Publications

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Building on recent work by Gammelmark et al. [Phys. Rev. Lett. 111, 160401 (2013)10.1103/PhysRevLett.111.160401] we develop a formalism for prediction and retrodiction of Gaussian quantum systems undergoing continuous measurements. We apply the resulting formalism to study the advantage of incorporating a full measurement record and retrodiction for impulselike force detection and accelerometry. We find that using retrodiction can only increase accuracy in a limited parameter regime, but that the reduction in estimation noise that it yields results in better detection of impulselike forces.

Single-photon detectors have achieved impressive performance and have led to a number of new scientific discoveries and technological applications. Existing models of photodetectors are semiclassical in that the field-matter interaction is treated perturbatively and time-separated from physical processes in the absorbing matter. An open question is whether a fully quantum detector, whereby the optical field, the optical absorption, and the amplification are considered as one quantum system, could have improved performance. Here we develop a theoretical model of such photodetectors and employ simulations to reveal the critical role played by quantum coherence and amplification backaction in dictating the performance. We show that coherence and backaction lead to trade-offs between detector metrics and also determine optimal system designs through control of the quantum-classical interface. Importantly, we establish the design parameters that result in a ideal photodetector with 100% efficiency, no dark counts, and minimal jitter, thus paving the route for next-generation detectors.

Many important chemical and biochemical processes in the condensed phase are notoriously difficult to simulate numerically. Often, this difficulty arises from the complexity of simulating dynamics resulting from coupling to structured, mesoscopic baths, for which no separation of time scales exists and statistical treatments fail. A prime example of such a process is vibrationally assisted charge or energy transfer. A quantum simulator, capable of implementing a realistic model of the system of interest, could provide insight into these processes in regimes where numerical treatments fail. We take a first step towards modeling such transfer processes using an ion-trap quantum simulator. By implementing a minimal model, we observe vibrationally assisted energy transport between the electronic states of a donor and an acceptor ion augmented by coupling the donor ion to its vibration. We tune our simulator into several parameter regimes and, in particular, investigate the transfer dynamics in the nonperturbative regime often found in biochemical situations.

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Analog quantum simulators (AQS) will likely be the first nontrivial application of quantum technology for predictive simulation. However, there remain questions regarding the degree of confidence that can be placed in the results of AQS since they do not naturally incorporate error correction. Specifically, how do we know whether an analog simulation of a quantum model will produce predictions that agree with the ideal model in the presence of inevitable imperfections? At the same time there is a widely held expectation that certain quantum simulation questions will be robust to errors and perturbations in the underlying hardware. Resolving these two points of view is a critical step in making the most of this promising technology. In this work we formalize the notion of AQS reliability by determining sensitivity of AQS outputs to underlying parameters, and formulate conditions for robust simulation. Our approach naturally reveals the importance of model symmetries in dictating the robust properties. To demonstrate the approach, we characterize the robust features of a variety of quantum many-body models.

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This the final report of the LDRD project entitled "Realizing the Power of Near-Term Quantum Technologies", which was tasked with laying a theoretical foundation and computational framework for quantum simulation on quantum devices, to support both future Sandia efforts and the broader academic research effort in this area. The unifying theme of the project has been the desire to delineate more clearly the interface between existent classical computing resources that are vast and reliable with emerging quantum computing resources that will be scarce and unreliable for the foreseeable future. We seek to utilize classical computing resources to judge the efficacy of quantum devices for quantum simulation tasks and determine when they exceed the performance of classical devices, thereby achieving "quantum supremacy". This task was initially pursued by adapting the general concept of "parameter space compression" to quantum simulation. An inability to scale this analysis efficiently to large-scale simulations precipitated a shift in focus to assessing quantum supremacy of a specific quantum device, a 1D Bose gas trapped in an optical lattice, that was more amenable to large-scale analysis. We also seek to reconstruct unobserved information from limited observations of a quantum device to enhance their utility. This task was initially pursued as an application of maximum entropy reconstruction. Initial attempts to improve entropy approximations for direct reconstruction by free energy minimization proved to be more difficult than expected, and the focus shifted to the development of a quantum thermostat to facilitate indirect reconstruction by evolving a quantum Markov process. An efficient quantum thermostat is broadly useful for quantum state preparation in almost any quantum simulation task. In the middle of the project, a small opportunistic investment was made in a high-risk experiment to build an analog quantum simulator out of hole quantum dots in Ge/SiGe heterostructures. While a useful simulator was not produced, hole quantum dots at a Ge/SiGe interface have been successfully observed for the first time.

Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric r. For Clifford gates with arbitrary small errors described by process matrices, r was believed to reliably correspond to the mean, over all Clifford gates, of the average gate infidelity between the imperfect gates and their ideal counterparts. We show that this quantity is not a well-defined property of a physical gate set. It depends on the representations used for the imperfect and ideal gates, and the variant typically computed in the literature can differ from r by orders of magnitude. We present new theories of the RB decay that are accurate for all small errors describable by process matrices, and show that the RB decay curve is a simple exponential for all such errors. These theories allow explicit computation of the error rate that RB measures (r), but as far as we can tell it does not correspond to the infidelity of a physically allowed (completely positive) representation of the imperfect gates.

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Many emerging quantum technologies demand precise engineering and control over networks consisting of quantum mechanical degrees of freedom connected by propagating electromagnetic fields, or quantum input-output networks. Here we review recent progress in theory and experiment related to such quantum input-output networks, with a focus on the SLH framework, a powerful modeling framework for networked quantum systems that is naturally endowed with properties such as modularity and hierarchy. We begin by explaining the physical approximations required to represent any individual node of a network, e.g. atoms in cavity or a mechanical oscillator, and its coupling to quantum fields by an operator triple (S,L,H). Then we explain how these nodes can be composed into a network with arbitrary connectivity, including coherent feedback channels, using algebraic rules, and how to derive the dynamics of network components and output fields. The second part of the review discusses several extensions to the basic SLH framework that expand its modeling capabilities, and the prospects for modeling integrated implementations of quantum input-output networks. In addition to summarizing major results and recent literature, we discuss the potential applications and limitations of the SLH framework and quantum input-output networks, with the intention of providing context to a reader unfamiliar with the field.

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Advances in the emerging field of coherent quantum feedback control (CQFC) have led to the development of new capabilities in the areas of quantum control and quantum engineering, with a particular impact on the theory and applications of quantum optical networks. For this study, we consider a CQFC network consisting of two coupled optical parametric oscillators (OPOs) and study the squeezing spectrum of its output field. The performance of this network as a squeezed-light source with desired spectral characteristics is optimized by searching over the space of model parameters with experimentally motivated bounds. We use the QNET package to model the network’s dynamics and the PyGMO package of global optimization algorithms to maximize the degree of squeezing at a selected sideband frequency or the average degree of squeezing over a selected bandwidth. The use of global search methods is critical for identifying the best possible performance of the CQFC network, especially for squeezing at higher-frequency sidebands and higher bandwidths. The results demonstrate that the CQFC network of two coupled OPOs makes it possible to vary the squeezing spectrum, effectively utilize the available pump power, and overall significantly outperform a single OPO. Additionally, the Hessian eigenvalue analysis shows that the squeezing generation performance of the optimally operated CQFC network is robust to small variations of phase parameters.

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