Learning the quantum algorithm for state overlap

TL;DR

This paper introduces a machine-learning method to discover short-depth quantum algorithms for computing state overlap, outperforming the traditional Swap Test in depth and error reduction on near-term quantum hardware.

Contribution

The authors develop a machine-learning approach to find shorter, more hardware-efficient quantum algorithms for state overlap measurement, including constant-depth solutions.

Findings

Discovered algorithms with shorter depths than the Swap Test.

Achieved constant-depth algorithms independent of problem size.

Significantly reduced error rates on Rigetti and IBM quantum computers.

Abstract

Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such algorithms. We apply our method to a ubiquitous primitive: computing the overlap ${\rm Tr}(\rho\sigma)$ between two quantum states $\rho$ and $\sigma$. The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines, and, when specialized to $\rho = \sigma$, quantifies the Renyi entanglement. Here, we find algorithms that have shorter depths than the Swap Test, including one that has a constant depth (independent of problem size). Furthermore, we apply our approach to the hardware-specific connectivity and gate sets used by Rigetti's and IBM's quantum computers and demonstrate that the shorter algorithms that we derive significantly reduce the error - compared to the Swap Test - on these computers.