Efficient classical simulation of the Deutsch–Jozsa and Simon’s algorithms

A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch–Jozsa and S...

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Bibliographic Details
Published in:Quantum information processing Vol. 16; no. 9; pp. 1 - 14
Main Authors: Johansson, Niklas, Larsson, Jan-Åke
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2017
Springer Nature B.V
Subjects:
Algorithms
Computer simulation
Data Structures and Information Theory
Mathematical Physics
Physics
Physics and Astronomy
Quantum computers
Quantum Computing
Quantum Information Technology
Quantum phenomena
Quantum Physics
Quantum theory
Spintronics
Deutsch-Jozsa Problem
Quantum Oracle
Classical Probabilistic Turing Machine
Quantum Algorithms
Spot Phase
ISSN:1570-0755, 1573-1332, 1573-1332
Online Access:Get full text
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Summary:A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch–Jozsa and Simon’s problem, both efficiently solvable on a quantum Turing machine, and both believed to lack efficient classical solutions. Here we present a framework that can simulate both quantum algorithms efficiently, solving the Deutsch–Jozsa problem with probability 1 using only one oracle query, and Simon’s problem using linearly many oracle queries, just as expected of an ideal quantum computer. The presented simulation framework is in turn efficiently simulatable in a classical probabilistic Turing machine. This shows that the Deutsch–Jozsa and Simon’s problem do not require any genuinely quantum resources, and that the quantum algorithms show no speed-up when compared with their corresponding classical simulation. Finally, this gives insight into what properties are needed in the two algorithms and calls for further study of oracle separation between quantum and classical computation.
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ISSN:1570-0755
1573-1332
1573-1332
DOI:10.1007/s11128-017-1679-7