Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the dynamics of thermalization. While contemporary methods in quantum chaos often rely on random ensembles of quantum states and Hamiltonians, this is not reflective of most real-world systems. In this paper, we introduce a new perspective: across a wide range of examples, a single nonrandom quantum state is shown to encode universal and highly random quantum state ensembles. We characterize these ensembles using the notion of quantum state $k$-designs from quantum information theory and investigate their universality using a combination of analytic and numerical techniques. In particular, we establish that $k$-designs emerge naturally from generic states in a Hilbert space as well as physical states associated with strongly interacting Hamiltonian dynamics. Our results offer a new approach for studying quantum chaos and provide a practical method for sampling approximately uniformly random states; the latter has wide-ranging applications in quantum information science from tomography to benchmarking.

Quantum error correction is crucial for any quantum computing platform to achieve truly scalable quantum computation. The surface code and its variants have been considered the most promising quantum error correction scheme due to their high threshold, low overhead, and relatively simple structure that can naturally be implemented in many existing qubit architectures, such as superconducting qubits. The recent development of Floquet codes by Hastings and Haah offers another promising approach. By going beyond the usual paradigm of stabilizer codes, Floquet codes achieve similar performance while being constructed entirely from two-qubit measurements. This makes them particularly suitable for platforms where two-qubit measurements can be implemented directly, such as the measurement-only topological qubits based on Majorana zero modes (MZMs) proposed by Karzig et al. Here, we explain how two variants of Floquet codes can be implemented on MZM-based architectures without any auxiliary qubits for syndrome measurement and with shallow syndrome-extraction sequences. We then numerically demonstrate their favorable performance. In particular, we show that they improve the threshold for scalable quantum computation in MZM-based systems by an order of magnitude and significantly reduce space and time overheads below threshold.

The impressive progress in quantum hardware of the last years has raised the interest of the quantum computing community in harvesting the computational power of such devices. However, in the absence of error correction, these devices can only reliably implement very shallow circuits or comparatively deeper circuits at the expense of a nontrivial density of errors. In this work, we obtain extremely tight limitation bounds for standard noisy intermediate-scale quantum proposals in both the noisy and noiseless regimes, with or without error-mitigation tools. The bounds limit the performance of both circuit model algorithms, such as the quantum approximate optimization algorithm, and also continuous-time algorithms, such as quantum annealing. In the noisy regime with local depolarizing noise $p$, we prove that at depths $L=\mathcal{O}(p^{-1})$ it is exponentially unlikely that the outcome of a noisy quantum circuit outperforms efficient classical algorithms for combinatorial optimization problems like max-cut. Although previous results already showed that classical algorithms outperform noisy quantum circuits at constant depth, these results only held for the expectation value of the output. Our results are based on newly developed quantum entropic and concentration inequalities, which constitute a homogeneous toolkit of theoretical methods from the quantum theory of optimal mass transport whose potential usefulness goes beyond the study of variational quantum algorithms.

Intense laser-matter interactions are at the center of interest in research and technology since the development of high-power lasers. They have been widely used for fundamental studies in atomic, molecular, and optical physics, and they are at the core of attosecond physics and ultrafast optoelectronics. Although the majority of these studies have been successfully described using classical electromagnetic fields, recent investigations based on fully quantized approaches have shown that intense laser-atom interactions can be used for the generation of controllable high-photon-number entangled coherent states and coherent state superpositions. In this tutorial, we provide a comprehensive fully quantized description of intense laser-atom interactions. We elaborate on the processes of high-harmonic generation, above-threshold ionization, and we discuss new phenomena that cannot be revealed within the context of semiclassical theories. We provide the description for conditioning the light field on different electronic processes, and their consequences for quantum state engineering of light. Finally, we discuss the extension of the approach to more complex materials, and the impact to quantum technologies for a new photonic platform composed of the symbiosis of attosecond physics and quantum information science.

