Quantum metrology promises unprecedented measurement precision but suffers in practice from the limited availability of resources such as the number of probes, their coherence time, or nonclassical quantum states. The adaptive Bayesian approach to parameter estimation allows an efficient use of resources because of adaptive experiment design. For its practical success, fast numerical solutions for the Bayesian update and the adaptive experiment design are crucial. Here we show that neural networks can be trained to become fast and strong experiment-design heuristics using a combination of an evolutionary strategy and reinforcement learning. Neural-network heuristics are shown to outperform established heuristics for the technologically important example of frequency estimation of a qubit that suffers from dephasing. Our method of creating neural-network heuristics is very general and complements the well-studied sequential Monte Carlo method for Bayesian updates to form a complete framework for adaptive Bayesian quantum estimation.

Many experiments in the field of quantum foundations seek to adjudicate between quantum theory and speculative alternatives to it. This requires one to analyze the experimental data in a manner that does not presume the correctness of the quantum formalism. The mathematical framework of generalized probabilistic theories (GPTs) provides a means of doing so. We present a scheme for determining which GPTs are consistent with a given set of experimental data. It proceeds by performing tomography on the preparations and measurements in a self-consistent manner, i.e., without presuming a prior characterization of either. We illustrate the scheme by analyzing experimental data for a large set of preparations and measurements on the polarization degree of freedom of a single photon. We first test various hypotheses for the dimension of the GPT vector space for this degree of freedom. Our analysis identifies the most plausible hypothesis to be dimension 4, which is the value predicted by quantum theory. Under this hypothesis, we can draw the following additional conclusions from our scheme: (i) that the smallest and largest GPT state spaces that could describe photon polarization are a pair of polytopes, each approximating the shape of the Bloch sphere and having a volume ratio of $0.977\pm 0.001$, which provides a quantitative bound on the scope for deviations from the state and effect spaces predicted by quantum theory, and (ii) that the maximal violation of the Clauser, Horne, Shimony, and Holt inequality can be at most $1.3\mathrm{\%}\pm 0.1$ greater than the maximum violation allowed by quantum theory, and the maximal violation of a particular inequality for universal noncontextuality can not differ from the quantum prediction by more than this factor on either side. The only possibility for a greater deviation from the quantum state and effect spaces or for greater degrees of supraquantum nonlocality or contextuality, according to our analysis, is if a future experiment (perhaps following the scheme developed here) discovers that additional dimensions of GPT vector space are required to describe photon polarization, in excess of the four dimensions predicted by quantum theory to be adequate to the task.

Although entanglement is necessary for observing nonlocality in a Bell experiment, there are entangled states that can never be used to demonstrate nonlocal correlations. In a seminal paper Buscemi [Phys. Rev. Lett. 108, 200401 (2012)] extended the standard Bell experiment by allowing Alice and Bob to be asked quantum, instead of classical, questions. This gives rise to a broader notion of nonlocality, one which can be observed for every entangled state. In this work we study a resource theory of this type of nonlocality referred to as Buscemi nonlocality. We propose a geometric quantifier measuring the ability of a given state and local measurements to produce Buscemi nonlocal correlations and prove the following results. First, we show that any distributed measurement that can demonstrate Buscemi nonlocal correlations provides strictly better performance than any distributed measurement that does not use entanglement in the task of distributed state discrimination, and that this advantage is quantified by the geometric quantifier we propose, thus establishing its operational significance. Second, we prove a quantitative relationship between Buscemi nonlocality, the ability to perform nonclassical teleportation, and entanglement. In particular, we show that the maximal amount of Buscemi nonlocality that can be generated using a given state is precisely equal to its entanglement content. Using this relationship, we propose new discrimination tasks for which nonclassical teleportation and entanglement lead to an advantage over their classical counterparts. Third, we interpret Buscemi nonlocality from the perspective of information theory and show that it is related to a single-shot capacity of a quantum-to-classical bipartite channel.

