Characterization, Verification and Control for Large Quantum Systems

Quantum information processing offers potential improvements to a wide range of computing endevaors, including cryptography, chemistry simulations and machine learning. The development of practical quantum information processing devices is impeded, however, by challenges arising from the apparent exponential dimension of the space one must consider in characterizing quantum systems, verifying their correct operation, and in designing useful control sequences. In this work, we address each in turn by providing useful algorithms that can be readily applied in experimental practice. In order to characterize the dynamics of quantum systems, we apply statistical methods based on Bayes' rule, thus enabling the use of strong prior information and parameter reduction. We first discuss an analytically-tractable special case, and then employ a numerical algorithm, sequential Monte Carlo, that uses simulation as a resource for characterization. We discuss several examples of SMC and show its application in nitrogen vacancy centers and neutron interferometry. We then discuss how characterization techniques such as SMC can be used to verify quantum systems by using credible region estimation, model selection, state-space modeling and hyperparameterization. Together, these techniques allow us to reason about the validity of assumptions used in analyzing quantum devices, and to bound the credible range of quantum dynamics. Next, we discuss the use of optimal control theory to design robust control for quantum systems. We show extensions to existing OCT algorithms that allow for including models of classical electronics as well as quantum dynamics, enabling higher-fidelity control to be designed for cutting-edge experimental devices. Moreover, we show how control can be implemented in parallel across node-based architectures, providing a valuable tool for implementing proposed fault-tolerant protocols. We close by showing how these algorithms can be augmented using quantum simulation resources to enable addressing characterization and control design challenges in even large quantum devices. In particular, we will introduce a novel genetic algorithm for quantum control design, MOQCA, that utilizes quantum coprocessors to design robust control sequences. Importantly, MOQCA is also memetic, in that improvement is performed between genetic steps. We then extend sequential Monte Carlo with quantum simulation resources to enable characterizing and verifying the dynamics of large quantum devices. By using novel insights in epistemic information locality, we are able to learn dynamics using strictly smaller simulators, leading to an algorithm we call quantum bootstrapping. We demonstrate by using a numerical example of learning the dynamics of a 50-qubit device using an 8-qubit simulator

Modeling quantum noise for efficient testing of fault-tolerant circuits

Understanding fault-tolerant properties of quantum circuits is important for the design of large-scale quantum information processors. In particular, simulating properties of encoded circuits is a crucial tool for investigating the relationships between the noise model, encoding scheme, and threshold value. For general circuits and noise models, these simulations quickly become intractable in the size of the encoded circuit. We introduce methods for approximating a noise process by one which allows for efficient Monte Carlo simulation of properties of encoded circuits. The approximations are as close to the original process as possible without overestimating their ability to preserve quantum information, a key property for obtaining more honest estimates of threshold values. We numerically illustrate the method with various physically relevant noise models.Comment: 6 pages, 1 figur

How to best sample a periodic probability distribution, or on the accuracy of Hamiltonian finding strategies

Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an important parameter in the Hamiltonian. Here, we explore how to design experiments so as to minimize error in the estimation of this parameter. While it has been shown that useful results may be obtained by minimizing the risk incurred by each experiment, such an approach is computationally intractable in general. Here, we motivate and derive heuristic strategies for experiment design that enjoy the same exponential scaling as fully optimized strategies. We then discuss generalizations to the case of finite relaxation times, T_2 < \infty.Comment: 7 pages, 2 figures, 3 appendices; Quantum Information Processing, Online First, 20 April 201

Robust Online Hamiltonian Learning

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.Comment: 24 pages, 12 figures; to appear in New Journal of Physic