High-dimensional entangled quantum states improve the performance of quantum technologies compared to qubit-based approaches. In particular, they enable quantum communications with higher information capacities or enhanced imaging protocols. However, the presence of optical disorder such as atmospheric turbulence or biological tissue perturbs quantum state propagation and hinders their practical use. Here, we demonstrate a wavefront shaping approach to transmit high-dimensional spatially entangled photon pairs through scattering media. Using a transmission matrix approach, we perform wave-front correction in the classical domain using an intense classical beam as a beacon to compensate for the disturbances suffered by a copropagating beam of entangled photons. Through violation of an Einstein-Podolski-Rosen criterion by 988$\sigma$, we show the presence of entanglement after the medium. Furthermore, we certify an entanglement dimensionality of 17. This work paves the way toward manipulation and transport of entanglement through scattering media, with potential applications in quantum microscopy and quantum key distribution.

Recent work has demonstrated that high-threshold quantum error correction is possible for biased-noise qubits, provided that one can implement a controlled-sc not ($\mathrm{CX}$) gate that preserves the bias. Bias-preserving $\mathrm{CX}$ gates have been proposed for several biased-noise qubit platforms, most notably Kerr cats. However, experimentally measuring the noise bias is challenging, as it requires accurately estimating certain low-probability Pauli errors in the presence of much larger state-preparation-and-measurement (SPAM) errors. In this paper, we introduce bias-randomized benchmarking (BRB) as a technique for measuring bias in quantum gates. BRB, like all RB protocols, is highly accurate and immune to SPAM errors. Our first protocol, $\mathrm{CX}$-dihedral BRB, is a straightforward method to measure the bias of the entire $\mathrm{CX}$-dihedral group. Our second protocol, interleaved-bias randomized benchmarking (IBRB), is a generalization of interleaved RB tailored to the experimental constraints of biased-noise qubits; this is a more involved procedure that directly targets the bias of the $\mathrm{CX}$ gate alone. Our BRB procedures occupy a middle ground between classic RB protocols that only estimate the average fidelity and tomographic RB protocols that provide more detailed characterization of noise but require more measurements as well as experimental capabilities that are not necessarily available in biased-noise qubits.

One-way nonreciprocal interactions between two quantum systems are typically described by a cascaded quantum master equation, and rely on an effective breaking of time-reversal symmetry (TRS) as well as the balancing of coherent and dissipative interactions. Here, we present a new approach for obtaining nonreciprocal quantum interactions that is completely distinct from cascaded quantum systems, and that does not in general require broken TRS. Our method relies on a local gauge symmetry present in any Markovian Lindblad master equation. This new kind of quantum nonreciprocity has many implications, including a new mechanism for performing dissipative steady-state unitary gate operations on a target quantum system. We also introduce a new, extremely general quantum-information-based metric for quantifying quantum nonreciprocity.

The preparation and computation of many properties of quantum Gibbs states is essential for algorithms such as quantum semidefinite programming and quantum Boltzmann machines. We propose a quantum algorithm that can predict $M$ linear functions of an arbitrary Gibbs state with only $\mathcal{O}(\log M)$ experimental measurements. Our main insight is that for sufficiently large systems we do not need to prepare the $n$-qubit mixed Gibbs state explicitly but, instead, we can evolve a random $n$-qubit pure state in imaginary time. The result then follows by constructing classical shadows of these random pure states. We propose a quantum circuit that implements this algorithm by using quantum signal processing for the imaginary time evolution. We numerically verify the efficiency of the algorithm by simulating the circuit for a ten-spin-1/2 XXZ-Heisenberg model. In addition, we show that the algorithm can be successfully employed as a subroutine for training an eight-qubit fully connected quantum Boltzmann machine.