Silicon spin qubits are promising candidates for realizing large-scale quantum processors, benefitting from a magnetically quiet host material and the prospects of leveraging the mature silicon device fabrication industry. We report the measurement of an electron spin in a singly occupied gate-defined quantum dot, fabricated using CMOS-compatible processes at the 300-mm wafer scale. For readout, we employ spin-dependent tunneling combined with a low-footprint single-lead quantum-dot charge sensor, measured using rf gate reflectometry. We demonstrate spin readout in two devices using this technique, obtaining valley splittings in the range 0.5–0.7 meV using excited-state spectroscopy, and measure a maximum electron-spin relaxation time ($T_1$) of $9\pm 3$ s at 1 T. These long lifetimes indicate the silicon-nanowire geometry and fabrication processes employed here show a great deal of promise for qubit devices, while the spin-readout method demonstrated here is well suited to a variety of scalable architectures.

A quantum many-body system whose dynamics includes local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions (MPTs) and also to entanglement transitions in random tensor networks. Many of our results are for “all-to-all” quantum circuits with unitaries and measurements, in which any qubit can couple to any other, and related settings where some of the complications of low-dimensional models are reduced. We also propose field-theory descriptions for spatially local systems of any finite dimensionality. To build intuition, we first solve the simplest “minimal cut” toy model for entanglement dynamics in all-to-all circuits, finding scaling forms and exponents within this approximation. We then show that certain all-to-all measurement circuits allow exact results by exploiting local treelike structure in the circuit geometry. For this reason, we make a detour to give general universal results for entanglement phase transitions in a class of random tree tensor networks with bond dimension 2, making a connection with the classical theory of directed polymers on a tree. We then compare these results with numerics in all-to-all circuits, both for the MPT and for the simpler “forced-measurement phase transition” (FMPT). We characterize the two different phases in all-to-all circuits using observables that are sensitive to the amount of information that is propagated between the initial and final time. We demonstrate signatures of the two phases that can be understood from simple models. Finally we propose Landau-Ginsburg-Wilson-like field theories for the measurement phase transition, the forced-measurement phase transition, and for entanglement transitions in random tensor networks. This analysis shows a surprising difference between the measurement phase transition and the other cases. We discuss variants of the measurement problem with additional structure (for example free-fermion structure), and questions for the future.

In this perspective we discuss conditions under which it would be possible for a modest fault-tolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best classical alternative. The challenge is that the computation must finish within a reasonable amount of time while being difficult enough that the small quantum scaling advantage would compensate for the large constant factor overheads associated with error correction. We compute several examples of such runtimes using state-of-the-art surface code constructions under a variety of assumptions. We conclude that quadratic speedups will not enable quantum advantage on early generations of such fault-tolerant devices unless there is a significant improvement in how we realize quantum error correction. While this conclusion persists even if we were to increase the rate of logical gates in the surface code by more than an order of magnitude, we also repeat this analysis for speedups by other polynomial degrees and find that quartic speedups look significantly more practical.

Randomized benchmarking (RB) is a powerful method for determining the error rate of experimental quantum gates. Traditional RB, however, is restricted to gatesets, such as the Clifford group, that form a unitary 2-design. The recently introduced character RB can benchmark more general gates using techniques from representation theory; up to now, however, this method has only been applied to “multiplicity-free” groups, a mathematical restriction on these groups. In this paper, we extend the original character RB derivation to explicitly treat non-multiplicity-free groups, and derive several applications. First, we derive a rigorous version of the recently introduced subspace RB, which seeks to characterize a set of one- and two-qubit gates that are symmetric under swap. Second, we develop a new leakage RB protocol that applies to more general groups of gates. Finally, we derive a scalable RB protocol for the matchgate group, a group that like the Clifford group is nonuniversal but becomes universal with the addition of one additional gate. This example provides one of the few examples of a scalable non-Clifford RB protocol. In all three cases, compared to existing theories, our method requires similar resources, but either provides a more accurate estimate of gate fidelity, or applies to a more general group of gates. In conclusion, we discuss the potential, and challenges, of using non-multiplicity-free character RB to develop new classes of scalable RB protocols and methods of characterizing specific gates.

