Automatic Post-selection by Ancillae Thermalisation

• URL: http://arxiv.org/abs/2010.04173v2
• Date: Fri, 21 Apr 2023 14:34:34 GMT
• Title: Automatic Post-selection by Ancillae Thermalisation
• Authors: Lewis Wright, Fergus Barratt, James Dborin, George H. Booth, Andrew G. Green
• Abstract summary: Post-selection and its extensions provide a way to harness the inherent non-unitarity of the measurement process. A typical computation might require $O(2m)$ 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.
• Score: 0.1259953341639576
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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