A topological defect network (TDN) is formed by a network of topological defects embedded within a topological quantum field theory (TQFT). TDNs were introduced recently for the purpose of describing fracton topological phases of matter using the framework of defect TQFT. Their effectiveness has been demonstrated through numerous examples, yet a systematic construction was lacking. Here we solve this problem by formulating a method to construct TDNs for a wide range of lattice Hamiltonians. Our method takes a lattice Hamiltonian as input, applies an ungauging procedure, then creates a refined lattice within each unit cell, followed by regauging the system to produce a TDN as output. For topological Calderbank-Shor-Steane (CSS) Pauli stabilizer models, this procedure is guaranteed to produce a phase-equivalent TDN. This provides TDN representations of canonical fracton models for which no such construction was previously known, including Haah’s cubic code and Yoshida’s infinite family of fractal spin liquid models. We demonstrate the applicability of our method beyond CSS stabilizer models by constructing TDNs for non-CSS models including Chamon’s model and the semionic $X$-cube model.

Mitigating errors in quantum information processing devices is especially important in the absence of fault tolerance. An effective method in suppressing state-preparation errors is using multiple copies to distill the ideal component from a noisy quantum state. Here, we use classical shadows and randomized measurements to circumvent the need for coherent access to multiple copies at an exponential cost. We study the scaling of resources using numerical simulations and find that the overhead is still favorable compared to full state tomography. We optimize measurement resources under realistic experimental constraints and apply our method to an experiment preparing a Greenberger-Horne-Zeilinger state with trapped ions. In addition to improving stabilizer measurements, the analysis of the improved results reveals the nature of errors affecting the experiment. Hence, our results provide a directly applicable method for mitigating errors in near-term quantum computers.

The trapped-ion quantum simulator has demonstrated qualitative properties of different physical models for up to tens of ions. In particular, a linear ion chain naturally hosts long-range Ising interactions under the laser driving, which has been used for various phenomena, such as quantum phase transition, localization, thermalization, and information propagation. For near-term practical usage, a central task is to find more quantitative applications of the noisy quantum simulators that are robust to small errors in the parameters. Here we report the quantum simulation of a long-range transverse-field Ising model using up to 61 ions and probe the critical behavior of its quantum phase transition through the Kibble-Zurek mechanism. By calibrating and verifying the coupling coefficients, we realize the same model for increasing ion numbers, so as to extract a critical exponent free of the finite-size effect. For ferromagnetic interaction, our experimental result agrees with the previous numerical prediction. As for the antiferromagnetic case, signals are too weak to fit a critical exponent due to the frustration in the interaction, but still consistent with the theory.

Nonstabilizerness or magic resource characterizes the amount of non-Clifford operations needed to prepare quantum states. It is a crucial resource for quantum computing and a necessary condition for quantum advantage. However, quantifying magic resource beyond a few qubits has been a major challenge. Here, we introduce efficient measures of magic resource for pure quantum states with a sampling cost that is independent of the number of qubits. Our method uses Bell measurements over two copies of a state, which we implement in experiment together with a cost-free error-mitigation scheme. We show the transition of classically simulable stabilizer states into intractable quantum states on the IonQ quantum computer. For applications, we efficiently distinguish stabilizer and nonstabilizer states with low measurement cost even in the presence of experimental noise. Further, we propose a variational quantum algorithm to maximize our measure via the shift rule. Our algorithm can be free of barren plateaus even for highly expressible variational circuits. Finally, we experimentally demonstrate a Bell-measurement protocol for the stabilizer Rényi entropy as well as the Wallach-Meyer entanglement measure. Our results pave the way to understanding the nonclassical power of quantum computers, quantum simulators, and quantum many-body systems.

