Non-unitary probabilistic quantum computing

TL;DR: In this article, the authors present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.

Abstract: We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity. Our scheme works by embedding the desired non-unitary operator within an anti-block-diagonal (n+1)-qubit Hamiltonian, H, which induces a unitary operator Ω = exp(ieH), with e a constant. By using Ω acting on the original state augmented with an ancilla prepared in the |1> state, we can obtain the desired non-unitary transformation whenever the ancilla is found to be |0>. Our scheme has the advantage that a "failure" result, i.e., finding the ancilla to be |1> rather than |0>, perturbs the remaining n-qubit state very little. As a result we can repeatedly re-evolve and measure the sequence of "failed" states until we find the ancilla in the |0> state, i.e., detect the "success" condition. We describe an application of our scheme to probabilistic state synthesis.