Computing in Science and Engineering
Progress in computational complexity theory
Journal of Computer Science and Technology
Holographic algorithms: from art to science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Holographic algorithms with unsymmetric signatures
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Holographic algorithms: guest column
ACM SIGACT News
Basis Collapse in Holographic Algorithms
Computational Complexity
Invited Talk: Embedding Classical into Quantum Computation
Mathematical Methods in Computer Science
Holographic algorithms: The power of dimensionality resolved
Theoretical Computer Science
Proceedings of the forty-first annual ACM symposium on Theory of computing
Classification of a Class of Counting Problems Using Holographic Reductions
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
On blockwise symmetric signatures for matchgates
Theoretical Computer Science
On symmetric signatures in holographic algorithms
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Maximum edge-disjoint paths problem in planar graphs
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Journal of Symbolic Computation
Holographic algorithms: From art to science
Journal of Computer and System Sciences
A trichotomy theorem for the approximate counting of complex-weighted bounded-degree boolean CSPs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
A computational proof of complexity of some restricted counting problems
Theoretical Computer Science
The computational complexity of linear optics
Proceedings of the forty-third annual ACM symposium on Theory of computing
Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond
Quantum Information & Computation
Adptive quantum computation, constant depth quantum circuits and arthur-merlin games
Quantum Information & Computation
The complexity of symmetric Boolean parity Holant problems
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Computational Complexity of Holant Problems
SIAM Journal on Computing
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Completeness for parity problems
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Dichotomy for Holant problems of Boolean domain
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Some results on matchgates and holographic algorithms
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
A dichotomy for k-regular graphs with {0, 1}-vertex assignments and real edge functions
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Classical simulation and complexity of quantum computations
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Simulating quantum computers with probabilistic methods
Quantum Information & Computation
Holographic algorithms on domain size k2
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Approximate counting for complex-weighted Boolean constraint satisfaction problems
Information and Computation
Spin systems on k-regular graphs with complex edge functions
Theoretical Computer Science
On block-wise symmetric signatures for matchgates
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Holographic algorithms: the power of dimensionality resolved
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Commuting quantum circuits: efficient classical simulations versus hardness results
Quantum Information & Computation
Partition functions on k-regular graphs with {0,1}-vertex assignments and real edge functions
Theoretical Computer Science
The complexity of planar boolean #CSP with complex weights
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
The rational approximations of the unitary groups
Quantum Information Processing
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A model of quantum computation based on unitary matrix operations was introduced by Feynman and Deutsch. It has been asked whether the power of this model exceeds that of classical Turing machines. We show here that a significant class of these quantum computations can be simulated classically in polynomial time. In particular we show that two-bit operations characterized by 4 × 4 matrices in which the sixteen entries obey a set of five polynomial relations can be composed according to certain rules to yield a class of circuits that can be simulated classically in polynomial time. This contrasts with the known universality of two-bit operations and demonstrates that efficient quantum computation of restricted classes is reconcilable with the Polynomial Time Turing Hypothesis. Therefore, it is possible that, The techniques introduced bring the quantum computational model within the realm of algebraic complexity theory. In a manner consistent with one view of quantum physics, the wave function is simulated deterministically, and randomization arises only in the course of making measurements. The results generalize the quantum model in that they do not require the matrices to be unitary. In a different direction these techniques also yield deterministic polynomial time algorithms for the decision and parity problems for certain classes of read-twice Boolean formulae. All our results are based on the use of gates that are defined in terms of their graph matching properties.