Automatic Post-selection by Ancillae Thermalisation

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.

References in corpus (12)

• Elementary gates for quantum computation
• Quantum Amplitude Amplification and Estimation
• Hamiltonian Simulation by Qubitization
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• The quest for a Quantum Neural Network
• Fixed-point quantum search with an optimal number of queries
• A different kind of quantum search
• Efficient Bayesian Phase Estimation
• On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimization
• Near-optimal ground state preparation
• Floating Point Representations in Quantum Circuit Synthesis
• Repeat-Until-Success circuits with fixed-point oblivious amplitude amplification

Cited by in corpus (4)

• Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation
• Optimal Coherent Quantum Phase Estimation via Tapering
• Simulation of exceptional-point systems on quantum computers for quantum sensing
• Fractional Conformal Map, Qubit Dynamics and the Leggett-Garg Inequality