22 research outputs found
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