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 lower bounds for read-k-times branching programs
Computational Complexity
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Computing with highly mixed states (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
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
Quantum automata and quantum grammars
Theoretical Computer Science
Quantum computation and quantum information
Quantum computation and quantum information
Quantum and Stochastic Branching Programs of Bounded Width
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the Power of Randomized Branching Programs
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
On the power of quantum finite state automata
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
A lower bound for integer multiplication on randomized ordered read-once branching programs
Information and Computation
Quantum branching programs and space-bounded nonuniform quantum complexity
Theoretical Computer Science
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In this paper, we show that one-qubit polynomial time computations are as powerful as NC circuits. More generally, we define syntactic models for quantum and stochastic branching programs of bounded width and prove upper and lower bounds on their power. We show that any NC language can be accepted exactly by a width-2 quantum branching program of polynomial length, in contrast to the classical case where width 5 is necessary unless NC = ACC. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in NC. For read-oncequantum branching programs (QBPs), we give a symmetric Boolean function which is computable by a read-once QBP with O(log n) width, but not by a deterministic read-once BP with o(n) width, or by a classical randomized read-once BP with o(n) width which is "stable" in the sense that its transitions depend on the value of the queried variable but do not vary from step to step. Finally, we present a general lower bound on the width of read-once QBPs, showing that our O(log n) upper bound for this symmetric function is almost tight.