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We characterize the set of ground states that can be synthesized by classical two-body Ising Hamiltonians. We then construct simple Ising planar blocks that simulate efficiently a universal set of logic gates and connections, and hence any Boolean function. We therefore provide a new method of encoding universal computation in the ground states of Ising lattices and a simpler alternative demonstration of the known fact that finding the ground state of a finite Ising spin glass model is NP complete. We relate this with our previous result about emergent properties in infinite lattices. [ABSTRACT FROM AUTHOR]

Quantifying how distinguishable two stochastic processes are is at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and ease of use. In this article, we suggest a set of requirements for a well-behaved measure of process distinguishability. Moreover, we propose a family of measures, called divergence rates, that satisfy all of these requirements. Focusing on a particular member of this family--the coemission divergence rate--we show that it can be computed efficiently, behaves qualitatively similar to other commonly used measures in their regimes of applicability, and remains well behaved in scenarios where other measures break down. [ABSTRACT FROM AUTHOR]

Stochastic processes are as ubiquitous throughout the quantitative sciences as they are notorious for being difficult to simulate and predict. In this Letter, we propose a unitary quantum simulator for discrete-time stochastic processes which requires less internal memory than any classical analogue throughout the simulation. The simulator's internal memory requirements equal those of the best previous quantum models. However, in contrast to previous models, it only requires a (small) finite-dimensional Hilbert space. Moreover, since the simulator operates unitarily throughout, it avoids any unnecessary information loss. We provide a stepwise construction for simulators for a large class of stochastic processes hence directly opening the possibility for experimental implementations with current platforms for quantum computation. The results are illustrated for an example process. [ABSTRACT FROM AUTHOR]

We consider one-dimensional Hamiltonian systems whose ground states display symmetry-protected topological order. We show that ground states within the topological phase cannot be connected with each other through local operations and classical communication between a bipartition of the system. Our claim is demonstrated by analyzing the entanglement spectrum and Rényi entropies of different physical systems that provide examples for symmetry-protected topological phases. Specifically, we consider the spin-1/2 cluster-Ising model and a class of spin-1 models undergoing quantum phase transitions to the Haldane phase. Our results provide a probe for symmetry-protected topological order. Since the picture holds even at the system's local scale, our analysis can serve as a local experimental test for topological order. [ABSTRACT FROM AUTHOR]

Deterministic quantum computation with one qubit (DQC1) is iconic in highlighting that exponential quantum speedup may be achieved with negligible entanglement. Its discovery catalyzed a heated study of general quantum resources, and various conjectures regarding their role in DQC1's performance advantage. Coherence and discord are prominent candidates, respectively, characterizing nonclassicality within localized and correlated systems. Here we realize DQC1 within a superconducting system, engineered such that the dynamics of coherence and discord can be tracked throughout its execution. We experimentally confirm that DQC1 acts as a resource converter, consuming coherence to generate discord during its operation. Our results highlight superconducting circuits as a promising platform for both realizing DQC1 and related algorithms, and experimentally characterizing resource dynamics within quantum protocols. [ABSTRACT FROM AUTHOR]

In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states (MPS) are known as a particularly efficient representation of 1D spin chains. In this Letter, we associate each stochastic process with a suitable quantum state of a spin chain. We then show that the optimal predictive model for the process leads directly to an MPS representation of the associated quantum state. Conversely, MPS methods offer a systematic construction of the best known quantum predictive models. This connection allows an improved method for computing the quantum memory needed for generating optimal predictions. We prove that this memory coincides with the entanglement of the associated spin chain across the past-future bipartition. [ABSTRACT FROM AUTHOR]

Many organisms capitalize on their ability to predict the environment to maximize available free energy and reinvest this energy to create new complex structures. This functionality relies on the manipulation of patterns--temporally ordered sequences of data. Here, we propose a framework to describe pattern manipulators--devices that convert thermodynamic work to patterns or vice versa--and use them to build a "pattern engine" that facilitates a thermodynamic cycle of pattern creation and consumption. We show that the least heat dissipation is achieved by the provably simplest devices, the ones that exhibit desired operational behavior while maintaining the least internal memory. We derive the ultimate limits of this heat dissipation and show that it is generally nonzero and connected with the pattern's intrinsic crypticity--a complexity theoretic quantity that captures the puzzling difference between the amount of information the pattern's past behavior reveals about its future and the amount one needs to communicate about this past to optimally predict the future. [ABSTRACT FROM AUTHOR]

Decoupling systems into independently evolving components has a long history of simplifying seemingly complex systems. They enable a better understanding of the underlying dynamics and causal structures while providing more efficient means to simulate such processes on a computer. Here we outline a variational decoupling algorithm for decoupling unitary quantum dynamics-allowing us to decompose a given n-qubit unitary gate into multiple independently evolving sub-components. We apply this approach to quantum circuit synthesis-the task of discovering quantum circuit implementations of target unitary dynamics. Our numerical studies illustrate significant benefits, showing that variational decoupling enables us to synthesize general two- and four-qubit gates to fidelity that conventional variational circuits cannot reach.

