Methods For General Stabilizer-Based Quantum Computing Simulation

摘要

The disclosed method and computer-readable medium allow efficient simulation of both stabilizer and non-stabilizer states in general quantum circuits on a classical computer by maintaining global phases and orthogonalizing linear combinations of stabilizer states during simulation. This is accomplished by representing arbitrary quantum states as superpositions of stabilizer states, which may be implemented using one or more stabilizer frames. Each stabilizer frame includes a stabilizer matrix, one or more phase vectors corresponding to the stabilizer states, and an amplitude vector corresponding to the global phases of each stabilizer state. Orthogonality is maintained throughout the simulation for efficient computation and measurement. Some embodiments utilize a multiframe representation of the quantum state to reduce the number of stabilizer states required to represent the quantum state, which multiframe representation may also be used to implement parallel simulation.

主权项

1. A method for maintaining global phases during simulation of at least one quantum gate of a quantum computer using a classical computer, the method comprising:
receiving, at a processor of the classical computer, a quantum state that is a superposition of a plurality of stabilizer states, wherein the quantum state is represented by a stabilizer matrix associated with the plurality of stabilizer states, a plurality of phase vectors representing each of the stabilizer states, and an amplitude vector, wherein each entry in the amplitude vector represents a global phase associated with one of the plurality of phase vectors; receiving, at a processor of the classical computer, a matrix representation of the at least one quantum gate; and determining, by a processor of the classical computer, the effect of the at least one quantum gate on the quantum state in a plurality of iterations, each iteration including:
applying, by a processor of the classical computer, one of the plurality of phase vectors to the stabilizer matrix;determining, by a processor of the classical computer, an input basis state associated with the one phase vector applied to the stabilizer matrix;determining, by a processor of the classical computer, an input non-zero amplitude associated with the input basis state;determining, by a processor of the classical computer, a first output non-zero amplitude associated with an output basis state by applying the matrix representation of the at least one quantum gate to the input non-zero amplitude and the input basis state;determining, by a processor of the classical computer, a second output non-zero amplitude of the output basis state using the stabilizer matrix and the matrix representation of the at least one quantum gate; andadjusting, by a processor of the classical computer, the entry in the amplitude vector associated with the one phase vector applied to the stabilizer matrix, wherein the entry is adjusted proportionally to the first output non-zero amplitude and the second output non-zero amplitude.