Magnetic flux tunability is an essential feature in most approaches to quantum computing based on superconducting qubits. Independent control of the fluxes in multiple loops is hampered by crosstalk. Calibrating flux crosstalk becomes a challenging task when the circuit elements interact strongly. We present a novel approach to flux crosstalk calibration, which is circuit model independent and relies on an iterative process to gradually improve calibration accuracy. This method allows us to reduce errors due to the inductive coupling between loops. The calibration procedure is automated and implemented on devices consisting of tunable flux qubits and couplers with up to 27 control loops. We devise a method to characterize the calibration error, which is used to show that the errors of the measured crosstalk coefficients are all below 0.17%.

In low-dimensional systems, indistinguishable particles can display statistics that interpolate between bosons and fermions. Signatures of these “anyons” have been detected in two-dimensional quasiparticle excitations of the fractional quantum Hall effect, however experimental access to these quasiparticles remains limited. As an alternative to these “topological anyons,” we propose “statistical anyons” realized through a statistical mixture of particles with bosonic and fermionic symmetry. We show that the framework of statistical anyons is equivalent to the generalized exclusion statistics (GES) pioneered by Haldane, significantly broadening the range of systems to which GES apply. We develop the full thermodynamic characterizations of these statistical anyons, including both equilibrium and nonequilibrium behavior. To develop a complete picture, we compare the performance of quantum heat engines with working mediums of statistical anyons and traditional topological anyons, demonstrating the effects of the anyonic phase in both local equilibrium and fully nonequilibrium regimes. In addition, methods of optimizing engine performance through shortcuts to adiabaticity are investigated, using both linear response and fast-forward techniques.

Quantum-simulator hardware promises new insights into problems from particle and nuclear physics. A major challenge is to reproduce gauge invariance, as violations of this quintessential property of lattice gauge theories can have dramatic consequences, e.g., the generation of a photon mass in quantum electrodynamics. Here, we introduce an experimentally friendly method to protect gauge invariance in $\mathrm{U}(1)$ lattice gauge theories against coherent errors in a controllable way. Our method employs only single-body energy-penalty terms, thus enabling practical implementations. As we derive analytically, some sets of penalty coefficients render undesired gauge sectors inaccessible by unitary dynamics for exponentially long times. Further, for few-body error terms, we show numerically that this is achieved with resources exhibiting little dependence on system size. These findings constitute an exponential improvement over previously known results from energy-gap protection or perturbative treatments. In our method, the gauge-invariant subspace is protected by an emergent global symmetry, meaning it can be immediately applied to other symmetries. In our numerical benchmarks for continuous-time and digital quantum simulations, gauge protection holds for all calculated evolution times (up to $t>{10}^{10}/J$ for continuous time, with $J$ the relevant energy scale). Crucially, our gauge-protection technique is simpler to realize than the associated ideal gauge theory, and can thus be readily implemented in current ultracold-atom analog simulators as well as digital noisy intermediate-scale quantum devices.

We present a quantitative theory of the suppression of the optical linewidth due to charge fluctuation noise in a $p$-$n$ diode, recently observed by Anderson et al. [Science 366, 1225 (2019)]. We connect the local electric field with the voltage across the diode, allowing the identification of the defect depth from the experimental threshold voltage. Furthermore, we show that an accurate description of the decoherence of such spin centers requires a complete spin-1 formalism that yields a biexponential decoherence process, and predict how reduced charge fluctuation noise suppresses the spin center’s decoherence rate.

To harness the potential of noisy intermediate-scale quantum devices, it is paramount to find the best type of circuits to run hybrid quantum-classical algorithms. Key candidates are parametrized quantum circuits that can be effectively implemented on current devices. Here, we evaluate the capacity and trainability of these circuits using the geometric structure of the parameter space via the effective quantum dimension, which reveals the expressive power of circuits in general as well as of particular initialization strategies. We assess the expressive power of various popular circuit types and find striking differences depending on the type of entangling gates used. Particular circuits are characterized by scaling laws in their expressiveness. We identify a transition in the quantum geometry of the parameter space, which leads to a decay of the quantum natural gradient for deep circuits. For shallow circuits, the quantum natural gradient can be orders of magnitude larger in value compared to the regular gradient; however, both of them can suffer from vanishing gradients. By tuning a fixed set of circuit parameters to randomized ones, we find a region where the circuit is expressive but does not suffer from barren plateaus, hinting at a good way to initialize circuits. We show an algorithm that prunes redundant parameters of a circuit without affecting its effective dimension. Our results enhance the understanding of parametrized quantum circuits and can be immediately applied to improve variational quantum algorithms.

