Automatic Post-selection by Ancillae Thermalisation

TL;DR

This paper introduces a novel quantum post-selection method inspired by the eigenstate thermalisation hypothesis, reducing resource requirements for tasks like classification and groundstate determination on current quantum hardware.

Contribution

It replaces traditional post-selection with a more efficient tracing method, significantly decreasing the number of measurements needed for accurate results.

Findings

Demonstrated on quantum perceptron and phase estimation algorithms

Reduces measurement complexity from exponential to logarithmic in error tolerance

Effective on superconducting quantum circuits

Abstract

Tasks such as classification of data and determining the groundstate of a Hamiltonian cannot be carried out through purely unitary quantum evolution. Instead, the inherent non-unitarity of the measurement process must be harnessed. Post-selection and its extensions provide a way to do this. However they make inefficient use of time resources -- a typical computation might require $O(2^m)$ measurements over $m$ qubits to reach a desired accuracy. We propose a method inspired by the eigenstate thermalisation hypothesis, that harnesses the induced non-linearity of measurement on a subsystem. Post-selection on $m$ ancillae qubits is replaced with tracing out $O(\log\epsilon / \log(1-p))$ (where p is the probability of a successful measurement) to attain the same accuracy as the post-selection circuit. We demonstrate this scheme on the quantum perceptron and phase estimation algorithm. This method is particularly advantageous on current quantum computers involving superconducting circuits.