Related papers: Computing exact moments of local random quantum ci…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
In this paper, we present a technically simple method to establish upper bounds on the expected injective norm of real and complex random tensors. Our approach is somewhat analogous to the moment method in random matrix theory, and is based…
Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
Simulating quantum circuits on classical computers is a notoriously hard, yet increasingly important task for the development and testing of quantum algorithms. In order to alleviate this inherent complexity, efficient data structures and…
Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…
Quantum Monte Carlo integration (QMCI) is a quantum algorithm to estimate expectations of random variables, with applications in various industrial fields such as financial derivative pricing. When QMCI is applied to expectations concerning…
We present a pedagogical, hands-on tutorial on \emph{replica tensor-network} techniques for random quantum circuits. At its core, the method recasts circuit-averaged observables acting on multiple copies of the system as the contraction of…
Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…
We investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. Using results from computational complexity, we observe that the approximate contraction of tensor networks…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than…
We develop an efficient algorithm for determining optimal adaptive quantum estimation protocols with arbitrary quantum control operations between subsequent uses of a probed channel. We introduce a tensor network representation of an…
The impressive pace of advance of quantum technology calls for robust and scalable techniques for the characterization and validation of quantum hardware. Quantum process tomography, the reconstruction of an unknown quantum channel from…
Entanglement is a key quantum phenomena and understanding transitions between phases of matter with different entanglement properties are an interesting probe of quantum mechanics. We numerically study a model of a 2D tensor network…
Quantum computers have a potential for solving quantum chemistry problems with higher accuracy than classical computers. Quantum computing quantum Monte Carlo (QC-QMC) is a QMC with a trial state prepared in quantum circuit, which is…
The rise of programmable quantum devices has motivated the exploration of circuit models which could realize novel physics. A promising candidate is a class of hybrid circuits, where entangling unitary dynamics compete with disentangling…
Based on the scheme of variational Monte Carlo sampling, we develop an accurate and efficient two-dimensional tensor-network algorithm to simulate quantum lattice models. We find that Monte Carlo sampling shows huge advantages in dealing…