Related papers: Perfect Sampling for Quantum Gibbs States
Gibbs sampling is a crucial computational technique used in physics, statistics, and many other scientific fields. For classical Hamiltonians, the most commonly used Gibbs sampler is the Metropolis algorithm, known for having the Gibbs…
State preparation is a fundamental routine in quantum computation, for which many algorithms have been proposed. Among them, perhaps the simplest one is the Grover-Rudolph algorithm. In this paper, we analyse the performance of this…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
Tensor network states are powerful variational ans\"atze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions,…
Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such…
We present a quantum algorithm to compute the entanglement spectrum of arbitrary quantum states. The interesting universal part of the entanglement spectrum is typically contained in the largest eigenvalues of the density matrix which can…
The particle Gibbs (PG) sampler is a systematic way of using a particle filter within Markov chain Monte Carlo (MCMC). This results in an off-the-shelf Markov kernel on the space of state trajectories, which can be used to simulate from the…
Gibbs sampling is a common procedure used to fit finite mixture models. However, it is known to be slow to converge when exploring correlated regions of a parameter space and so blocking correlated parameters is sometimes implemented in…
We study the problem of state synthesis in the DQC1 (One Clean Qubit) model of quantum computation, which provides a single pure qubit and $n$ maximally mixed qubits, and after applying any quantum circuit some subset of the qubits are…
We propose a new type of approximate counting algorithms for the problems of enumerating the number of independent sets and proper colorings in low degree graphs with large girth. Our algorithms are not based on a commonly used Markov chain…
We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an…
A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schr\"odinger's quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in…
Markov jump processes (MJPs) are continuous-time stochastic processes widely used in a variety of applied disciplines. Inference for MJPs typically proceeds via Markov chain Monte Carlo, the state-of-the-art being a uniformization-based…
We propose a strategy for perfect state transfer in spin chains based on the use of an unmodulated coupling Hamiltonian whose coefficients are explicitly time dependent. We show that, if specific and non-demanding conditions are satisfied…
Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
We present a perfect marginal sampler of the unique Gibbs measure of a spin system on $\mathbb Z^2$. The algorithm is an adaptation of a previous `lazy depth-first' approach by the authors, but relaxes the requirement of strong spatial…
We introduce a hybrid machine-learning algorithm for designing quantum optics experiments that produce specific quantum states. Our algorithm successfully found experimental schemes to produce all 5 states we asked it to, including…
It has been shown that, starting from the state |0>, in the general case, an arbitrary quantum state |\psi> cannot be prepared with exponential precision in polynomial time. However, we show that for the important special case when |\psi>…
Preparing the Gibbs state of an interacting quantum many-body system on noisy intermediate-scale quantum (NISQ) devices is a crucial task for exploring the thermodynamic properties in the quantum regime. It encompasses understanding…
For many quantum systems intended for information processing, one detects the logical state of a qubit by integrating a continuously observed quantity over time. For example, ion and atom qubits are typically measured by driving a cycling…