We propose entanglement negativity as a fine-grained probe of measurement-induced criticality. We motivate this proposal in stabilizer states, where for two disjoint subregions, comparing their “mutual negativity” and their mutual information leads to a precise distinction between bipartite and multipartite entanglement. In a measurement-only stabilizer circuit that maps exactly to two-dimensional critical percolation, we show that the mutual information and the mutual negativity are governed by boundary conformal fields of different scaling dimensions at long distances. We then consider a class of “hybrid” circuit models obtained by perturbing the measurement-only circuit with unitary gates of progressive levels of complexity. While other critical exponents vary appreciably for different choices of unitary gate ensembles at their respective critical points, the mutual negativity has scaling dimension $3$ across remarkably many of the hybrid circuits, which is notably different from that in percolation. We contrast our results with limiting cases where a geometrical minimal-cut picture is available.

One of the major application areas of interest for both near-term and fault-tolerant quantum computers is the optimization of classical objective functions. In this work, we develop intuitive constructions for a large class of these algorithms based on connections to simple dynamics of quantum systems, quantum walks, and classical continuous relaxations. We focus on developing a language and tools connected with kinetic energy on a graph for understanding the physical mechanisms of success and failure to guide algorithmic improvement. This physical language, in combination with uniqueness results related to unitarity, allow us to identify some potential pitfalls from kinetic energy fundamentally opposing the goal of optimization. This is connected to effects from wavefunction confinement, phase randomization, and shadow defects lurking in the objective far away from the ideal solution. As an example, we explore the surprising deficiency of many quantum methods in solving uncoupled spin problems and how this is both predictive of performance on some more complex systems while immediately suggesting simple resolutions. Further examination of canonical problems like the Hamming ramp or bush of implications show that entanglement can be strictly detrimental to performance results from the underlying mechanism of solution in approaches like the quantum approximate optimization algorithm (QAOA). Kinetic energy and graph Laplacian perspectives provide new insights to common initialization and optimal solutions in QAOA as well as new methods for more effective layerwise training. Connections to classical methods of continuous extensions, homotopy methods, and iterated rounding suggest new directions for research in quantum optimization. Throughout, we unveil many pitfalls and mechanisms in quantum optimization using a physical perspective, which aim to spur the development of novel quantum optimization algorithms and refinements.

Preparing and measuring physical systems are the operational building blocks of any physical experiment, and to describe them is the first purpose of any physical theory. Remarkably, even when only uncharacterized preparation and measurement devices are present, it is sometimes possible to distinguish between the behaviors of quantum and classical systems from only observational data. Certifying the physical origin of measurement statistics in the prepare and measure scenario is of primal importance for developing quantum networks, distributing quantum keys, and certifying randomness, to mention a few applications, but, surprisingly, no general methods to do so are known. We progress on this problem by crafting a general, sufficient condition to certify that a given set of preparations can only generate classical statistics, for any number of generalized measurements. As an application, we employ the method to demonstrate nonclassicality activation in the prepare and measure scenario, also considering its application in random access codes. Following that, we adapt our method to certify, again through a sufficient condition, whether a given set of measurements can never give rise to nonclassical behaviors, irrespective of what preparations they may act upon. This, in turn, allows us to find a large set of incompatible measurements that cannot be used to demonstrate nonclassicality, thus showing incompatibility is not sufficient for nonclassicality in the prepare and measure scenario.

