Related papers: Statistical properties of random matrix product st…
We discuss a generalized quantum microcanonical ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by a combination of a time average and a maximum…
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
We quantify how well matrix product states approximate exact ground states of 1-D quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density…
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in (C^d)^{otimes k}, where k and p/d^k are fixed while d grows. When k=1,…
Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…
Preparing matrix product states (MPSs) on quantum computers is an essential routine in the simulation of many-body physics. However, widely-used schemes based on staircase circuits are often too deep to execute on current hardware. Here we…
We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
We present a general method to compute canonical averages for physical models sampled via quantum or classical quadratic unconstrained binary optimization (QUBO). First, we introduce a histogram reweighting scheme applicable to QUBO-based…
We present the Random Permutation Sorting System (RPSS), a novel framework for true uniform randomness generation grounded in statistical quantum mechanics. RPSS is built on a pair of conjugate observables, the permutation count and the…
In recent years, a close connection between the description of open quantum systems, the input-output formalism of quantum optics, and continuous matrix product states in quantum field theory has been established. So far, however, this…
Quantum statistical models (i.e., families of normalized density matrices) and quantum measurements (i.e., positive operator-valued measures) can be regarded as linear maps: the former, mapping the space of effects to the space of…
We study quantum states generated by a sequence of nearest neighbor bipartite entangling operations along a one-dimensional chain of spin qubits. After a single sweep of such a set of operations, the system is effectively described by a…
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…
Ultra-short pulses propagating in nonlinear nanophotonic waveguides can simultaneously leverage both temporal and spatial field confinement, promising a route towards single-photon nonlinearities in an all-photonic platform. In this…
Quantum many body physics simulations with Matrix Product States can often be accelerated if the quantum symmetries present in the system are explicitly taken into account. Conventionally, quantum symmetries have to be determined before…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
Randomness is a fundamental aspect of quantum mechanics, arising from the measurement process that collapses superpositions into definite outcomes according to Born's rule. Generating large-scale random quantum states is crucial for quantum…
An algorithm is proposed for constructing quasi-random "peaked" quantum circuits, i.e., circuits whose final qubit state exhibits a high probability concentration on a specific computational basis state. These circuits consist of random…