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.

Entangled-photon pairs are an essential resource for quantum-information technologies. Chip-scale sources of entangled pairs have been integrated with various photonic platforms, including silicon, nitrides, indium phosphide, and lithium niobate, but each has fundamental limitations that restrict the photon-pair brightness and quality, including weak optical nonlinearity or high waveguide loss. Here, we demonstrate a novel ultralow-loss $\mathrm{Al}\mathrm{Ga}\mathrm{As}$-on-insulator platform capable of generating time-energy entangled photons in a $Q>1$ million microring resonator with nearly 1000-fold improvement in brightness compared to existing sources. The waveguide-integrated source exhibits an internal generation rate greater than $20\times {10}^9$ pairs ${\mathrm{s}}^{-1}{\mathrm{mW}}^{-2}$, emits near 1550 nm, produces heralded single photons with $>99\mathrm{\%}$ purity, and violates Bell’s inequality by more than 40 standard deviations with visibility $>97\mathrm{\%}$. Combined with the high optical nonlinearity and optical gain of $\mathrm{Al}\mathrm{Ga}\mathrm{As}$ for active component integration, these are all essential features for a scalable quantum photonic platform.

In this perspective we discuss verification of quantum devices in the context of specific examples formulated as proposed experiments. Our first example is verification of analog quantum simulators as Hamiltonian learning, where the input Hamiltonian as the design goal is compared with the parent Hamiltonian for the quantum states prepared on the device. The second example discusses cross-device verification on the quantum level (i.e., by comparing quantum states prepared on different quantum devices). We focus in particular on protocols using randomized measurements, and we propose establishing a central data repository, where existing experimental devices and platforms can be compared. In our final example, we address verification of the output of a quantum device from a computer science perspective, addressing the question of how a user of a quantum processor can be certain of the correctness of its output, and propose minimal demonstrations on present-day devices.

Recently implemented quantum devices such as quantum processors and quantum simulators combine highly complicated quantum dynamics with high-resolution measurements. We present a passivity deformation methodology that sets constraints on the evolution of such quantum devices. The approach yields bounds that are often tighter, and thus more predictive, than the quantum microscopic analogue of the second law of thermodynamics. In particular, (i) it yields tight bounds even when the environment is microscopic; (ii) it successfully handles the ultracold limit; (iii) it enables one to account for constrained dynamics; and (iv) it bounds observables that do not appear in the second law of thermodynamics. Furthermore, this framework provides insights into nonthermal environments, correlated environments, coarse graining in microscopic setups, and the ability to detect heat leaks. Our findings can be explored and used in physical setups such as trapped ions, superconducting circuits, neutral atoms in optical lattices, and more.

Oblivious transfer is an important primitive in modern cryptography. Applications include secure multiparty computation, oblivious sampling, $e$-voting, and signatures. Information-theoretically secure perfect 1-out-of 2 oblivious transfer is impossible to achieve. Imperfect variants, where both participants’ ability to cheat is still limited, are possible using quantum means while remaining classically impossible. Precisely what security parameters are attainable remains unknown. We introduce a theoretical framework for studying semirandom quantum oblivious transfer, which is shown to be equivalent to regular oblivious transfer in terms of cheating probabilities. We then use it to derive bounds on cheating. We also present a protocol with lower cheating probabilities than previous schemes, together with its optical realization. We show that a lower bound of $\frac{2}{3}$ on the minimum achievable cheating probability can be directly derived for semirandom protocols using a different method and definition of cheating than used previously. The lower bound increases from $\frac{2}{3}$ to approximately $0.749$ if the states output by the protocol are pure and symmetric. The oblivious transfer scheme we present uses unambiguous state elimination measurements and can be implemented with the same technological requirements as standard quantum cryptography. In particular, it does not require honest participants to prepare or measure entangled states. The cheating probabilities are $\frac{3}{4}$ and approximately 0.729 for sender and receiver, respectively, which is lower than in existing protocols. Using a photonic testbed, we have implemented the protocol with honest parties, as well as optimal cheating strategies. Because of the asymmetry of the receiver’s and sender’s cheating probabilities, the protocol can be combined with a “trivial” protocol to achieve an overall protocol with lower average cheating probabilities of approximately 0.74 for both sender and receiver. This demonstrates that, interestingly, protocols where the final output states are pure and symmetric are not optimal in terms of average cheating probability.

