Ashley Montanaro

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Peter J. Cameron, Michael W. Newman, ∗ Ashley Montanaro, Simone Severini, † and Andreas Winter School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, U.K. Department of Computer Science, University of Bristol, Bristol BS8 1UB, U.K. Department of Mathematics, University of York, York YO10 5DD, U.K. Department of Mathematics,(More)
We present several families of total boolean functions which have exact quantum query complexity which is a constant multiple (between 1/2 and 2/3) of their classical query complexity, and show that optimal quantum algorithms for these functions cannot be obtained by simply computing parities of pairs of bits. We also characterise the model of nonadaptive(More)
The calculation of ground-state energies of physical systems can be formalised as the k-local Hamiltonian problem, which is the natural quantum analogue of classical constraint satisfaction problems. One way of making the problem more physically meaningful is to restrict the Hamiltonian in question by picking its terms from a fixed set S. Examples of such(More)
We use the class of commuting quantum computations known as IQP (instantaneous quantum polynomial time) to strengthen the conjecture that quantum computers are hard to simulate classically. We show that, if either of two plausible average-case hardness conjectures holds, then IQP computations are hard to simulate classically up to constant additive error.(More)
We develop two analytic lower bounds on the probability of success p of identifying a state picked from a known ensemble of pure states: a bound based on the pairwise inner products of the states, and a bound based on the eigenvalues of their Gram matrix. We use the latter to lower bound the asymptotic distinguishability of ensembles of n random quantum(More)
We study the complexity of the popular one player combinatorial game known as Flood-It. In this game the player is given an n×n board of tiles where each tile is allocated one of c colours. The goal is to make the colours of all tiles equal via the shortest possible sequence of flooding operations. In the standard version, a flooding operation consists of(More)
Estimation of the minimum eigenvalue of a quantum Hamiltonian can be formalised as the Local Hamiltonian problem. We study the natural special case of the Local Hamiltonian problem where the same 2-local interaction, with differing weights, is applied across each pair of qubits. First we consider antiferromagnetic/ferromagnetic interactions, where the(More)
We consider two combinatorial problems. The first we call “search with wildcards”: given an unknown n-bit string x, and the ability to check whether any subset of the bits of x is equal to a provided query string, the goal is to output x. We give an optimal O( √ n) quantum query algorithm for search with wildcards. Rather than using amplitude amplification(More)