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.
Highlights
Algorithms for classification of data, optimizing the energy to find the ground state properties of a Hamiltonian require the use of nonlinear operations that cannot be achieved solely through unitary quantum evolution
In the following we demonstrate the application of ancillae thermalization to the quantum perception, quantum gearbox and a ground state preparation algorithm
For a direct comparison with our method, we focus upon an implemen
Summary
Algorithms for classification of data, optimizing the energy to find the ground state properties of a Hamiltonian (and optimizing classifiers for a given data set) require the use of nonlinear operations that cannot be achieved solely through unitary quantum evolution. When carrying out these tasks on a quantum computer we must use the nonunitarity of the measurement process. Coupling a small system at high temperatures to a large, low temperature bath allows us to cool the small system Eigenstate thermalization extends this notion to closed quantum systems. Coupling a large number of ancillae qubits in a low entropy state (e.g., |00000... ) to a small system and evolving the total system under some unitary evolution allows entropy to flow from the small system of interest to the ancillae
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