We study $\mathrm{SU}(2{)}_k$ anyon models, assessing their prospects for topological quantum computation. In particular, we compare the Ising ($k=2$) anyon and Fibonacci ($k=3$) anyon models, motivated by their potential for future realizations based on Majorana fermion quasiparticles or exotic fractional quantum Hall states, respectively. The quantum computational performance of the different anyon models is quantified at the single-qubit level by the difference between a target unitary operator and its approximation realized by anyon braiding. To facilitate efficient comparisons, we develop a Monte Carlo enhanced Solovay-Kitaev quantum compiler algorithm that finds near-optimal braid words in polynomial time from the exponentially large search tree. Since universal quantum computation cannot be achieved within the Ising anyon model by braiding alone, we introduce an additional elementary phase gate to model a nontopological measurement process, which restores universality of the anyon model at the cost of breaking the full topological protection. We model conventional kinds of decoherence processes algorithmically by introducing a controllable noise term to all nontopological gate operations. We find that, for reasonable levels of decoherence, even the hybrid Ising anyon model retains a significant topological advantage over a conventional, nontopological, quantum computer. Furthermore, we find that only surprisingly short anyon braids are ever required to be compiled due to the gate noise exceeding the intrinsic error of the braid words already for word lengths of the order of 100 elementary braids. We conclude that the future for hybrid topological quantum computation remains promising.

We propose a quantum-classical hybrid algorithm of the power method, here dubbed as the quantum power method, to evaluate ${\hat{\mathcal{H}}}^n|\psi ⟩$ with quantum computers, where $n$ is a non-negative integer, $\hat{\mathcal{H}}$ is a time-independent Hamiltonian of interest, and $|\psi ⟩$ is a quantum state. We show that the number of gates required for approximating ${\hat{\mathcal{H}}}^n$ scales linearly in the power and the number of qubits, making it a promising application for near-term quantum computers. Using numerical simulation, we show that the power method can control systematic errors in approximating the Hamiltonian power ${\hat{\mathcal{H}}}^n$ for $n$ as large as 100. As an application, we combine our method with a multireference Krylov-subspace-diagonalization scheme to show how one can improve the estimation of ground-state energies and the ground-state fidelities found using a variational-quantum-eigensolver scheme. Finally, we outline other applications of the quantum power method, including several moment-based methods. We numerically demonstrate the connected-moment expansion for the imaginary-time evolution and compare the results with the multireference Krylov-subspace diagonalization.

Quantum enhanced receivers are endowed with resources to achieve higher sensitivities than conventional technologies. For application in optical communications, they provide improved discriminatory capabilities for multiple nonorthogonal quantum states. In this work, we propose and experimentally demonstrate a new decoding scheme for quadrature phase-shift encoded signals. Our receiver surpasses the standard quantum limit and outperforms all previously known nonadaptive detectors at low input powers. Unlike existing approaches, the receiver only exploits linear optical elements and on-off photodetection. This circumvents the requirement for challenging feed-forward operations that limit communication transmission rates and can be readily implemented with current technology.

To make precise the sense in which the operational predictions of quantum theory conflict with a classical worldview, it is necessary to articulate a notion of classicality within an operational framework. A widely applicable notion of classicality of this sort is whether or not the predictions of a given operational theory can be explained by a generalized-noncontextual ontological model. We here explore what notion of classicality this implies for the generalized probabilistic theory (GPT) that arises from a given operational theory, focusing on prepare-measure scenarios. We first show that, when mapping an operational theory to a GPT by quotienting relative to operational equivalences, the constraint of explainability by a generalized-noncontextual ontological model is mapped to the constraint of explainability by an ontological model. We then show that, under the additional assumption that the ontic state space is of finite cardinality, this constraint on the GPT can be expressed as a geometric condition which we term simplex embeddability. Whereas the traditional notion of classicality for a GPT is that its state space be a simplex and its effect space be the dual of this simplex, simplex embeddability merely requires that its state space be embeddable in a simplex and its effect space in the dual of that simplex. We argue that simplex embeddability constitutes an intuitive and freestanding notion of classicality for GPTs. Our result also has applications to witnessing nonclassicality in prepare-measure experiments.

