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Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated…
We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs…
Working within the stochastic series expansion framework, we introduce and characterize a new quantum cluster algorithm for quantum Monte Carlo simulations of transverse field Ising models with frustrated Ising exchange interactions. As a…
Numerical approximation of quantum states via convex combinations of states with positive partial transposes (bi-PPT state) in multipartite systems constitutes a fundamental challenge in quantum information science. We reformulate this…
A quantum simulator is a well controlled quantum system that can simulate the behavior of another quantum system which may require exponentially large classical computing resources to understand otherwise. In the 1980s, Feynman proposed the…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
The quantum phase transitions provide a paradigm for studying collective quantum phenomena that are a result of competing non-commuting interactions. This paper will study the ground state properties and quantum critical dynamics of the…
Discovering and categorizing quantum orders in mixed many-body systems are currently one of the most important problems. Specific types of decoherence applied to typical quantum many-body states can induce a novel kind of mixed state…
Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional…
We introduce a $0.611$-approximation algorithm for Quantum MaxCut and a $\frac{1+\sqrt{5}}{4} \approx 0.809$-approximation algorithm for the EPR Hamiltonian of [arXiv:2209.02589]. A novel ingredient in both of these algorithms is to…
We consider the optimization problem (ground energy search) for fermionic Hamiltonians with classical interactions. This QMA-hard problem is motivated by the Coulomb electron-electron interaction being diagonal in the position basis, a…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
We present an exact ansatz for the eigenstate problem of mixed fermion-boson systems that can be implemented on quantum devices. Based on a generalization of the electronic contracted Schr\"odinger equation (CSE), our approach guides a…
When preparing a pure state with a quantum circuit, there is an unavoidable approximation error due to the compilation error in fault-tolerant implementation. A recently proposed approach called probabilistic state synthesis, where the…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…
We propose and analyze an approximate message passing (AMP) algorithm for the matrix tensor product model, which is a generalization of the standard spiked matrix models that allows for multiple types of pairwise observations over a…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available…
The matrix product state (MPS) ansatz offers a promising approach for finding the ground state of molecular Hamiltonians and solving quantum chemistry problems. Building on this concept, the proposed technique of quantum circuit MPS (QCMPS)…
Variational quantum algorithms are practical approaches to prepare ground states, but their potential for quantum advantage remains unclear. Here, we use differentiable 2D tensor networks (TN) to optimize parameterized quantum circuits that…