Related papers: Variational Microcanonical Estimator
Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
We study the fluctuations of eigenstate expectation values in a microcanonical ensemble. Assuming the eigenstate thermalization hypothesis, an analytical formula for the finite-size scaling of the fluctuations is derived. The same problem…
Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
The Eigenstate Thermalization Hypothesis (ETH) was developed as a framework for understanding how the principles of statistical mechanics emerge in the long-time limit of isolated quantum many-body systems. Since then, ETH has shifted the…
We investigate dynamical equilibration of expectation values in closed quantum systems for realistic non-equilibrium initial states. Thereby we find that the corresponding long time expectation values depend on the initial expectation…
We present a holographic quantum simulation algorithm to variationally prepare thermal states of $d$-dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a ($d$-1)-dimensional cross-section. This…
We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…
Variational quantum algorithms involve training parameterized quantum circuits using a classical co-processor. An important variational algorithm, designed for combinatorial optimization, is the quantum approximate optimization algorithm.…
Quantum computers have the potential to help solve a range of physics and chemistry problems, but noise in quantum hardware currently limits our ability to obtain accurate results from the execution of quantum-simulation algorithms. Various…
We propose a method for the numerical computation of microcanonical expectation values--i.e. averages over energy eigenstates with the same eigenvalue-without any prior knowledge about the spectrum of the Hamiltonian. This is accomplished…
Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
Using a Krylov-subspace time evolution algorithm, we simulate the real-time dynamics of translation invariant non-integrable finite spin rings to quite long times with high accuracy. We systematically study the finite-size deviation between…
The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap between quantum mechanical and statistical mechanical descriptions of isolated quantum systems. Here, we define unbiased measures for how well the ETH works in…
The Variational Quantum Eigensolver (VQE) is a Variational Quantum Algorithm (VQA) to determine the ground state of quantum-mechanical systems. As a VQA, it makes use of a classical computer to optimize parameter values for its quantum…
Besides perturbation theory (which clearly requires the knowledge of the exact unperturbed solution), variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum…