Latency considerations for stochastic optimizers in variational quantum algorithms

Matt Menickelly1, Yunsoo Ha2, and Matthew Otten3

1Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Lemont, IL 60439
2Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, 915 Partners Way, Raleigh, NC 27601
3HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, CA 90265

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Variational quantum algorithms, which have risen to prominence in the noisy intermediate-scale quantum setting, require the implementation of a stochastic optimizer on classical hardware. To date, most research has employed algorithms based on the stochastic gradient iteration as the stochastic classical optimizer. In this work we propose instead using stochastic optimization algorithms that yield stochastic processes emulating the dynamics of classical deterministic algorithms. This approach results in methods with theoretically superior worst-case iteration complexities, at the expense of greater per-iteration sample (shot) complexities. We investigate this trade-off both theoretically and empirically and conclude that preferences for a choice of stochastic optimizer should explicitly depend on a function of both latency and shot execution times.

Variational quantum algorithms are promising candidates for solving practical problems on near-term quantum computers. However, the process of optimizing these algorithms can be computationally expensive due to the two needs to 1) perform repeated measurements (shots) on the quantum computer and 2) adjust the quantum circuit parameters. Here, we propose a new stochastic optimization algorithm called SHOALS (SHOt Adaptive Line Search) that is designed under the assumption that the time spent in optimization performing shots is dominated by the time spent in optimization performing circuit adjustments. We demonstrate that SHOALS outperforms other stochastic optimization algorithms in this setting. On the contrary, when the shot time is comparable to the circuit switching time, stochastic gradient descent algorithms are found to be more efficient. By considering the trade-offs between shot time, circuit switching time, and the efficiency of the optimization algorithm, we show that the total run time of variational quantum algorithms can be significantly reduced.

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