The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well approximated by matrix product states. In this work, we introduce a picture of generic states within the trivial phase of matter with respect to their nonequilibrium and entropic properties. We do so by rigorously exploring nontranslation-invariant matrix product states drawn from a local independent and identically distributed Haar measure. We arrive at these results by exploiting techniques for computing moments of random unitary matrices and by exploiting a mapping to partition functions of classical statistical models, a method that has lead to valuable insights on local random quantum circuits. Specifically, we prove that such disordered random matrix product states equilibrate exponentially well with overwhelming probability under the time evolution of Hamiltonians featuring a nondegenerate spectrum. Moreover, we prove two results about the entanglement Rényi entropy: the entropy with respect to sufficiently disconnected subsystems is generically extensive in the system size, and for small connected systems, the entropy is almost maximal for sufficiently large bond dimensions.

For scalable quantum communication and networks, a key step is to realize a quantum repeater node that can efficiently connect different segments of atom-photon entanglement using quantum memories. We report a compact and hardware-efficient realization of a quantum repeater node using a single atomic ensemble for multicell quantum memories. A millisecond lifetime is achieved for individual memory cells after suppressing the magnetic-field-induced inhomogeneous broadening and the atomic-motion-induced spin-wave dephasing. Based on these long-lived memory cells, we achieve heralded asynchronous entanglement generation in two quantum repeater segments one after another and then an on-demand entanglement connection of these two repeater segments. As another application of the multicell atomic quantum memory, we further demonstrate storage and on-demand retrieval of heralded atomic spin-wave qubits by implementing a random access quantum memory with individual addressing capacity. This work provides a promising constituent for efficient realization of quantum repeaters for large-scale quantum networks.

Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called “quantum low-density parity-check (LDPC) codes.” The codes we discuss are alternatives to the surface code, which is currently the leading candidate to implement quantum fault tolerance. We introduce the zoo of quantum LDPC codes and discuss their potential for making quantum computers robust with regard to noise. In particular, we explain recent advances in the theory of quantum LDPC codes related to certain product constructions and discuss open problems in the field.

In many physical approaches to quantum computation, error-correction schemes assume the ability to form two-dimensional qubit arrays with nearest-neighbor couplings and parallel operations at multiple qubit sites. While semiconductor spin qubits exhibit long coherence times relative to their operation speed and single-qubit fidelities above error correction thresholds, multiqubit operations in two-dimensional arrays have been limited by fabrication, operation, and readout challenges. We present a two-by-two array of four singlet-triplet qubits in gallium arsenide and show simultaneous coherent operations and four-qubit measurements via exchange oscillations and frequency-multiplexed single-shot measurements. A larger multielectron quantum dot is fabricated in the center of the array as a tunable interqubit link, which we utilize to demonstrate coherent spin exchange with selected qubits. Our techniques are extensible to other materials, indicating a path towards quantum processors with gate-controlled spin qubits.

Quantum simulation has wide applications in quantum chemistry and physics. Recently, scientists have begun exploring the use of randomized methods for accelerating quantum simulation. Among them, a simple and powerful technique, called qDRIFT, is known to generate random product formulas for which the average quantum channel approximates the ideal evolution. qDRIFT achieves a gate count that does not explicitly depend on the number of terms in the Hamiltonian, which contrasts with Suzuki formulas. This work aims to understand the origin of this speedup by comprehensively analyzing a single realization of the random product formula produced by qDRIFT. The main results prove that a typical realization of the randomized product formula approximates the ideal unitary evolution up to a small diamond-norm error. The gate complexity is already independent of the number of terms in the Hamiltonian, but it depends on the system size and the sum of the interaction strengths in the Hamiltonian. Remarkably, the same random evolution starting from an arbitrary, but fixed, input state yields a much shorter circuit suitable for that input state. In contrast, in deterministic settings, such an improvement usually requires initial state knowledge. The proofs depend on concentration inequalities for vector and matrix martingales, and the framework is applicable to other randomized product formulas. Our bounds are saturated by certain commuting Hamiltonians.

