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We study the problems of state preparation, ground state preparation and quantum state preparation. We propose an analytic approach to a stochastic quantum algorithm which prepares the ground state for $n$-qubit Hamiltonian that is…
Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the…
Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient…
Determining ground state energies of quantum systems by hybrid classical/quantum methods has emerged as a promising candidate application for near-term quantum computational resources. Short of large-scale fault-tolerant quantum computers,…
For each $n$, let RD$(n)$ denote the minimum $d$ for which there exists a formula for the general polynomial of degree $n$ in algebraic functions of at most $d$ variables. In this paper, we recover an algorithm of Sylvester for determining…
Quantum magnetism in low dimensions has been one of the central areas of theoretical research for many decades now. One of the key reasons for the long standing interest in this field has been the existence of simplified models, which serve…
Random unitaries sampled from the Haar measure serve as fundamental models for generic quantum many-body dynamics. Under standard cryptographic assumptions, recent works have constructed polynomial-size quantum circuits that are…
In this article, we provide a new algorithm for solving constraint satisfaction problems over templates with few subpowers, by reducing the problem to the combination of solvability of a polynomial number of systems of linear equations over…
Searching for degenerate ground spaces in quantum many-body systems is central to understanding spontaneous symmetry breaking and topological order. Although existing numerical methods can approximate individual ground states with high…
We investigate the space complexity of solving linear systems of equations. While all known deterministic or randomized algorithms solving a square system of $n$ linear equations in $n$ variables require $\Omega(\log^2 n)$ space, Ta-Shma…
The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…
One-dimensional self-gravitating systems admit genuine thermodynamical equilibria. For systems with strictly monotonic orbital frequency profile, the Landau and Balescu-Lenard theories predict a relaxation time scaling linearly with the…
Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…
The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
Density matrix downfolding (DMD) is a technique for regressing low-energy effective Hamiltonians from quantum many-body Hamiltonians. One limiting factor in the accuracy of classical implementations of DMD is the presence of…
The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area…
Shadow tomography aims to build a classical description of a quantum state from a sequence of simple random measurements. Physical observables are then reconstructed from the resulting classical shadow. Shadow protocols which use…
We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We assume that the Lindbladian is gapped and satisfies quantum detailed balance with respect to a unique full-rank steady state…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…