Generalized contextuality refers to our inability of explaining measurement statistics using a context-independent probabilistic and ontological model. On the other hand, measurement statistics can also be modeled using the framework of general probabilistic theories (GPTs). Here, starting from a construction of GPTs based on a Gleason-type theorem, we fully characterize these structures with respect to their permission and rejection of generalized (non)contextual ontological models. It follows that in any GPT construction the three insistence of (i) the no-restriction hypothesis, (ii) the ontological noncontextuality, and (iii) multiple nonrefinable measurements for any fixed number of outcomes are incompatible. Hence, any GPT satisfying the no-restriction hypothesis is ontologically noncontextual if and only if it is simplicial. We give a detailed discussion of GPTs for which the no-restriction hypothesis is violated, and show that they can always be considered as subtheories (subGPTs) of GPTs satisfying the hypothesis. It is shown that subGPTs are ontologically noncontextual if and only if they are subtheories of simplicial GPTs of the same dimensionality. Finally, we establish as a corollary the necessary and sufficient condition for a single resourceful measurement or state to promote an ontologically noncontextual (i.e., classical) general probabilistic theory to an ontologically contextual (i.e., nonclassical) one under the no-restriction hypothesis.

Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behavior to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the National Science Foundation workshop on “Programmable Quantum Simulators,” that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multidisciplinary collaborations with resources for quantum simulator software, hardware, and education.This document is a summary from a U.S. National Science Foundation supported workshop held on 16–17 September 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum simulators over the next 2–5 years.

Just as “classical” information technology rests on a foundation built of interconnected information-processing systems, quantum information technology (QIT) must do the same. A critical component of such systems is the “interconnect,” a device or process that allows transfer of information between disparate physical media, for example, semiconductor electronics, individual atoms, light pulses in optical fiber, or microwave fields. While interconnects have been well engineered for decades in the realm of classical information technology, quantum interconnects (QuICs) present special challenges, as they must allow the transfer of fragile quantum states between different physical parts or degrees of freedom of the system. The diversity of QIT platforms (superconducting, atomic, solid-state color center, optical, etc.) that will form a “quantum internet” poses additional challenges. As quantum systems scale to larger size, the quantum interconnect bottleneck is imminent, and is emerging as a grand challenge for QIT. For these reasons, it is the position of the community represented by participants of the NSF workshop on “Quantum Interconnects” that accelerating QuIC research is crucial for sustained development of a national quantum science and technology program. Given the diversity of QIT platforms, materials used, applications, and infrastructure required, a convergent research program including partnership between academia, industry, and national laboratories is required.

The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by codesigning full-stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, a sampling of a few use case studies, and significant challenges for the development of quantum computers for science over the next 2–10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21–22, 2019 in Alexandria, VA.

Characterizing the quantum complexity of local random quantum circuits is a very deep problem with implications to the seemingly disparate fields of quantum information theory, quantum many-body physics, and high-energy physics. While our theoretical understanding of these systems has progressed in recent years, numerical approaches for studying these models remains severely limited. In this paper, we discuss a special class of numerically tractable quantum circuits, known as quantum automaton circuits, which may be particularly well suited for this task. These are circuits that preserve the computational basis, yet can produce highly entangled output wave functions. Using ideas from quantum complexity theory, especially those concerning unitary designs, we argue that automaton wave functions have high quantum state complexity. We look at a wide variety of metrics, including measurements of the output bit-string distribution and characterization of the generalized entanglement properties of the quantum state, and find that automaton wave functions closely approximate the behavior of fully Haar random states. In addition to this, we identify the generalized out-of-time ordered $2k$-point correlation functions as a particularly useful probe of complexity in automaton circuits. Using these correlators, we are able to numerically study the growth of complexity well beyond the scrambling time for very large systems. As a result, we are able to present evidence of a linear growth of design complexity in local quantum circuits, consistent with conjectures from quantum information theory.

Quantum algorithms have been successfully applied to provide computational speed ups to various machine-learning tasks and methods. A notable exception to this has been deep reinforcement learning (RL). Deep RL combines the power of deep neural networks with reinforcement learning, and has provided some of the most impressive recent artificial-intelligence (AI) results including the famous AlphaGo system—yet, no possibilities for quantum advantages have been identified to date. In this work, we show how quantum computers can enhance the performance of deep RL, especially where the action spaces are large. Specifically, we introduce so-called deep energy-based models, inspired by statistical physics, which we show outperform standard deep RL machinery in learning performance. These models are computationally more demanding, but this can be ameliorated by quantum techniques. Specifically, we provide quantum algorithms, some of which can be run on near-term quantum computers, that can be used to speed up deep energy-based RL. This result opens up a new playing field for quantum enhancements in machine learning and AI.