Practical quantum networking architectures are crucial for scaling the connection of quantum resources. Yet quantum network testbeds have thus far underutilized the full capabilities of modern lightwave communications, such as flexible-grid bandwidth allocation. In this work, we implement flex-grid entanglement distribution in a deployed network for the first time, connecting nodes in three distinct campus buildings time synchronized via the Global Positioning System. We quantify the quality of the distributed polarization entanglement via log-negativity, which offers a generic metric of link performance in entangled bits per second. After demonstrating successful entanglement distribution for two allocations of our eight dynamically reconfigurable channels, we realize the first deployed fiber network demonstration of remote state preparation (RSP), a fundamental quantum communications protocol with utility for performing remote private “blind” quantum computing. We further demonstrate RSP not only at one location but over three nodes in three locations. In general, our results highlight an advanced paradigm for managing entanglement resources in quantum networks of ever-increasing complexity and service demands.

We report on the efficient design of quantum optimal-control protocols to manipulate the motional states of an atomic Bose-Einstein condensate (BEC) in a one-dimensional optical lattice. Our protocols operate on the momentum comb associated with the lattice. In contrast to previous works also dealing with control in discrete and large Hilbert spaces, our control schemes allow us to reach a wide variety of targets by varying a single parameter, the lattice position. With this technique, we experimentally demonstrate a precise, robust, and versatile control: we optimize the transfer of the BEC to a single or multiple quantized momentum states with full control on the relative phase between the different momentum components. This also allows us to prepare the BEC in a given eigenstate of the lattice band structure, or superposition thereof.

With the development of delegated quantum computation, clients will want to ensure confidentiality of their data and algorithms and the integrity of their computations. While protocols for blind and verifiable quantum computation exist, they suffer from high overheads and from oversensitivity: when running on noisy devices, imperfections trigger the same detection mechanisms as malicious attacks, resulting in perpetually aborted computations. We introduce the first blind and verifiable protocol for delegating bounded-error quantum polynomial (BQP) computations to a powerful server, with repetition as the only overhead. It is composable and statistically secure with exponentially low bounds and can tolerate a constant amount of global noise.

Quantum phase estimation (QPE) is one of the most important subroutines in quantum computing. In general applications, current QPE algorithms either suffer an exponential time overload or require a set of—notoriously quite fragile—GHZ states. These limitations have so far prevented the demonstration of QPE beyond proof of principles. Here we propose a new QPE algorithm based on a cascade of Gaussian spin states (GSSs) and a suitable adaptive measurement protocol. GSSs are renownedly resilient and have been created experimentally in a variety of platforms, from hundreds of ions up to millions of cold and ultracold neutral atoms. We show that our protocol achieves a QPE sensitivity overcoming previous schemes, including that obtained with GHZ states, scales linearly with time, and is robust against certain sources of noise and decoherence, such as detection noise, in particular. Our work paves the way toward an efficient implementation of the QPE, as well as applications of atomic squeezed states for quantum computation.

Inspired by the idea that quantum computers can be useful in advancing basic science, we use a quantum processor to experimentally validate a number of theoretical results in non-equilibrium quantum thermodynamics, that were not (or were very little) corroborated so far. In order to do so, we first put forward a novel method to implement the so called two-point measurement scheme, which is at the basis of the study of nonequilibrium energetic exchanges in quantum systems. Like previously established methods, our method uses an ancillary system, but at variance with them, it provides direct access to the energy exchange statistics, and is, accordingly more effective, at least when applied to small quantum systems. Using a quantum computer as a remotely programmable experimental platform, we first validate our ancilla-assisted two-point measurement scheme, and then apply it to (i) experimentally verify that fluctuation theorems are robust against projective measurements, a theoretical prediction, which was not validated so far; (ii) experimentally verify the so-called heat-engine fluctuation relation, by implementing a swap quantum heat engine; (iii) experimentally verify that the heat-engine fluctuation relation holds for measurement-fueled quantum heat engines, by implementing the design at the basis of the so-called quantum-measurement-cooling concept. For both engines, we report the measured average heat and work exchanged and single out their operation mode. Our experiments constitute an experimental basis for the understanding of the nonequilibrium energetics of quantum computation and for the implementation of energy-management devices on quantum processors.

