Engineering topics

Gurevich, Yuri

Publications and source records attributed to Gurevich, Yuri.

2 records

DOE OSTI2015

Optimal ancilla-free Pauli+V circuits for axial rotations

We address the problem of optimal representation of single-qubit rotations in a certain unitary basis consisting of the so-called V gates and Pauli matrices. The V matrices were proposed by Lubotsky, Philips, and Sarnak [Commun. Pure Appl. Math. 40, 401–420 (1987)] as a purely geometric construct in 1987 and recently found applications in quantum computation. They allow for exceptionally simple quantum circuit synthesis algorithms based on quaternionic factorization. We adapt the deterministic-search technique initially proposed by Ross and Selinger to synthesize approximating Pauli+V circuits of optimal depth for single-qubit axial rotations. Our synthesis procedure based on simple SL{sub 2}(ℤ) geometry is almost elementary.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Ancilla-approximable quantum state transformations

We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined system. Measure the state of the auxiliary subsystem. If (and only if) it is in a specified final state, consider the process successful, and take the resulting state of the original (principal) system as the result of the process. We review known information about exact realization of transformations by such a process. Then we present results about approximate realization of finite partial transformations. We not only consider primarily the issue of approximation to within a specified positive ε, but also address the question of arbitrarily close approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