Recent years have enjoyed an overwhelming interest in quantum thermodynamics, a field of research aimed at understanding thermodynamic tasks performed in the quantum regime. Further progress, however, seems to be obstructed by the lack of experimental implementations of thermal machines in which quantum effects play a decisive role. In this work, we introduce a blueprint of quantum field machines, which—once experimentally realized—would fill this gap. Even though the concept of the QFM presented here is very general and can be implemented in any many-body quantum system that can be described by a quantum field theory. We provide here a detailed proposal of how to realize a quantum machine in one-dimensional ultracold atomic gases, which consists of a set of modular operations giving rise to a piston. These can then be coupled sequentially to thermal baths, with the innovation that a quantum field takes up the role of the working fluid. In particular, we propose models for compression on the system to use it as a piston, and coupling to a bath that gives rise to a valve controlling heat flow. These models are derived within Bogoliubov theory, which allows us to study the operational primitives numerically in an efficient way. By composing the numerically modeled operational primitives we design complete quantum thermodynamic cycles that are shown to enable cooling and hence giving rise to a quantum field refrigerator. The active cooling achieved in this way can operate in regimes where existing cooling methods become ineffective. We describe the consequences of operating the machine at the quantum level and give an outlook of how this work serves as a road map to explore open questions in quantum information, quantum thermodynamic, and the study of non-Markovian quantum dynamics.

Magnetic fields break time-reversal symmetry, which is leveraged in many settings to enable the nonreciprocal behavior of light. This is the core physics of circulators and other elements used in a variety of microwave and optical settings. Commercial circulators in the microwave domain typically use ferromagnetic materials and wave interference, requiring large devices and large fields. However, quantum information devices for sensing and computation require small sizes, lower fields, and better on-chip integration. Equivalences to ferromagnetic order—such as the $XY$ model—can be realized at much lower magnetic fields by use of arrays of superconducting islands connected by Josephson junctions. Here we show that the quantum-coherent motion of a single vortex in such an array suffices to induce nonreciprocal behavior, enabling a small-scale, moderate-bandwidth, and low insertion loss circulator at very low magnetic fields and at microwave frequencies relevant for experiments with qubits.

The field of classical stochastic processes forms a major branch of mathematics. Stochastic processes are, of course, also very well studied in biology, chemistry, ecology, geology, finance, physics, and many more fields of natural and social sciences. When it comes to quantum stochastic processes, however, the topic is plagued with pathological issues that have led to fierce debates amongst researchers. Recent developments have begun to untangle these issues and paved the way for generalizing the theory of classical stochastic processes to the quantum domain without ambiguities. This tutorial details the structure of quantum stochastic processes, in terms of the modern language of quantum combs, and is aimed at students in quantum physics and quantum-information theory. We begin with the basics of classical stochastic processes and generalize the same ideas to the quantum domain. Along the way, we discuss the subtle structure of quantum physics that has led to troubles in forming an overarching theory for quantum stochastic processes. We close the tutorial by laying out many exciting problems that lie ahead in this branch of science.

A universal programmable quantum processor uses “program” quantum states to apply an arbitrary quantum channel to an input state. We generalize the concept of a finite-dimensional programmable quantum processor to infinite dimension assuming an energy constraint on the input and output of the target quantum channels. By proving reductions to and from finite-dimensional processors, we obtain upper and lower bounds on the program dimension required to approximately implement energy-limited quantum channels. In particular, we consider the implementation of Gaussian channels. Due to their practical relevance, we investigate the resource requirements for gauge-covariant Gaussian channels. Additionally, we give upper and lower bounds on the program dimension of a processor implementing all Gaussian unitary channels. These lower bounds rely on a direct information-theoretic argument, based on the generalization from finite to infinite dimension of a certain “replication lemma” for unitaries.

We propose a general-purpose, self-adaptive approach to construct a variational wave-function ansatz for highly accurate quantum dynamics simulations based on McLachlan’s variational principle. The key idea is to dynamically expand the variational ansatz along the time-evolution path such that the “McLachlan distance”, which is a measure of the simulation accuracy, remains below a set threshold. We apply this adaptive variational quantum dynamics simulation (AVQDS) approach to the integrable Lieb-Schultz-Mattis spin chain and the nonintegrable mixed-field Ising model, where it captures both finite-rate and sudden post-quench dynamics with high fidelity. The AVQDS quantum circuits that prepare the time-evolved state are much shallower than those obtained from first-order Trotterization and contain up to 2 orders of magnitude fewer cnot gate operations. We envision that a wide range of dynamical simulations of quantum many-body systems on near-term quantum-computing devices will be made possible through the AVQDS framework.

