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The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties, without the sign problem. The list spans condensed matter, nuclear physics, and…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
Building on recent solutions of the fermion sign problem for specific models we present two continuous-time quantum Monte Carlo methods for efficient simulation of mass-imbalanced Hubbard models on bipartite lattices at half-filling. For…
Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic…
The variational determination of the two-fermion reduced density matrix is described for harmonically trapped, ultracold few-fermion systems in one dimension with equal spin populations. This is accomplished by formulating the problem as a…
The simulated tempering (ST) is an important method to deal with systems whose phase spaces are hard to sample ergodically. However, it uses accepting probabilities weights which often demand involving and time consuming calculations. Here…
State space subspace algorithms for input-output systems have been widely applied but also have a reasonably well-developedasymptotic theory dealing with consistency. However, guaranteeing the stability of the estimated system matrix is a…
Several natural partial orders on integral partitions, such as the embeddability, the stable embeddability, the bulk embeddability and the supermajorization, raise in the quantum computation, bin-packing and matrix analysis. We find the…
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to…
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…
Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum…
A widely used strategy to reduce the computational cost in quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts and an environment that is treated at a lower…
Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…
Variational Monte Carlo is a many-body numerical method that scales well with system size. It has been extended to study the Green function only recently by Charlebois and Imada (2020). Here we generalize the approach to systems with open…
One bottleneck of quantum Monte Carlo (QMC) simulation of strongly correlated electron systems lies at the scaling relation of computational complexity with respect to the system sizes. For generic lattice models of interacting fermions,…
We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wavefunction by a branching random walk in an over-complete basis space of Slater determinants. By…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling…
We present a method for quantum state tomography that enables the efficient estimation, with fixed precision, of any of the matrix elements of the density matrix of a state, provided that the states from the basis in which the matrix is…