Testing permanent oracles - Revisited

Sanjeev Arora, Arnab Bhattacharyya, Rajsekar Manokaran, Sushant Sachdeva

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Suppose we are given an oracle that claims to approximate the permanent for most matrices X, where X is chosen from the Gaussian ensemble (the matrix entries are i.i.d. univariate complex Gaussians). Can we test that the oracle satisfies this claim? This paper gives a polynomial-time algorithm for the task. The oracle-testing problem is of interest because a recent paper of Aaronson and Arkhipov showed that if there is a polynomial-time algorithm for simulating boson-boson interactions in quantum mechanics, then an approximation oracle for the permanent (of the type described above) exists in BPP NP. Since computing the permanent of even 0/1 matrices is #P-complete, this seems to demonstrate more computational power in quantum mechanics than Shor's factoring algorithm does. However, unlike factoring, which is in NP, it was unclear previously how to test the correctness of an approximation oracle for the permanent, and this is the contribution of the paper. The technical difficulty overcome here is that univariate polynomial self-correction, which underlies similar oracle-testing algorithms for permanent over -and whose discovery led to a revolution in complexity theory-does not seem to generalize to complex (or even, real) numbers. We believe that this tester will motivate further progress on understanding the permanent of Gaussian matrices.

Original languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Proceedings
Pages362-373
Number of pages12
DOIs
StatePublished - Aug 28 2012
Event15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012 - Cambridge, MA, United States
Duration: Aug 15 2012Aug 17 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7408 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2012 and the 16th International Workshop on Randomization and Computation, RANDOM 2012
CountryUnited States
CityCambridge, MA
Period8/15/128/17/12

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Testing permanent oracles - Revisited'. Together they form a unique fingerprint.

Cite this