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
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum Circuits with Unbounded Fan-out
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Fast parallel circuits for the quantum Fourier transform
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Classical and Quantum Computation
Classical and Quantum Computation
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum Computation and Quantum Information: 10th Anniversary Edition
Counting, fanout and the complexity of quantum ACC
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
ACM SIGACT News
Efficient Universal Quantum Circuits
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Computational depth complexity of measurement-based quantum computation
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
A lower bound method for quantum circuits
Information Processing Letters
Efficient universal quantum circuits
Quantum Information & Computation
Quantum addition circuits and unbounded fan-out
Quantum Information & Computation
A fast quantum circuit for addition with few qubits
Quantum Information & Computation
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We consider the resource bounded quantum circuit model with circuits restricted by thenumber of qubits they act upon and by their depth. Focusing on natural universal setsof gates which are familiar from classical circuit theory, several new lower bounds forconstant depth quantum circuits are proved. The main result is that parity (and hencefanout) requires log depth quantum circuits, when the circuits are composed of singlequbit and arbitrary size Toffoli gates, and when they use only constantly many ancillæ.Under this constraint, this bound is close to optimal. In the case of a non-constantnumber a of ancillæ and n input qubits, we give a tradeoff between a and the requireddepth, that results in a non-constant lower bound for fanout when a = n1-o(1). We alsoshow that, regardless of the number of ancillæ arbitrary arity Toffoli gates cannot besimulated exactly by a constant depth circuit family with gates of bounded arity.