Related papers: Cavity approach to variational quantum mechanics
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…
In this paper we introduce an approximate method to solve the quantum cavity equations for transverse field Ising models. The method relies on a projective approximation of the exact cavity distributions of imaginary time trajectories…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to determine a complete set of wave functions describing quantum decodings based on quasi-measurements…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical variational algorithm that produces an upper-bound estimate of the ground-state energy of a Hamiltonian. As quantum computers become more powerful and go beyond the…
We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
The number of measurements demanded by hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) is prohibitively high for many problems of practical value. For such problems, realizing quantum advantage will…
We study the regimes in which Hamiltonian simulation benefits from randomization. We introduce a sparse-QSVT construction based on composite stochastic decompositions, where dominant terms are treated deterministically and smaller…
Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing algorithms to calculate the ground state…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
We propose a quantum-classical hybrid algorithm to simulate the non-equilibrium steady state of an open quantum many-body system, named the dissipative-system Variational Quantum Eigensolver (dVQE). To employ the variational optimization…
The current state of quantum computing is commonly described as the Noisy Intermediate-Scale Quantum era. Available computers contain a few dozens of qubits and can perform a few dozens of operations before the inevitable noise erases all…
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…
Discrete combinatorial optimization consists in finding the optimal configuration that minimizes a given discrete objective function. An interpretation of such a function as the energy of a classical system allows us to reduce the…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…
A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that…