Despite being at the heart of the theory of the “Big Bang” and cosmic inflation, the quantum-field-theory prediction of false vacuum tunneling has not been tested. To address the exponential complexity of the problem, a table-top quantum simulator in the form of an engineered Bose-Einstein condensate (BEC) has been proposed to give dynamical solutions of the quantum-field equations. In this paper, we give a numerical feasibility study of the BEC quantum simulator under realistic conditions and temperatures, with an approximate truncated Wigner phase-space method. We report the observation of false vacuum tunneling in these simulations, and the formation of multiple bubble “universes” with distinct topological properties. The tunneling gives a transition of the relative phase of coupled Bose fields from a metastable to a stable “vacuum.” We include finite-temperature effects that would be found in a laboratory experiment and also analyze the cutoff dependence of modulational instabilities in Floquet space. Our numerical phase-space model does not use thin-wall approximations, which are inapplicable to cosmologically interesting models. It is expected to give the correct quantum treatment, including superpositions and entanglement during dynamics. By analyzing a nonlocal observable called the topological phase entropy (TPE), our simulations provide information about phase structure in the true vacuum. We observe a cooperative effect in which true vacua bubbles representing distinct universes each have one or the other of two distinct topologies. The TPE initially increases with time, reaching a peak as multiple universes are formed, and then decreases with time to the phase-ordered vacuum state. This gives a model for the formation of universes with one of two distinct phases, which is a possible solution to the problem of particle-antiparticle asymmetry.

We design and implement a quantum annealing simulation platform to observe and study dynamical processes in quantum field theory (QFT). Our approach encodes the field theory as an Ising model, which is then solved by a quantum annealer. As a proof of concept, we encode a scalar field theory and measure the probability for it to tunnel from the false vacuum to the true vacuum for various tunneling times, vacuum displacements, and potential profiles. The results are in accord with those predicted theoretically, showing that a quantum annealer is a promising platform for encoding QFTs. This is the first time it has been possible to measure instanton processes across a freely chosen QFT energy barrier. We argue that this novel and flexible method to study the dynamics of quantum systems has potential application to many field theories of interest. Measurements of the dynamical behavior of such encoded field theories are independent of theoretical calculations and can be used to infer their properties without being limited by the availability of suitable perturbative or nonperturbative computational methods. Soon, measurements using such a quantum annealing simulation platform could therefore be used to improve theoretical and computational methods conceptually and may enable the measurement and detailed study of previously unobserved quantum phenomena.

The strong spin-orbit coupling in hole spin qubits enables fast and electrically tunable gates, but at the same time enhances the susceptibility of the qubit to charge noise. Suppressing this noise is a significant challenge in semiconductor quantum computing. Here, we show theoretically that hole $\mathrm{Si}$ fin field-effect transistors (FinFETs) are not only very compatible with modern CMOS technology, but they present operational sweet spots where the charge noise is completely removed. The presence of these sweet spots is a result of the interplay between the anisotropy of the material and the triangular shape of the FinFET cross section, and it does not require an extreme fine-tuning of the electrostatics of the device. We present how the sweet spots appear in FinFETs grown along different crystallographic axes and we study in detail how the behavior of these devices changes when the cross-section area and aspect ratio are varied. We identify designs that maximize the qubit performance and could pave the way towards a scalable spin-based quantum computer.

We study the time-fluctuating magnetic gradient noise mechanisms in pairs of $\mathrm{Si}$/$\mathrm{Si}\mathrm{Ge}$ quantum dots using exchange echo noise spectroscopy. We find through a combination of spectral inversion and correspondence to theoretical modeling that quadrupolar precession of the ${}^{73}\mathrm{Ge}$ nuclei play a key role in the spin-echo decay time $T_2$, with a characteristic dependence on the magnetic field and the width of the $\mathrm{Si}$ quantum well. The ${}^{73}\mathrm{Ge}$ noise peaks appear at the fundamental and first harmonic of the ${}^{73}\mathrm{Ge}$ Larmor resonance, superimposed over $1/f$ noise due to ${}^{29}\mathrm{Si}$ dipole-dipole dynamics, and are dependent on material epitaxy and the applied magnetic field. These results may inform the needs of dynamical decoupling when using $\mathrm{Si}$/$\mathrm{Si}\mathrm{Ge}$ quantum dots as qubits in quantum information processing devices.

