Discrete Wigner functions and the phase space representation of quantum computers

2001/06/15 by Pablo Bianucci, Cesar Miquel, Juan Pablo Paz +2 · 4 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems #quant-ph

paper · pdf · doi:10.1016/s0375-9601(02)00391-2

4 pages, 2 figures, submitted to PRL

arxiv created 2001/06/15 · openalex publication_date 2002/05/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

Abstract

We show how to represent the state and the evolution of a quantum computer (or any system with an N--dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary N, is defined in a phase space grid of 2N× 2N points. We compute such Wigner function for states which are relevant for quantum computation. Finally, we discuss properties of quantum algorithms in phase space and present the phase space representation of Grover's quantum search algorithm.

Citations

• Distribution functions in physics: Fundamentals
• Discrete Wigner function and quantum-state tomography

Cited by

• Understanding Squeezed States of Light Through Wigner's Phase-Space
• Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems
• Phase-space patterns of quantum transport on ordered and disordered networks
• Extended Cahill–Glauber formalism for finite-dimensional spaces: I. Fundamentals