1102.3354 (Niel de Beaudrap)

A linearized stabilizer formalism for systems of finite dimension    [PDF]

Niel de Beaudrap

The stabilizer formalism is a well-known scheme for efficiently simulating a class of transformations ("stabilizer circuits", which include the quantum Fourier transform and highly entangling operations) on standard basis states of d-dimensional qudits, generalizing techniques developed by Gottesman [quant-ph/9705052] in the case of qubits. To determine the state of a simulated system, existing treatments involve the computation of cumulative phase factors which involve quadratic dependencies. We present a simple formalism in which Pauli operators are represented using displacement operators in discrete phase space, allowing the evolution of the state is expressed via linear transformations modulo D <= 2d. As a consequence, we obtain a simple proof that simulating stabilizer circuits on n qudits, involving any constant number of measurement rounds, may be simulated by O(log(n)^2)-depth circuits for any constant d >= 2.

View original: http://arxiv.org/abs/1102.3354