Shortcuts to adiabaticity is a general method for speeding up adiabatic quantum protocols, and has many potential applications in quantum information processing. Unfortunately, analytically constructing shortcuts to adiabaticity for systems having complex interactions and more than a few levels is a challenging task. This is usually overcome by assuming an idealized Hamiltonian [e.g., only a limited subset of energy levels are retained, and the rotating-wave approximation (RWA) is made]. Here we develop an analytic approach that allows one to go beyond these limitations. Our method is general and results in analytically derived pulse shapes that correct both nonadiabatic errors and non-RWA errors. We also show that our approach can yield pulses requiring a smaller driving power than conventional nonadiabatic protocols. We show in detail how our ideas can be used to analytically design high-fidelity single-qubit “tripod” gates in a realistic superconducting fluxonium qubit.

We describe quantum circuits with only $\tilde{\mathcal{O}}(N)$ Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of $N$ arbitrary (e.g., molecular) orbitals. With $\mathcal{O}(\lambda /ϵ)$ repetitions of these circuits one can use phase estimation to sample in the molecular eigenbasis, where $\lambda$ is the 1-norm of Hamiltonian coefficients and $ϵ$ is the target precision. This is the lowest complexity shown for quantum computations of chemistry within an arbitrary basis. Furthermore, up to logarithmic factors, this matches the scaling of the most efficient prior block encodings that can work only with orthogonal-basis functions diagonalizing the Coloumb operator (e.g., the plane-wave dual basis). Our key insight is to factorize the Hamiltonian using a method known as tensor hypercontraction (THC) and then to transform the Coulomb operator into an isospectral diagonal form with a nonorthogonal basis defined by the THC factors. We then use qubitization to simulate the nonorthogonal THC Hamiltonian, in a fashion that avoids most complications of the nonorthogonal basis. We also reanalyze and reduce the cost of several of the best prior algorithms for these simulations in order to facilitate a clear comparison to the present work. In addition to having lower asymptotic scaling space-time volume, compilation of our algorithm for challenging finite-sized molecules such as FeMoCo reveals that our method requires the least fault-tolerant resources of any known approach. By laying out and optimizing the surface-code resources required of our approach we show that FeMoCo can be simulated using about four million physical qubits and under 4 days of runtime, assuming 1-$\mu \mathrm{s}$ cycle times and physical gate-error rates no worse than $0.1\mathrm{\%}$.

Controlling the energy of unauthorized light signals in a quantum cryptosystem is an essential criterion for implementation security. Here, we propose a passive optical power limiter device based on thermo-optical defocusing effects, providing a reliable power limiting threshold that can be readily adjusted to suit various quantum applications. In addition, the device is robust against a wide variety of signal variations (e.g., wavelength, pulse width), which is important for implementation security. We experimentally show that the proposed device does not compromise quantum communication signals. It only has a minimal impact (if not, negligible impact) on the intensity, phase, or polarization degrees of freedom of the photons, thus making it suitable for general communication purposes. To show its practical utility for quantum cryptography, we demonstrate and discuss three potential applications: (1) measurement-device-independent quantum key distribution with enhanced security against a general class of Trojan-horse attacks, (2) using the power limiter as a countermeasure against bright illumination attacks, and (3) the application of power limiters to potentially enhance the implementation security of plug-and-play quantum key distribution.

The energy-time uncertainty relation puts a fundamental limit on the precision of lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity (through Doppler frequency shifts) of a target are inversely related to each other and are dictated by the bandwidth of the signal. Here, we use the theoretical toolbox of multiparameter quantum metrology to determine the ultimate precision of the simultaneous estimation of range and velocity. We consider the case of a single target as well as a pair of closely separated targets. In the latter case, we focus on the relative position and velocity. We show that the tradeoff between the estimation precision of position and velocity is relaxed for entangled probe states and is completely lifted in the limit of perfect photon time-frequency correlations. In the regime where the two targets are close to each other, the relative position and velocity can be estimated nearly optimally and jointly, even without entanglement, using the measurements determined by the symmetric logarithmic derivatives.

