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We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
A projective measurement of energy (PME) on a quantum system is a quantum measurement, determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
The energy gap is calculated for the ground state quantum computer circuit, which was recently proposed by Mizel et.al. When implementing a quantum algorithm by Hamiltonians containing only pairwise interaction, the inverse of energy gap…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and…
Despite progress in quantum Hamiltonian complexity, little is known about the computational complexity of quantum physics at the thermodynamic limit. Even defining the problem is not straight forward. We study the complexity of estimating…
In recent years, energy correlators have emerged as powerful observables for probing the fragmentation dynamics of high-energy collisions. We introduce the first numerical strategy for calculating energy correlators using the Hamiltonian…
We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion of Neto\v{c}n\'y and Redig and the cluster expansion approach…
We give a reduction from $(1+\varepsilon)$-approximate Earth Mover's Distance (EMD) to $(1+\varepsilon)$-approximate Closest Pair (CP). As a consequence, we improve the fastest known approximation algorithm for high-dimensional EMD. Here,…
Trotter approximation in conjunction with Quantum Phase Estimation can be used to extract eigen-energies of a many-body Hamiltonian on a quantum computer. There were several ways proposed to assess the quality of this approximation based on…
We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at…
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless $2$-local Hamiltonians $H$ describing a…
We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is…
Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
Expectation value estimation is ubiquitous in quantum algorithms. The expectation value of a Hamiltonian, which is essential in various practical applications, is often estimated by measuring a large number of Pauli strings on quantum…
We introduce a family of fourth order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. Each method in the family may be viewed as a correction of a linear two-step method, where the correction…
The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total…
The classical work of (Arora et al., 1999) provides a scheme that gives, for any $\epsilon>0$, a polynomial time $1-\epsilon$ approximation algorithm for dense instances of a family of $\mathcal{NP}$-hard problems, such as Max-CUT and…