Sketching the Best Approximate Quantum Compiling Problem

TL;DR

This paper introduces scalable algorithms for approximate quantum compiling, enabling the optimization of larger quantum circuits by fixing circuit structures and efficiently computing gradients, thus overcoming previous scalability limitations.

Contribution

It proposes sketch-and-solve algorithms with efficient gradient computation, significantly improving the scalability of quantum compilation for larger circuits.

Findings

Successfully compiled 15-qubit circuits with 15 CNOTs within an hour

Sketch-and-solve algorithms outperform standard optimization in scalability

Standard methods are limited by barren plateaus beyond small circuit sizes

Abstract

This paper considers the problem of quantum compilation from an optimization perspective by fixing a circuit structure of CNOTs and rotation gates then optimizing over the rotation angles. We solve the optimization problem classically and consider algorithmic tools to scale it to higher numbers of qubits. We investigate stochastic gradient descent and two sketch-and-solve algorithms. For all three algorithms, we compute the gradient efficiently using matrix-vector instead of matrix-matrix computations. Allowing for a runtime on the order of one hour, our implementation using either sketch-and-solve algorithm is able to compile 9 qubit, 27 CNOT circuits; 12 qubit, 24 CNOT circuits; and 15 qubit, 15 CNOT circuits. Without our algorithmic tools, standard optimization does not scale beyond 9 qubit, 9 CNOT circuits, and, beyond that, is theoretically dominated by barren plateaus.