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An n-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of n. We describe a classical algorithm with quasipolynomial runtime n^O(logn) that approximately samples from the ...

Let A be an s-sparse Hermitian matrix, f(x) be a univariate function, and i, j be two indices. In this work, we investigate the query complexity of approximating i f(A) j. We show that for any continuous function f(x):[−1,1]→ [−1,1], the quantum query ...

We define a map from an arbitrary quantum circuit to a local Hamiltonian whose ground state encodes the quantum computation. All previous maps relied on the Feynman-Kitaev construction, which introduces an ancillary "clock register" to track the ...

We prove lower bounds on the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Using a novel way of applying recording query methods we ...

The approximate stabilizer rank of a quantum state is the minimum number of terms in any approximate decomposition of that state into stabilizer states. Bravyi and Gosset showed that the approximate stabilizer rank of a so-called “magic” state like |T⟩^{⊗ ...}