Related papers: Quantum Langevin Dynamics for Optimization
We examine the nonequilibrium dynamics of a self-interacting $\lambda\phi^4$ scalar field theory. Using a real time formulation of finite temperature field theory we derive, up to two loops and $O(\lambda^2)$, the effective equation of…
Stochastic Langevin dynamics has been traditionally used as a tool to describe non-equilibrium processes. When utilized in systems with collective modes, traditional Langevin dynamics relaxes all modes indiscriminately, regardless of their…
We develop an open-source, end-to-end software (named QHDOPT), which can solve nonlinear optimization problems using the quantum Hamiltonian descent (QHD) algorithm. QHDOPT offers an accessible interface and automatically maps tasks to…
Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought…
The purely relaxational non-equilibrium dynamics of the quantum spherical model as described through a Lindblad equation is analysed. It is shown that the phenomenological requirements of reproducing the exact quantum equilibrium state as…
We study the real time dynamics of a quantum system with potential barrier coupled to a heat-bath environment. Employing the path integral approach an evolution equation for the time dependent density matrix is derived. The time evolution…
We consider a decentralized learning problem, where a set of computing nodes aim at solving a non-convex optimization problem collaboratively. It is well-known that decentralized optimization schemes face two major system bottlenecks:…
Acceleration is a celebrated cornerstone of convex optimization, enabling gradient-based algorithms to converge sublinearly in the condition number. A major open question is whether an analogous acceleration phenomenon is possible for…
In this paper we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm…
We consider the Langevin dynamics of a many-body system of interacting particles in $d$ dimensions, in a very general setting suitable to model several out-of-equilibrium situations, such as liquid and glass rheology, active self-propelled…
Quantum cooling has demonstrated its potential in quantum computing, which can reduce the number of control channels needed for external signals. Recent progress also supports the possibility of maintaining quantum coherence in large-scale…
Motivated by the computation of the non-parametric maximum likelihood estimator (NPMLE) and the Bayesian posterior in statistics, this paper explores the problem of convex optimization over the space of all probability distributions. We…
Molecules like water have vibrational modes with a zero-point energy well above room temperature. As a consequence, classical molecular dynamics simulations of their liquids largely underestimate the energy of modes with a higher zero-point…
We construct a quantum-circuit framework for finite-temperature molecular dynamics in the canonical ensemble (NVT) with a Langevin thermostat, connecting canonical state preparation to subsequent physical-property readouts. The classical…
Quantum optimization, a key application of quantum computing, has traditionally been stymied by the linearly increasing complexity of gradient calculations with an increasing number of parameters. This work bridges the gap between Koopman…
Most of the mathematical approaches for quantum Langevin equation are based on the non-commutativity of the random force operators. Non-commutative random force operators are introduced in order to guarantee that the equal-time commutation…
In the context of non-convex optimization, we let the temperature of a Langevin diffusion to depend on the diffusion's own density function. The rationale is that the induced density captures to some extent the landscape imposed by the…
Mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional defined over the space of probability distributions. MFLD has gained attention due to its connection with noisy gradient descent for mean-field…
We develop an hybrid quantum-classical algorithm to solve an optimal population transfer problem for a molecule subject to a laser pulse. The evolution of the molecular wavefunction under the laser pulse is simulated on a quantum computer,…
Many physical and chemical processes in the condensed phase environment exhibit non-Markovian quantum dynamics. As such simulations are challenging on classical computers, we developed a variational quantum algorithm that is capable of…