We present generalized adiabatic theorems for closed and open quantum systems that can be applied to slow modulations of rapidly varying fields, such as oscillatory fields that occur in optical experiments and light-induced processes. The generalized adiabatic theorems show that a sufficiently slow modulation conserves the dynamical modes of time-dependent reference Hamiltonians. In the limiting case of modulations of static fields, the standard adiabatic theorems are recovered. Applying these results to periodic fields shows that they remain in Floquet states rather than in energy eigenstates. More generally, these adiabatic theorems can be applied to transformations of arbitrary time-dependent fields, by accounting for the rapidly varying part of the field through the dynamical normal modes, and treating the slow modulation adiabatically. As examples, we apply the generalized theorem to (a) predict the dynamics of a two-level system driven by a frequency-modulated resonant oscillation, a pathological situation beyond the applicability of traditional adiabatic theorems, and (b) to show that open quantum systems driven by slowly turned-on incoherent light, such as biomolecules under natural illumination conditions, can display only coherences that survive in the steady state.

We present a new hybrid quantum-classical algorithm for optimizing unitary coupled-cluster (UCC) wave functions deemed the projective quantum eigensolver (PQE), amenable to near-term noisy quantum hardware. Contrary to variational quantum algorithms, PQE optimizes a trial state using residuals (projections of the Schrödinger equation) rather than energy gradients. We show that the residuals may be evaluated by simply measuring two energy expectation values per element. We also introduce a selected variant of PQE (SPQE) that uses an adaptive ansatz built from arbitrary-order particle-hole operators, offering an alternative to gradient-based selection procedures. PQE and SPQE are tested on a set of molecular systems covering both the weak and strong correlation regimes, including hydrogen clusters with four to ten atoms and the ${\mathrm{Be}\mathrm{H}}_2$ molecule. When employing a fixed ansatz, we find that PQE can converge disentangled (factorized) UCC wave functions to essentially identical energies as variational optimization while requiring fewer computational resources. A comparison of SPQE and adaptive variational quantum algorithms shows that—for ansätze containing the same number of parameters—the two methods yield results of comparable accuracy. Finally, we show that for a target energy accuracy, SPQE provides a parameterization of similar size or more concise than the one obtained via selected configuration interaction and the density matrix renormalization group on one- to three-dimensional strongly correlated ${\mathrm{H}}_{10}$ systems in terms of number of variational parameters.

We introduce the task of random-receiver quantum communication, in which a sender transmits a quantum message to a receiver selected from a list of $n$ spatially separated parties. At the moment of transmission, the choice of receiver is unknown to the sender. Later, it becomes known to the $n$ parties, who coordinate their actions by exchanging classical messages. In normal conditions, random-receiver quantum communication requires a noiseless quantum communication channel between the sender and each of the $n$ receivers. In contrast, we show that random-receiver quantum communication can take place through noisy, entanglement-breaking channels if the order of such channels is coherently controlled by a quantum bit that is accessible through measurements. While this phenomenon is achieved with a single control qubit, it cannot be mimicked by adding a noiseless qubit channel from the sender to any of the receivers, or more generally, from the sender to any subset of $k<n$ parties.

Computational physics is an important tool for analyzing, verifying, and—at times—replacing physical experiments. Nevertheless, simulating quantum systems and analyzing quantum data has so far resisted an efficient classical treatment in full generality. While programmable quantum systems have been developed to address this challenge, the resources required for classically intractable problems still lie beyond our reach. In this work, we consider a new target for quantum-simulation algorithms; analyzing the data arising from physics experiments—specifically, muon-spectroscopy experiments. These experiments can be used to probe the quantum interactions present in condensed-matter systems. However, fully analyzing their results can require classical computational resources scaling exponentially with the simulated system size, which can limit our understanding of the studied system. We show that this task may be a natural fit for the coming generations of quantum computers. We use classical emulations of our quantum algorithm on systems of up to 29 qubits to analyze real experimental data, and to estimate both the near-term and error-corrected resources required for our proposal. We find that our algorithm exhibits good noise resilience, stemming from our desire to extract global parameters from a fitted curve, rather than targeting any individual data point. In some respects, our fault tolerant resource estimates go further than some prior work in quantum simulation, by estimating the resources required to solve a complete task, rather than just to run a given circuit. Taking the overhead of observable measurement and calculating multiple datapoints into account, we find that significant challenges still remain if our algorithm is to become practical for analyzing muon-spectroscopy data.

