Non-Unitary Probabilistic Quantum Computing

Jet Propulsion Laboratory, Califomia Institute of Technolog) 4800 Oak Grove Drive, Pasadena, California 91 109-8099. (Dated: September 15,2003) 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 success probability and fidelity. Our scheme works by embedding the desired non-unitaiy operator 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 augmented 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" condition. We describe an application of our scheme to probabilistic state synthesis,