Automatic Post-selection by Ancillae Thermalisation

Tasks such as classification of data and determining the ground state of a Hamiltonian cannot be carried out through purely unitary quantum evolution. Instead, the inherent nonunitarity 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 and cannot be done intermittently on current (superconducting-based) NISQ devices. We propose a method inspired by thermalization that harnesses insensitivity to the details of the bath. We find a greater robustness to gate noise by coupling to this bath, with a similar cost in time and more qubits compared to alternate methods for inducing nonlinearity such as fixed-point quantum search for oblivious amplitude amplification. Post-selection on $m$ ancillae qubits is replaced with tracing out $O[log\ensuremath{\epsilon}/log(1\ensuremath{-}p)]$ (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, quantum gearbox, and phase estimation algorithm. This method is particularly advantageous on current quantum computers involving superconducting circuits.