We use a metalearning neural-network approach to analyze data from a measured quantum state. Once our neural network has been trained, it can be used to efficiently sample measurements of the state in measurement bases not contained in the training data. These samples can be used to calculate expectation values and other useful quantities. We refer to this process as “state sample tomography.” We encode the state’s measurement outcome distributions using an efficiently parameterized generative neural network. This allows each stage in the tomography process to be performed efficiently even for large systems. Our scheme is demonstrated on recent IBM Quantum devices, producing a model for a six-qubit state’s measurement outcomes with a predictive accuracy (classical fidelity) greater than $95\mathrm{\%}$ for all test cases using only 100 random measurement settings as opposed to the 729 settings required for standard full tomography using local measurements. This reduction in the required number of measurements scales favorably, with training data in 200 measurement settings, yielding a predictive accuracy greater than $92\mathrm{\%}$ for a ten-qubit state where 59 049 settings are typically required for full local measurement-based quantum state tomography. A reduction in the number of measurements by a factor, in this case, of almost 600 could allow for estimations of expectation values and state fidelities in practicable times on current quantum devices.

Nuclear spins show long coherence times and are well isolated from the environment, which are properties making them promising for quantum information applications. Here, we present a method for nuclear spin readout by probing the transmission of a microwave resonator. We consider a single electron in a silicon quantum dot-donor device interacting with a microwave resonator via the electric dipole coupling and subjected to a homogeneous magnetic field and a transverse magnetic field gradient. In our scenario, the electron spin interacts with a ${}^{31}\mathrm{P}$ defect nuclear spin via the hyperfine interaction. We theoretically investigate the influence of the $\mathrm{P}$ nuclear spin state on the microwave transmission through the cavity and show that nuclear spin readout is feasible with current state-of-the-art devices. Moreover, we identify optimal readout points with strong signal contrast to facilitate the experimental implementation of nuclear spin readout. Furthermore, we investigate the potential for achieving coherent excitation exchange between a nuclear spin qubit and cavity photons.

Self-testing is a method of quantum state and measurement estimation that does not rely on assumptions about the inner working of the devices used. Its experimental realization has been limited to sources producing single quantum states so far. In this work, we experimentally implement two significant building blocks of a quantum network involving two independent sources: namely, a parallel configuration, in which two parties share two copies of a state, and a tripartite configuration, where a central node shares two independent states with peripheral nodes. Then, by extending previous self-testing techniques, we provide device-independent lower bounds on the fidelity between the generated states and an ideal target made by the tensor product of two maximally entangled two-qubit states. Given its scalability and versatility, this technique can find application in the certification of larger networks of different topologies for quantum communication and cryptography tasks and randomness generation protocols.

The Gottesman-Kitaev-Preskill (GKP) code was proposed in 2001 by Daniel Gottesman, Alexei Kitaev, and John Preskill as a way to encode a qubit in an oscillator. The GKP codewords are coherent superpositions of periodically displaced squeezed vacuum states. Because of the challenge of merely preparing the codewords, the GKP code was for a long time considered to be impractical. However, the remarkable developments in quantum hardware and control technology in the last two decades has made the GKP code a frontrunner in the race to build practical, fault-tolerant bosonic quantum technology. In this Perspective, we provide an overview of the GKP code with emphasis on its implementation in the circuit-QED architecture and present our outlook on the challenges and opportunities for scaling it up for hardware-efficient, fault-tolerant quantum error correction.