Related papers: Local minima in quantum systems
A measurement-based quantum computer could consist of a local-gapped Hamiltonian system, whose thermal states --at sufficiently low temperature-- are universal resources for the computation. Initialization of the computer would correspond…
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…
We consider a quantum system consisting of a regular chain of elementary subsystems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state…
Sampling from Gibbs states -- states corresponding to system in thermal equilibrium -- has recently been shown to be a task for which quantum computers are expected to achieve super-polynomial speed-up compared to classical computers,…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
We present a quantum algorithm for the microcanonical thermal pure quantum (TPQ) method, which has an advantage in evaluating thermodynamic quantities at finite temperatures, by combining with some recently developed techniques derived from…
Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties…
The question whether a given quantum state is a ground or thermal state of a few-body Hamiltonian can be used to characterize the complexity of the state and is important for possible experimental implementations. We provide methods to…
In this paper we develop a quantum algorithm to realize finite temperature simulation on a quantum computer. As quantum computers use real-time evolution we did not use the imaginary time methods popular on classical algorithms. Instead, we…
We consider measurement-based quantum computation using the state of a spin-lattice system in equilibrium with a thermal bath and free to evolve under its own Hamiltonian. Any single qubit measurements disturb the system from equilibrium…
Preparation of low-energy quantum many-body states has a wide range of applications in quantum information processing and condensed matter physics. Quantum cooling algorithms offer a promising alternative to other methods based, for…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms we…
As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a…
The long-time dynamics of quantum systems, typically, but not always, results in a thermal steady state. The microscopic processes that lead to or circumvent this fate are of interest, since everyday experience tells us that not all spatial…
Obtaining precise estimates of quantum observables is a crucial step of variational quantum algorithms. We consider the problem of estimating expectation values of molecular Hamiltonians, obtained on states prepared on a quantum computer.…
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…
The development of novel quantum many-body computational algorithms relies on robust benchmarking. However, generating such benchmarks is often hindered by the massive computational resources required for exact diagonalization or quantum…
We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that for problems that have exponentially large number of…