Characterization, Verification and Control for Large Quantum Systems

Abstract

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.