Precision magnetometry is fundamental to the development of novel magnetic materials and devices. Recently, the nitrogen-vacancy (NV) center in diamond has emerged as a promising probe for static magnetism in two-dimensional (2D) van der Waals materials, capable of quantitative imaging with nanoscale spatial resolution. However, the dynamic character of magnetism, crucial for understanding the magnetic phase transition and achieving technological applications, has rarely been experimentally accessible in single 2D crystals. Here, we coherently control the NV center’s spin precession to achieve ultrasensitive, quantitative ac susceptometry of a 2D ferromagnet. Combining dc hysteresis with ac susceptibility measurements varying temperature, field, and frequency, we illuminate the formation, mobility, and consolidation of magnetic domain walls in few-layer ${\mathrm{Cr}\mathrm{Br}}_3$. We show that domain wall mobility is enhanced in ultrathin ${\mathrm{Cr}\mathrm{Br}}_3$, with minimal decrease for excitation frequencies exceeding hundreds of kilohertz, and is influenced by the domain morphology and local pinning of the flake. Our technique extends NV magnetometry to the multifunctional ac and dc magnetic characterization of wide-ranging spintronic materials at the nanoscale.

Gaussian states have played an important role in the physics of continuous-variable quantum systems. They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description. Nevertheless, many proposed quantum technologies require us to go beyond the realm of Gaussian states and introduce non-Gaussian elements. In this Tutorial, we provide a roadmap for the physics of non-Gaussian quantum states. We introduce the phase-space representations as a framework to describe the different properties of quantum states in continuous-variable systems. We then use this framework in various ways to explore the structure of the state space. We explain how non-Gaussian states can be characterized not only through the negative values of their Wigner function, but also via other properties such as quantum non-Gaussianity and the related stellar rank. For multimode systems, we are naturally confronted with the question of how non-Gaussian properties behave with respect to quantum correlations. To answer this question, we first show how non-Gaussian states can be created by performing measurements on a subset of modes in a Gaussian state. Then, we highlight that these measured modes must be correlated via specific quantum correlations to the remainder of the system to create quantum non-Gaussian or Wigner-negative states. On the other hand, non-Gaussian operations are also shown to enhance or even create quantum correlations. Finally, we demonstrate that Wigner negativity is a requirement to violate Bell inequalities and to achieve a quantum computational advantage. At the end of the Tutorial, we also provide an overview of several experimental realizations of non-Gaussian quantum states in quantum optics and beyond.

Quantum Darwinism proposes that the proliferation of redundant information plays a major role in the emergence of objectivity out of the quantum world. Is this kind of objectivity necessarily classical? We show that if one takes Spekkens’s notion of noncontextuality as the notion of classicality and the approach of Brandão, Piani, and Horodecki to quantum Darwinism, the answer to the above question is “‘yes,” if the environment encodes the proliferated information sufficiently well. Moreover, we propose a threshold on this encoding, above which one can unambiguously say that classical objectivity has emerged under quantum Darwinism.

Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state. This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing. We analyze such processes in detail and establish a complexity transition between simulable and nonsimulable systems as a function of a tuning parameter. We determine important classes of simulable and nonsimulable two-body dissipation. Finally, we show how using resonant dissipation in cold atoms can enhance the performance of two-qubit gates.

Experiments performed on strongly interacting Rydberg atoms have revealed surprising persistent oscillations of local observables. These oscillations have been attributed to a special set of nonergodic states, referred to as quantum many-body scars. Although these states have enriched our understanding of thermalization in quantum systems, their interplay with disorder in realistic quantum simulators has remained unclear. We address this question by studying numerically and analytically the magnetization and spatiotemporal correlators of a scar model of disordered and interacting qubits that can be realized in present-day simulators. While the oscillation amplitudes of these observables decay with time as the disorder strength is increased, their oscillation frequency remains remarkably constant. This stability stems from resonances of the disordered spectrum in the overlap with the clean scar eigenstates that are approximately centered at the same scar energies of the clean system. We also find that multiple additional sets of scar resonances become accessible due to the presence of disorder and further enhance the oscillation amplitudes. Our results show the robustness of nonergodic dynamics in scar systems, and opens the door to understanding their behavior in near-term quantum devices and potentially using them as a resource in quantum-sensing protocols to calibrate quantum hardware.