Related papers: Local minima in quantum systems
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…
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…
The partition function and free energy of a quantum many-body system determine its physical properties in thermal equilibrium. Here we study the computational complexity of approximating these quantities for $n$-qubit local Hamiltonians.…
Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all N configurations of the system to…
Quantum cooling, a deterministic process that drives any state to the lowest eigenstate, has been widely used from studying ground state properties of chemistry and condensed matter quantum physics, to general optimization problems.…
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…
Nature is governed by precise physical laws, which can inspire the discovery of new computer-run simulation algorithms. Thermal states are the most ubiquitous for they are the equilibrium states of matter. Simulating thermal states of…
Controlled quantum mechanical devices provide a means of simulating more complex quantum systems exponentially faster than classical computers. Such "quantum simulators" rely heavily upon being able to prepare the ground state of…
The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete. The Local Consistency problem (deciding whether descriptions of small pieces of a quantum system are consistent) is also known…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
We consider blocks of quantum spins in a chain at thermal equilibrium, focusing on their properties from a thermodynamical perspective. Whereas in classical systems the temperature behaves as an intensive magnitude, a deviation from this…
The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, \emph{provably efficient} algorithms for preparing…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
We construct classical algorithms computing an approximation of the ground state energy of an arbitrary $k$-local Hamiltonian acting on $n$ qubits. We first consider the setting where a good ``guiding state'' is available, which is the main…
Finding eigenstates of a given many-body Hamiltonian is a long-standing challenge due to the perceived computational complexity. Leveraging on the hardware of a quantum computer accommodating the exponential growth of the Hilbert space size…
A quantum system coupled to a bath at some fixed, finite temperature converges to its Gibbs state. This thermalization process defines a natural, physically-motivated model of quantum computation. However, whether quantum computational…
Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath.…
Learning the Hamiltonian underlying a quantum many-body system in thermal equilibrium is a fundamental task in quantum learning theory and experimental sciences. To learn the Gibbs state of local Hamiltonians at any inverse temperature…
Real quantum systems couple to their environment and lose their intrinsic quantum nature through the process known as decoherence. Here we present a method for minimizing decoherence by making it energetically unfavorable. We present a…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…