Related papers: Variational Microcanonical Estimator
The eigenstate thermalization hypothesis (ETH) postulates that the energy eigenstates of an isolated many-body system are thermal, i.e., each of them already yields practically the same expectation values as the microcanonical ensemble at…
The grand canonical ensemble lies at the core of quantum and classical statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange quantities represented…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
Determining low-energy eigenstates in electronic many-body quantum systems is a key challenge in computational chemistry and condensed-matter physics. Hybrid quantum-classical approaches, such as the Variational Quantum Eigensolver and…
We present a variational Monte Carlo (VMC) method that works equally well for the ground and the excited states of a quantum system. The method is based on the minimization of the variance of energy, as opposed to the energy itself in…
Quantum error correction, thermalization, and quantum chaos are fundamental aspects of quantum many-body physics that have each developed largely independently, despite their deep conceptual overlap. In this work, we establish a precise…
The McLachlan "minimum-distance" principle for optimizing approximate solutions of the time-dependent Schrodinger equation is revisited, with a focus on the local-in-time error accompanying the variational solutions. Simple, exact…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
Variational Quantum Algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In variational quantum algorithm, wavefunction represented by a parametrized…
The variational quantum eigensolver (VQE) is an algorithm to compute ground and excited state energy of quantum many-body systems. A key component of the algorithm and an active research area is the construction of a parametrized trial…
We investigate how the temperature calculated from the microcanonical entropy compares with the canonical temperature for finite isolated quantum systems. We concentrate on systems with sizes that make them accessible to numerical exact…
We propose incorporating multi-qubit nonunitary operations in Variational Quantum Thermalizers (VQTs). VQTs are hybrid quantum-classical algorithms that generate the thermal (Gibbs) state of a given Hamiltonian, with applications in quantum…
We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i.i.d. samples are known to have lower accuracy than the classical $n^{- \frac{1}{2}}$ error. We investigate…
Quantum computers are a highly promising tool for efficiently simulating quantum many-body systems. The preparation of their eigenstates is of particular interest and can be addressed, e.g., by quantum phase estimation algorithms. The…
The preparation of Gibbs thermal states is an important task in quantum computation with applications in quantum simulation, quantum optimization, and quantum machine learning. However, many algorithms for preparing Gibbs states rely on…
We design a variational quantum algorithm to solve multi-dimensional Poisson equations with mixed boundary conditions that are typically required in various fields of computational science. Employing an objective function that is formulated…
We study the validity of the eigenstate thermalization hypothesis (ETH) and its role for the occurrence of initial-state independent (ISI) equilibration in closed quantum many-body systems. Using the concept of dynamical typicality, we…
We derive a new formulation to calculate the excess chemical potential of a fraction of $N_1$ particles interacting with $N_2$ particles of a different species. The excess chemical potential is calculated numerically from first principles…
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…
Quantum dynamics can be analyzed via the structure of energy eigenstates. However, in the many-body setting, preparing eigenstates associated with finite temperatures requires time scaling exponentially with system size. In this work we…