A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Classical and Quantum Computation
Classical and Quantum Computation
Tight bounds on quantum searching
Tight bounds on quantum searching
Both Toffoli and controlled-NOT need little help to do universal quantum computing
Quantum Information & Computation
Quantum lower bound for recursive Fourier sampling
Quantum Information & Computation
On the Role of Hadamard Gates in Quantum Circuits
Quantum Information Processing
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We initiate the study of quantifying the quantumness of a quantum circuit by the number of gates that do not preserve the computational basis, as a means to understand the nature of quantum algorithmic speedups. Intuitively, a reduction in the quantumness requires an increase in the amount of classical computation, thus giving a "quantum and classical tradeoff'.In this paper we present two results on this measure of quantumness. The first gives almost matching upper and lower bounds on the question: "what is the minimum number of non-basis-preserving gates required to generate a good approximation to a given state". This question is the quantum analogy of the following classical question, "how many fair coins are needed to generate a given probability distribution", which was studied and resolved by Knuth and Yao in 1976 [Algorithms and Complexity: New Directions and Recent Results, Academic Press, New York, 1976, pp. 357-428]. Our second result shows that any quantum algorithm that solves Grover's Problem of size n using k queries and l levels of non-basis-preserving gates must have kl = Ω(n).