From correlations in measurement outcomes alone, can two otherwise isolated parties establish whether such correlations are atemporal? That is, can they rule out that they have been given the same system at two different times? Classical statistics says no, yet quantum theory disagrees. Here, we introduce the necessary and sufficient conditions by which such quantum correlations can be identified as atemporal. We demonstrate the asymmetry of atemporality under time reversal and reveal it to be a measure of spatial quantum correlation distinct from entanglement. Our results indicate that certain quantum correlations possess an intrinsic arrow of time and enable classification of general quantum correlations across space-time based on their (in)compatibility with various underlying causal structures.

In covert target detection, Alice attempts to send optical or microwave probes to determine the presence or absence of a weakly reflecting target embedded in thermal background radiation within a target region, while striving to remain undetected by an adversary, Willie, who is co-located with the target and collects all light that does not return to Alice. We formulate this problem in a realistic setting and derive quantum-mechanical limits on Alice's error probability performance in entanglement-assisted target detection for any fixed level of her detectability by Willie. We demonstrate how Alice can approach this performance limit using two-mode squeezed vacuum probes in the regime of small to moderate background brightness, and how such protocols can outperform any conventional approach using Gaussian-distributed coherent states. In addition, we derive a universal performance bound for nonadversarial quantum illumination without requiring the passive-signature assumption.

Distillation, or purification, is central to the practical use of quantum resources in noisy settings often encountered in quantum communication and computation. Conventionally, distillation requires using some restricted "free" operations to convert a noisy state into one that approximates a desired pure state. Here, we propose to relax this setting by only requiring the approximation of the measurement statistics of a target pure state, which allows for additional classical postprocessing of the measurement outcomes. We show that this extended scenario, which we call "virtual resource distillation," provides considerable advantages over standard notions of distillation, allowing for the purification of noisy states from which no resources can be distilled conventionally. We show that general states can be virtually distilled with a cost (measurement overhead) that is inversely proportional to the amount of existing resource, and we develop methods to efficiently estimate such cost via convex and semidefinite programming, giving several computable bounds. We consider applications to coherence, entanglement, and magic distillation, and an explicit example in quantum teleportation (distributed quantum computing). This work opens a new avenue for investigating generalized ways to manipulate quantum resources.

Numerous quantum error-mitigation protocols have been proposed, motivated by the critical need to suppress noise effects on intermediate-scale quantum devices. Yet, their general potential and limitations remain elusive. In particular, to understand the ultimate feasibility of quantum error mitigation, it is crucial to characterize the fundamental sampling cost-how many times an arbitrary mitigation protocol must run a noisy quantum device. Here, we establish universal lower bounds on the sampling cost for quantum error mitigation to achieve the desired accuracy with high probability. Our bounds apply to general mitigation protocols, including the ones involving nonlinear postprocessing and those yet to be discovered. The results imply that the sampling cost required for a wide class of protocols to mitigate errors must grow exponentially with the circuit depth for various noise models, revealing the fundamental obstacles in the scalability of useful noisy near-term quantum devices.

Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system we can simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time. In contrast, inferring causal dependencies in complex processes often requires interactive experimentation-multiple rounds of interventions where we adaptively probe the process with different inputs to observe how they affect outputs. Here, we demonstrate universal uncertainty principles for general interactive measurements involving arbitrary rounds of interventions. As a case study, we show that they imply an uncertainty trade-off between measurements compatible with different causal dependencies.

Phase-insensitive optical amplifiers uniformly amplify each quadrature of an input field and are of both fundamental and technological importance. We find the quantum limit on the precision of estimating the gain of a quantum-limited phase-insensitive amplifier using a multimode probe that may also be entangled with an ancilla system. In stark contrast to the sensing of loss parameters, the average photon number N and number of input modes M of the probe are found to be equivalent and interchangeable resources for optimal gain sensing. All pure-state probes whose reduced state on the input modes to the amplifier is diagonal in the multimode number basis are proven to be quantum optimal under the same gain-independent measurement. We compare the best precision achievable using classical probes to the performance of an explicit photon-counting-based estimator on quantum probes and show that an advantage exists even for single-photon probes and inefficient photodetection. A closed-form expression for the energy-constrained Bures distance between two product amplifier channels is also derived.