The trading of fidelity for scale enables approximate classical simulators such as matrix product states (MPSs) to run quantum circuits beyond exact methods. A control parameter, the so-called bond dimension $\chi$ for MPSs, governs the allocated computational resources and the output fidelity. Here, we characterize the fidelity for the quantum approximate optimization algorithm by the expectation value of the cost function that it seeks to minimize and find that it follows a scaling law $\mathcal{F}(\ln \chi /N)$, where $N$ is the number of qubits. With $\ln \chi$ amounting to the entanglement that a MPS can encode, we show that the relevant variable for investigating the fidelity is the entanglement per qubit. Importantly, our results calibrate the classical computational power required to achieve the desired fidelity and benchmark the performance of quantum hardware in a realistic setup. For instance, we quantify the hardness of performing better classically than a noisy superconducting quantum processor by readily matching its output to the scaling function. Moreover, we relate the global fidelity to that of individual operations and establish its relationship with $\chi$ and $N$. We sharpen the requirements for noisy quantum computers to outperform classical techniques at running a quantum optimization algorithm in speed, size, and fidelity.

Designing the spatial profile of the superconducting gap—gap engineering—has long been recognized as an effective way of controlling quasiparticles in superconducting devices. In aluminum films, their thickness modulates the gap; therefore, standard fabrication of $\mathrm{Al}$/$\mathrm{Al}\mathrm{O}$${}_x$/$\mathrm{Al}$ Josephson junctions, which relies on overlapping a thicker film on top of a thinner one, always results in gap-engineered devices. Here, we reconsider quasiparticle effects in superconducting qubits to explicitly account for the unavoidable asymmetry in the gap on the two sides of a Josephson junction. We find that different regimes can be encountered in which the quasiparticles have either similar densities in the two junction leads or are largely confined to the lower-gap lead. Qualitatively, for similar densities the qubit excited-state population is lower but its relaxation rate is higher than when the quasiparticles are confined; therefore, there is a potential trade-off between two desirable properties in a qubit.

The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback (“adaptive circuits”) can evade such restrictions. We introduce three classes of local adaptive circuits that enable low-depth preparation of long-range entangled quantum matter characterized by gapped topological orders and conformal field theories (CFTs). The three classes are inspired by distinct physical insights, including tensor-network constructions, the multiscale entanglement renormalization ansatz, and parton constructions. A large class of topological orders, including chiral topological order, can be prepared in constant depth or time, and one-dimensional CFT states and non-Abelian topological orders with both solvable and nonsolvable groups can be prepared in depth scaling logarithmically with system size. We also build on a recently discovered correspondence between symmetry-protected topological phases and long-range entanglement to derive efficient protocols for preparing symmetry-enriched topological order and arbitrary Calderbank-Shor-Steane codes. Our work illustrates the practical and conceptual versatility of measurement for state preparation.

Long coherence times, large anharmonicity, and robust charge-noise insensitivity render fluxonium qubits an interesting alternative to transmons. Recent experiments have demonstrated record coherence times for low-frequency fluxonium qubits. Here, we propose a galvanic coupling scheme with flux-tunable $\mathit{\text{XX}}$ coupling. To implement a high-fidelity entangling $\sqrt{i\mathrm{SWAP}}$ gate, we modulate the strength of this coupling and devise variable-time identity gates to synchronize required single-qubit operations. Both types of gates are implemented using strong ac flux drives, lasting for only a few drive periods. We employ a theoretical framework capable of capturing qubit dynamics beyond the rotating-wave approximation as required for such strong drives. We predict an open-system fidelity of $F>0.999$ for the $\sqrt{i\mathrm{SWAP}}$ gate under realistic conditions.

Pauli-spin-blockade (PSB) measurements have so far achieved the highest fidelity of spin readout in semiconductor quantum dots, overcoming the 99% threshold. Moreover, in contrast to energy-selective readout, PSB is less error prone to thermal energy, an important feature for large-scale architectures that could be operated at temperatures above a few hundreds of millikelvins. In this work, we use rf reflectometry on a single-lead quantum dot to perform charge sensing and to probe the spin state of a double quantum dot at 0.5 K. At this relatively elevated temperature, we characterize both singlet-triplet and parity readout, which are complementary measurements to perform a complete readout of a two-spin system. We demonstrate high-fidelity spin readout with an average fidelity above 99.9 % for a readout time of 20 µs and 99 % for 4 µs. Finally, we succeed in initializing a singlet state in a single dot with a fidelity higher than 99 % and separate the two electrons while retaining the same spin state with a 95.6 % fidelity.

