NDLI: Adiabatic Quantum State Generation

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	TaShma, Amnon Aharonov, Dorit
Copyright Year	2007
Abstract	The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to this task by studying the problem of quantum state generation. We motivate this problem by showing that the entire class of statistical zero knowledge, which contains natural candidates for efficient quantum algorithms such as graph isomorphism and lattice problems, can be reduced to the problem of quantum state generation. To study quantum state generation, we define a paradigm which we call adiabatic state generation ASG and which is based on adiabatic quantum computation. The ASG paradigm is not meant to replace the standard quantum circuit model or to improve on it in terms of computational complexity. Rather, our goal is to provide a natural theoretical framework, in which quantum state generation algorithms could be designed. The new paradigm seems interesting due to its intriguing links to a variety of different areas: the analysis of spectral gaps and groundstates of Hamiltonians in physics, rapidly mixing Markov chains, adiabatic computation, and approximate counting. To initiate the study of ASG, we prove several general lemmas that can serve as tools when using this paradigm. We demonstrate the application of the paradigm by using it to turn a variety of classical approximate counting algorithms into efficient quantum state generators of nontrivial quantum states, including, for example, the uniform superposition over all perfect matchings in a bipartite graph.
Starting Page	47
Ending Page	82
Page Count	36
File Format	PDF
ISSN	00975397
DOI	10.1137/060648829
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	1 (Special Section on Foundations of Computer Science)
Volume Number	37
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2007-03-30
Access Restriction	Subscribed
Subject Keyword	Quantum computation adiabatic theorem quantum sampling Hamiltonians state generation spectral gap quantum algorithm Markov chains statistical zero knowledge Zeno effect quantum computation
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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