Exact results about the nonequilibrium thermodynamics of open quantum systems at arbitrary timescales are obtained by considering all possible variations of initial conditions of a system. First we obtain a quantum-information theoretic equality for entropy production, valid for an arbitrary initial joint state of system and environment. For any finite-time process with a fixed initial environment, we then show that the system's loss of distinction-relative to the minimally dissipative state-exactly quantifies its thermodynamic dissipation. The quantum component of this dissipation is the change in coherence relative to the minimally dissipative state. Implications for quantum state preparation and local control are explored. For nonunitary processes-like the preparation of any particular quantum state-we find that mismatched expectations lead to divergent dissipation as the actual initial state becomes orthogonal to the anticipated one.

Effective and efficient forecasting relies on identification of the relevant information contained in past observations-the predictive features-and isolating it from the rest. When the future of a process bears a strong dependence on its behavior far into the past, there are many such features to store, necessitating complex models with extensive memories. Here, we highlight a family of stochastic processes whose minimal classical models must devote unboundedly many bits to tracking the past. For this family, we identify quantum models of equal accuracy that can store all relevant information within a single two-dimensional quantum system (qubit). This represents the ultimate limit of quantum compression and highlights an immense practical advantage of quantum technologies for the forecasting and simulation of complex systems.

The information-carrying capacity of a memory is known to be a thermodynamic resource facilitating the conversion of heat to work. Szilard's engine explicates this connection through a toy example involving an energy-degenerate two-state memory. We devise a formalism to quantify the thermodynamic value of memory in general quantum systems with nontrivial energy landscapes. Calling this the thermal information capacity, we show that it converges to the nonequilibrium Helmholtz free energy in the thermodynamic limit. We compute the capacity exactly for a general two-state (qubit) memory away from the thermodynamic limit, and find it to be distinct from known free energies. We outline an explicit memory-bath coupling that can approximate the optimal qubit thermal information capacity arbitrarily well.

Quantum resource theories seek to quantify sources of nonclassicality that bestow quantum technologies their operational advantage. Chief among these are studies of quantum correlations and quantum coherence. The former isolates nonclassicality in the correlations between systems, and the latter captures nonclassicality of quantum superpositions within a single physical system. Here, we present a scheme that cyclically interconverts between these resources without loss. The first stage converts coherence present in an input system into correlations with an ancilla. The second stage harnesses these correlations to restore coherence on the input system by measurement of the ancilla. We experimentally demonstrate this interconversion process using linear optics. Our experiment highlights the connection between nonclassicality of correlations and nonclassicality within local quantum systems and provides potential flexibilities in exploiting one resource to perform tasks normally associated with the other.

Simulating quantum contextuality with classical systems requires memory. A fundamental yet open question is what is the minimum memory needed and, therefore, the precise sense in which quantum systems outperform classical ones. Here, we make rigorous the notion of classically simulating quantum state-independent contextuality (QSIC) in the case of a single quantum system submitted to an infinite sequence of measurements randomly chosen from a finite QSIC set. We obtain the minimum memory needed to simulate arbitrary QSIC sets via classical systems under the assumption that the simulation should not contain any oracular information. In particular, we show that, while classically simulating two qubits tested with the Peres-Mermin set requires log_{2}24≈4.585 bits, simulating a single qutrit tested with the Yu-Oh set requires, at least, 5.740 bits.

Recent results in quantum information theory characterize quantum coherence in the context of resource theories. Here, we study the relation between quantum coherence and quantum discord, a kind of quantum correlation which appears even in nonentangled states. We prove that the creation of quantum discord with multipartite incoherent operations is bounded by the amount of quantum coherence consumed in its subsystems during the process. We show how the interplay between quantum coherence consumption and creation of quantum discord works in the preparation of multipartite quantum correlated states and in the model of deterministic quantum computation with one qubit.

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.

We propose a scheme to unconditionally entangle the internal states of atoms trapped in separate high-finesse optical cavities. The scheme uses the technique of quantum reservoir engineering in a cascaded cavity-QED setting, and for ideal (lossless) coupling between the cavities generates an entangled pure state. Highly entangled states are also shown to be possible for realizable cavity-QED parameters and with nonideal coupling.