Heat engines usually operate by exchanging heat with thermal baths at different (positive) temperatures. Nonthermal baths may, however, lead to a significant performance boost. Here, we experimentally analyze the power output of a single-atom quantum Otto engine realized in the quasispin states of individual cesium atoms interacting with an atomic rubidium bath. From measured time-resolved populations of the quasispin state, we determine the dynamics during the cycle of both the effective spin temperature and of the quantum fluctuations of the engine, which we quantify with the help of the Shannon entropy. We find that power is enhanced in the negative-temperature regime and that it reaches its maximum value at half the maximum entropy. Quantitatively, operating our engine at negative effective temperatures increases the power by up to $30\mathrm{\%}$ compared to operation at positive temperatures, including the case of infinite temperature. At the same time, entering the negative-temperature regime allows for reducing the entropy to values close to zero, offering highly stable operation at high power output. We further numerically investigate the influence of the size of the Hilbert space on the performance of the quantum engine by varying the number of levels of the working medium. Our work thereby demonstrates control of a multilevel single-atom quantum engine interacting with a realistic atomic bath having many degrees of freedom.

As quantum computers with large numbers of qubits become increasingly available, experiments executed on a given device may not utilize all available qubits. In this case, the outcome of executing a quantum program will depend on the ability to efficiently select a subset of high-performing physical qubits. For any given quantum program and device there are many ways to assign physical qubits for execution of the program, and assignments will differ in performance due to the variability in quality across qubits and entangling operations on a single device. Evaluating the performance of each assignment using fidelity estimation introduces significant experimental overhead and will be infeasible for many applications, while relying on standard device benchmarks provides incomplete information about the performance of any specific program. Furthermore, the number of possible assignments grows combinatorially in the number of qubits on the device and in the program, motivating the use of heuristic optimization techniques. We demonstrate a practical solution to the problem of qubit assignment by using simulated annealing with a cost function based on the Loschmidt echo, a diagnostic that measures the reversibility of a quantum process. We provide theoretical justification for this choice of cost function by demonstrating that the optimal qubit assignment coincides with the optimal qubit assignment based on state fidelity in the weak error limit, and we provide experimental justification using diagnostics performed on Google’s superconducting qubit devices. We then establish the performance of simulated annealing for qubit assignment using classical simulations of noisy devices as well as optimization experiments performed on a quantum processor. Our results demonstrate that the use of Loschmidt echoes and simulated annealing provides a scalable and flexible approach to optimizing qubit assignment on near-term hardware.

Parasitic two-level-system (TLS) defects are one of the major factors limiting the coherence times of superconducting qubits. Although there has been significant progress in characterizing basic parameters of TLS defects, exact mechanisms of interactions between a qubit and various types of TLS defects remained largely unexplored due to the lack of experimental techniques able to probe the form of qubit-defect couplings. Here we present an experimental method of TLS defect spectroscopy using a strong qubit drive that allowed us to distinguish between various types of qubit-defect interactions. By applying this method to a capacitively shunted flux qubit, we detected a rare type of TLS defect with a nonlinear qubit-defect coupling due to critical-current fluctuations, as well as conventional TLS defects with a linear coupling to the qubit caused by charge fluctuations. The presented approach could become the routine method for high-frequency defect inspection and quality control in superconducting qubit fabrication, providing essential feedback for fabrication process optimization. The reported method is a powerful tool to uniquely identify the type of noise fluctuations caused by TLS defects, enabling the development of realistic noise models relevant to noisy intermediate-scale quantum computing and fault-tolerant quantum control.