The number of measurements demanded by hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) is prohibitively high for many problems of practical value. For such problems, realizing quantum advantage will require methods that dramatically reduce this cost. Previous quantum algorithms that reduce the measurement cost (e.g., quantum amplitude and phase estimation) require error rates that are too low for near-term implementation. Here we propose methods that take advantage of the available quantum coherence to maximally enhance the power of sampling on noisy quantum devices, reducing the measurement number and runtime compared to the standard sampling method of the VQE. Our scheme derives inspiration from quantum metrology, phase estimation, and the more recent “alpha-VQE” proposal, arriving at a general formulation that is robust to error and does not require ancilla qubits. The central object of this method is what we call the “engineered likelihood function” (ELF), used for carrying out Bayesian inference. We show how the ELF formalism enhances the rate of information gain in sampling as the physical hardware transitions from the regime of noisy intermediate-scale quantum computers to that of quantum error–corrected ones. This technique speeds up a central component of many quantum algorithms, with applications including chemistry, materials, finance, and beyond. Similar to the VQE, we expect small-scale implementations to be realizable on today’s quantum devices.

Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by establishing precise connections with a family of magic monotones. Our first simulator introduces a new class of quasiprobability distributions and connects its runtime to a generalized notion of negativity. We prove that this algorithm has significantly improved exponential scaling compared to all prior quasiprobability simulators for qubits. Our second simulator is a new variant of the stabilizer-rank simulation algorithm, extended to work with mixed states and with significantly improved runtime bounds. Our third simulator trades precision for speed by discarding negative quasiprobabilities. We connect each algorithm’s performance to a corresponding magic monotone and, by comprehensively characterizing the monotones, we obtain a precise understanding of the simulation runtime and error bounds. Our analysis reveals a deep connection between all three seemingly unrelated simulation techniques and their associated monotones. For tensor products of single-qubit states, we prove that our monotones are all equal to each other, multiplicative and efficiently computable, allowing us to make clear-cut comparisons of the simulators’ performance scaling. Furthermore, our monotones establish several asymptotic and nonasymptotic bounds on state interconversion and distillation rates. Beyond the theory of magic states, our classical simulators can be adapted to other resource theories under certain axioms, which we demonstrate through an explicit application to the theory of quantum coherence.

We develop a universal approximation for the Renyi entropies of a pure state at late times in a nonintegrable many-body system, which macroscopically resembles an equilibrium density matrix. The resulting expressions are fully determined by properties of the associated equilibrium density matrix, and are hence independent of the details of the initial state, while also being manifestly consistent with unitary time evolution. For equilibrated pure states in gravity systems, such as those involving black holes, this approximation gives a prescription for calculating entanglement entropies using Euclidean path integrals, which is consistent with unitarity and hence can be used to address the information loss paradox of Hawking. Applied to recent models of evaporating black holes and eternal black holes coupled to baths, it provides a derivation of replica wormholes, and elucidates their mathematical and physical origins. In particular, it shows that replica wormholes can arise in a system with a fixed Hamiltonian, without the need for ensemble averages.

The quantum Fisher information (QFI), as a function of quantum states, measures the amount of information that a quantum state carries about an unknown parameter. The (entanglement-assisted) QFI of a quantum channel is defined to be the maximum QFI of the output state assuming an entangled input state over a single probe and an ancilla. In quantum metrology, people are interested in calculating the QFI of $N$ identical copies of a quantum channel when $N\to \mathrm{\infty }$, which is called the asymptotic QFI. Over the years, researchers found various types of upper bounds of the asymptotic QFI, but they were proven achievable only in several specific situations. It was known that the asymptotic QFI of an arbitrary quantum channel grows either linearly or quadratically with $N$. Here we show that a simple criterion can determine whether the scaling is linear or quadratic. In both cases, the asymptotic QFI and a quantum error correction protocol to achieve it are computable via a semidefinite program. When the scaling is quadratic, the Heisenberg limit, a feature of noiseless quantum channels, is recovered. When the scaling is linear, we show that the asymptotic QFI is still in general larger than $N$ times the single-channel QFI and, furthermore, that sequential estimation strategies provide no advantage over parallel ones.

The current generation of noisy intermediate-scale quantum computers introduces new opportunities to study quantum many-body systems. In this paper, we show that quantum circuits can provide a dramatically more efficient representation than current classical numerics of the quantum states generated under nonequilibrium quantum dynamics. For quantum circuits, we perform both real- and imaginary-time evolution using an optimization algorithm that is feasible on near-term quantum computers. We benchmark the algorithms by finding the ground state and simulating a global quench of the transverse-field Ising model with a longitudinal field on a classical computer. Furthermore, we implement (classically optimized) gates on a quantum processing unit and demonstrate that our algorithm effectively captures real-time evolution.

