Under suitable assumptions, some recently developed quantum algorithms can estimate the ground-state energy and prepare the ground state of a quantum Hamiltonian with near …
An n-qubit quantum circuit performs a unitary operation on an exponentially large, 2 n- dimensional, Hilbert space, which is a major source of quantum speed-ups. We develop a …
We develop a phase-estimation method with a distinct feature: its maximal run time (which determines the circuit depth) is δ/ϵ, where ϵ is the target precision, and the preconstant δ …
Under suitable assumptions, the quantum-phase-estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground-state energy …
This work presents a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant probability distributions can be prepared in quantum …
We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous …
We give two new quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with m constraint matrices, each of …
The original motivation to build a quantum computer came from Feynman, who imagined a machine capable of simulating generic quantum mechanical systems—a task that is …
We study the distribution over measurement outcomes of noisy random quantum circuits in the regime of low fidelity, which corresponds to the setting where the computation …