Non-unitary probabilistic quantum computing
Robert M. Gingrich, Colin P. Williams · 2004
We present a method for designing quantum circuits that perform non-unitary quantum computations on n-quhit states prohabilistically, and give analytic expressions for the suc-cess probability and fidelity. Our scheme works by embedding the desired non-unitaiy op-erator within an anti-block-diagonal (n+l)-qubit Hamiltonian, H, which induces a unitary operator!J = exp(iEH), with E a constant. By using $2 acting on the original state aug-mented with an ancilla prepared in the 11) state, we can obtain the desired nowunitary transformation whenever the ancilla is found to be IO). Our scheme has the advantage that a "failure " result, i.e., fmding the ancilla to be 11) rather than 10) , 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 fmd the ancilla in the 10) state, i.e., detect the "success " condi-tion. We describe an application of our scheme to probabilistic state synthesis, I.