challenging—one might well ask is there any virtue in pursuing multipartite entanglement-based schemes? Here, we answer this question in the affirmative for a class of secret-sharing protocols based on continuous-variable graph states. We establish security in a composable framework and identify a network topology, specifically a bottleneck network of lossy channels, and parameter regimes within the reach of present-day experiments for which a multipartite scheme outperforms the corresponding QKD-based method in the asymptotic and finite-size setting. Finally, we establish experimental parameters where the multipartite schemes outperform any possible QKD-based protocol. This is one of the first concrete compelling examples of multipartite entangled resources achieving a genuine advantage over point-to-point protocols for quantum communication and represents a rigorous, operational benchmark to assess the usefulness of such resources.

Crosstalk is a leading source of failure in multiqubit quantum information processors. It can arise from a wide range of disparate physical phenomena, and can introduce subtle correlations in the errors experienced by a device. Several hardware characterization protocols are able to detect the presence of crosstalk, but few provide sufficient information to distinguish various crosstalk errors from one another. In this article we describe how gate set tomography, a protocol for detailed characterization of quantum operations, can be used to identify and characterize crosstalk errors in quantum information processors. We demonstrate our methods on a two-qubit trapped-ion processor and a two-qubit subsystem of a superconducting transmon processor.

Quantum computing offers a powerful new paradigm of information processing that has the potential to transform a wide range of industries. In the pursuit of the tantalizing promises of a universal quantum computer, a multitude of new knowledge and expertise has been developed, enabling the construction of novel quantum algorithms as well as increasingly robust quantum hardware. In particular, we have witnessed rapid progress in the circuit quantum electrodynamics (cQED) technology, which has emerged as one of the most promising physical systems that is capable of addressing the key challenges in realizing full-stack quantum computing on a large scale. In this Tutorial, we present some of the most crucial building blocks developed by the cQED community in recent years and a précis of the latest achievements towards robust universal quantum computation. More importantly, we aim to provide a synoptic outline of the core techniques that underlie most cQED experiments and offer a practical guide for a novice experimentalist to design, construct, and characterize their first quantum device.

Quantum neural network (QNN), or equivalently, the parameterized quantum circuit (PQC) with a gradient-based classical optimizer, has been broadly applied to many experimental proposals for noisy intermediate-scale quantum (NISQ) devices. However, the learning capability of QNN remains largely unknown due to the nonconvex optimization landscape, the measurement error, and the unavoidable gate noise introduced by NISQ machines. In this study, we theoretically explore the learnability of QNN in the view of the trainability and generalization. Particularly, we derive the convergence performance of QNN under the NISQ setting, and identify classes of computationally hard concepts that can be efficiently learned by QNN. Our results demonstrate that large gate noise, few quantum measurements, and deep circuit depth will lead to poor convergence rates of QNN towards the empirical risk minimization. Moreover, we prove that any concept class, which is efficiently learnable by a quantum statistical query (QSQ) learning model, can also be efficiently learned by PQCs. Since the QSQ learning model can tackle certain problems such as parity learning with a runtime speedup, our result suggests that PQCs established on NISQ devices will retain the quantum advantage measured by generalization ability. Our work provides theoretical guidance for developing advanced QNNs and opens up avenues for exploring quantum advantages beyond hybrid quantum-classical learning protocols in the NISQ era.

The implementation of high-fidelity swapping operations is of vital importance for executing quantum algorithms on a quantum processor with limited connectivity. We present an efficient pulse-control technique, the cross-cross resonance (CCR) gate, to implement iswap and swap gates with dispersively coupled fixed-frequency transmon qubits. The key to the operation of the CCR gate is the simultaneous driving of both of the coupled qubits at the frequency of another qubit, whereby a fast two-qubit interaction roughly equivalent to $ZX+XZ$ entangling gates is realized without strongly driving the qubits. We develop a calibration technique for the CCR gate and evaluate the performance of the iswap and swap gates. The CCR gate shows remarkable improvements in the average gate error from the conventional decomposition based on the cross-resonance gate.

Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily accurate, provided that errors per physical component are smaller than a certain threshold and independent of the computer size. However, in current experiments, physical-resource limitations such as energy, volume, or available bandwidth induce error rates that typically grow as the computer grows. We analyse how error correction performs under such constraints and show that the amount of error correction can be optimized, leading to a maximum attainable computational accuracy. We find this maximum for generic situations where noise is scale dependent. By inverting the logic, we provide experimenters with a tool for finding the minimum resources required to run an algorithm with a given computational accuracy. When combined with a full-stack quantum computing model, this provides the basis for energetic estimates of future large-scale quantum computers.

Discrete-modulated continuous-variable quantum key distribution with homodyne detection is widely recognized for its ease of implementation, efficiency with respect to error correction, and its compatibility with modern optical communication devices. However, recent studies report that the application of homodyne detection obtains poor tolerance to excess noise and insufficient transmission distance, hence seriously restricting the large-scale deployment of quantum secure communication networks. In this paper, we propose a homodyne detection protocol using the quadrature phase shift keying technique. By limiting information leakage, our proposed protocol enhances excess noise tolerance to a high level. Furthermore, we demonstrate that homodyne detection performs better than heterodyne detection in quaternary-modulated continuous-variable quantum key distribution under the untrusted detector noise scenario. The security is analyzed using the tight numerical method against collective attacks in the asymptotic regime. Our results imply that the current protocol can distribute keys in nearly intercity area and, thus, paves the way for constructing low-cost quantum secure communication networks.