The ability to perform gates in multiqubit systems that are robust to noise is of crucial importance for the advancement of quantum information technologies. However, finding control pulses that cancel noise while performing a gate is made difficult by the intractability of the time-dependent Schrödinger equation, especially in multiqubit systems. Here, we show that this issue can be sidestepped by using a formalism in which the cumulative error during a gate is represented geometrically as a curve in a multidimensional Euclidean space. Cancelation of noise errors to leading order corresponds to closure of the curve, a condition that can be satisfied without solving the Schrödinger equation. We develop and uncover general properties of this geometric formalism, and derive a recursion relation that maps control fields to curvatures for Hamiltonians of arbitrary dimension. We demonstrate the utility of the formalism by employing it to design pulses that simultaneously correct against both noise errors and crosstalk for two qubits coupled by an Ising interaction. We give examples both of a single-qubit rotation and a two-qubit maximally entangling gate. The results obtained in this example are relevant to both superconducting transmon qubits and semiconductor quantum-dot spin qubits. We propose this geometric formalism as a general technique for pulse-induced error suppression in quantum computing gate operations.

Describing open quantum systems far from equilibrium is challenging, in particular when the environment is mesoscopic, when it develops nonequilibrium features during the evolution, or when memory effects cannot be disregarded. Here we derive a master equation that explicitly accounts for system-bath correlations and includes, at a coarse-grained level, a dynamically evolving bath. It applies to a wide variety of environments; for instance, those that can be described by random matrix theory or the eigenstate thermalization hypothesis. We obtain a local detailed balance condition that does not forbid the emergence of stable negative temperature states in unison with the definition of temperature through the Boltzmann entropy. We benchmark the master equation against the exact evolution and observe very good agreement in a situation where the conventional Born-Markov-secular master equation breaks down. The present description of the dynamics is robust and it remains accurate even if some of the assumptions are relaxed. Even though our master equation describes a dynamically evolving bath not described by a Gibbs state, we provide a consistent nonequilibrium thermodynamic framework and derive the first and second law as well as the Clausius inequality. Our work paves the way for studying a variety of nanoscale quantum technologies, including engines, refrigerators, and heat pumps, beyond the conventionally used assumption of a static thermal bath.

Encoding a qubit in logical quantum states with wave functions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. One of the most promising candidates for such a fully protected superconducting qubit is the $0$–$\pi$ circuit [Brooks et al., Phys. Rev. A 87, 052306 (2013)]. Here we realize the proposed circuit topology in an experimentally obtainable parameter regime, where the ground-state degeneracy is lifted but the qubit is still largely noise protected. More precisely, the logical states of this qubit feature disjoint support and are exponentially protected against relaxation and exponentially (first order) protected against dephasing due to charge (flux) noise. We name the resultant device the “soft $0$–$\pi$ qubit.” Multitone spectroscopy measurements reveal the energy-level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. Using a Raman-type protocol, we exploit a higher-lying charge-insensitive energy level of the device to realize coherent population transfer and logical operations. The measured relaxation ($T_1=1.6$ ms) and dephasing ($T_R=9\mu \mathrm{s}$, $T_{2E}=25\mu \mathrm{s}$) times demonstrate that the soft $0$–$\pi$ circuit not only broadens the family of superconducting qubits but also constitutes an important step toward quantum computing with intrinsically protected superconducting qubits.

There are well-developed theoretical tools to analyze how quantum dynamics can solve computational problems by varying Hamiltonian parameters slowly, near the adiabatic limit. On the other hand, there are relatively few tools to understand the opposite limit of rapid quenches, as used in quantum annealing and (in the limit of infinitely rapid quenches) in quantum walks. In this paper, we develop several tools that are applicable in the rapid-quench regime. Firstly, we analyze the energy expectation value of different elements of the Hamiltonian. From this, we show that monotonic quenches, where the strength of the problem Hamiltonian is consistently increased relative to fluctuation (driver) terms, will yield a better result on average than random guessing. Secondly, we develop methods to determine whether dynamics will occur locally under rapid-quench Hamiltonians and identify cases where a rapid quench will lead to a substantially improved solution. In particular, we find that a technique we refer to as “preannealing” can significantly improve the performance of quantum walks. We also show how these tools can provide efficient heuristic estimates for Hamiltonian parameters, a key requirement for practical application of quantum annealing.