Related papers: Efficient Unitary T-designs from Random Sums
We uncover a hidden Gaussian ensemble inside each of the three circular ensembles of random matrices, which provide novel diagrammatic rules for the calculation of moments. The matrices involved are generic complex for $\beta=2$, complex…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to…
Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor…
We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2) and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as T-gate counts and…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
In the age of noisy quantum processors, the exploitation of quantum symmetries can be quite beneficial in the efficient preparation of trial states, an important part of the variational quantum eigensolver algorithm. The benefits include…
Understanding how fast physical systems can resemble Haar-random unitaries is a fundamental question in physics. Many experiments of interest in quantum gravity and many-body physics, including the butterfly effect in quantum information…
The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
In this paper, we present a method for the Hamiltonian simulation in the context of eigenvalue estimation problems which improves earlier results dealing with Hamiltonian simulation through the truncated Taylor series. In particular, we…
The native gate set is fundamental to the performance of quantum devices, as it governs the accuracy of basic quantum operations and dictates the complexity of implementing quantum algorithms. Traditional approaches to extending gate sets…
We present an efficient algorithm for generating unitary maps on a $d$-dimensional Hilbert space from a time-dependent Hamiltonian through a combination of stochastic searches and geometric construction. The protocol is based on the…
We construct random walks on simple Lie groups that quickly converge to the Haar measure for all moments up to order $t$. Specifically, a step of the walk on the unitary or orthognoal group of dimension $2^{\mathsf n}$ is a random Pauli…
Quantum circuits for basic mathematical functions such as the square root are required to implement scientific computing algorithms on quantum computers. Quantum circuits that are based on Clifford+T gates can easily be made fault tolerant…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
Given a multiset $S$ of $n$ positive integers and a target integer $t$, the Subset Sum problem asks to determine whether there exists a subset of $S$ that sums up to $t$. The current best deterministic algorithm, by Koiliaris and Xu…
We provide a graphical calculus for computing averages of tensor network diagrams with respect to the distribution of random vectors containing independent uniform complex phases. Our method exploits the order structure of the partially…
Distributed inner product estimation (DIPE) is a fundamental task in quantum information, aiming to estimate the inner product between two unknown quantum states prepared on distributed quantum platforms. Existing rigorous sample complexity…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…