Related papers: Perfect Sampling for Quantum Gibbs States
Preparation of Gibbs distributions is an important task for quantum computation. It is a necessary first step in some types of quantum simulations and further is essential for quantum algorithms such as quantum Boltzmann training. Despite…
Gibbs sampling is a widely used Markov chain Monte Carlo (MCMC) method for numerically approximating integrals of interest in Bayesian statistics and other mathematical sciences. Many implementations of MCMC methods do not extend easily to…
The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout…
The design of new quantum algorithms has proven to be an extremely difficult task. This paper considers a different approach to the problem, by studying the problem of 'quantum state generation'. This approach provides intriguing links…
We consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of Lipschitz observables on this state; and (b) learning the expectation values of local observables within a thermal or quantum…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
We describe and analyze algorithms for classically simulating measurement of an $n$-qubit quantum state $\psi$ in the standard basis, that is, sampling a bit string $x$ from the probability distribution $|\langle x|\psi\rangle|^2$. Our…
Classical Markov Chain Monte Carlo methods have been essential for simulating statistical physical systems and have proven well applicable to other systems with many degrees of freedom. Motivated by the statistical physics origins, Chen,…
Gibbs sampling is fundamental to a wide range of computer algorithms. Such algorithms are set to be replaced by physics based processors$-$be it quantum or stochastic annealing devices$-$which embed problem instances and evolve a physical…
The preparation of quantum Gibbs state is an essential part of quantum computation and has wide-ranging applications in various areas, including quantum simulation, quantum optimization, and quantum machine learning. In this paper, we…
Many quantum algorithms, such as adiabatic algorithms (e.g. AQC) and phase randomisation, require simulating Hamiltonian evolution. In addition, the simulation of physical systems is an important objective in its own right. In many cases,…
Preparing the thermal density matrix $\rho_{\beta} \propto e^{-\beta H}$ corresponding to a given Hamiltonian $H$ is a task of central interest across quantum many-body physics, and is particularly salient when attempting to study it with…
We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd,…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that performs quantum phase estimation on an initial trial state that…
The target measure $\mu$ is the distribution of a random vector in a box $\cB$, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure $\mu$. A ``coupling from the past'' construction of the…
We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact…
We propose a quantum key distribution scheme which closely matches the performance of a perfect single photon source. It nearly attains the physical upper bound in terms of key generation rate and maximally achievable distance. Our scheme…
Faithfully transferring the quantum state is essential for quantum information processing. Here we demonstrate a fast (in 84 ns) and high-fidelity (99.2%) transfer of arbitrary quantum states in a chain of four superconducting qubits with…
Gibbs states (i.e., thermal states) can be used for several applications such as quantum simulation, quantum machine learning, quantum optimization, and the study of open quantum systems. Moreover, semi-definite programming, combinatorial…