Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Finite monoids and the fine structure of NC1
Journal of the ACM (JACM)
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
On Optimal Depth Threshold Circuits for Multiplication andRelated Problems
SIAM Journal on Discrete Mathematics
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
SIAM Journal on Computing
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
SIAM Journal on Computing
Information Processing Letters
Circuits and expressions with nonassociative gates
Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Parallel Quantum Computation and Quantum Codes
SIAM Journal on Computing
On the Complexity of Quantum ACC
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Fault-tolerant quantum computation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum Circuits with Unbounded Fan-out
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Multilinear formulas and skepticism of quantum computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
ACM SIGACT News
Quantum Information Processing
Parallelizing quantum circuits
Theoretical Computer Science
Computational depth complexity of measurement-based quantum computation
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
Efficient universal quantum circuits
Quantum Information & Computation
Quantum addition circuits and unbounded fan-out
Quantum Information & Computation
Adptive quantum computation, constant depth quantum circuits and arthur-merlin games
Quantum Information & Computation
Quantum lower bounds for fanout
Quantum Information & Computation
Bounds on the power of constant-depth quantum circuits
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We propose definitions of QAC0, the quantum analog of the classical class AC0 of constant-depth circuits with AND and OR gates of arbitrary fan-in, and QACC[q], the analog of the class ACC[q] where Modq gates are also allowed. We prove that parity or fanout allows us to construct quantum MODq gates in constant depth for any q, so QACC [2] = QACC. More generally, we show that for any q, p 1, MODq is equivalent to MODp (up to constant depth and polynomial size). This implies that QAC0 with unbounded fanout gates, denoted QACwf0, is the same as QACC [q] and QACC for all q. Since ACC[p] ≠ ACC[q] whenever p and q are distinct primes, QACC [q] is strictly more powerful than its classical counterpart, as is QAC0 when fanout is allowed. This adds to the growing list of quantum complexity classes which are provably more powerful than their classical counterparts. We also develop techniques for proving upper bounds for QACC in terms of related language classes. We define classes of languages closely related to QACC [2] and show that restricted versions of them can be simulated by polynomial-size circuits. With further restrictions, language classes related to QACC [2] operators can be simulated by classical threshold circuits of polynomial size and constant depth.