Related papers: An efficient simulation algorithm based on abstrac…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…
Calculating the energy gradient in parameter space has become an almost ubiquitous subroutine of variational near-term quantum algorithms. "Faithful" classical emulation of this subroutine mimics its quantum evaluation, and scales as O(P^2)…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
One central issue in the formal design and analysis of reactive systems is the notion of refinement that asks whether all behaviors of the implementation is allowed by the specification. The local interpretation of behavior leads to the…
While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…
Given a set $Z$ of $n$ positive integers and a target value $t$, the Subset Sum problem asks whether any subset of $Z$ sums to $t$. A textbook pseudopolynomial time algorithm by Bellman from 1957 solves Subset Sum in time $O(nt)$. This has…
We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on…
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
We develop an analog classical simulation algorithm of noiseless quantum dynamics. By formulating the Schr\"{o}dinger equation into a linear system of real-valued ordinary differential equations (ODEs), the probability amplitudes of a…
The suffix array is a fundamental data structure for many applications that involve string searching and data compression. Designing time/space-efficient suffix array construction algorithms has attracted significant attention and…
In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse…
We study the fundamental scheduling problem $1\|\sum p_jU_j$. Given a set of $n$ jobs with processing times $p_j$ and deadlines $d_j$, the problem is to select a subset of jobs such that the total processing time is maximized without…
We propose a computationally efficient method to solve the dynamics of operators of bosonic quantum systems coupled to their environments. The method maps the operator under interest to a set of complex-valued functions, and its adjoint…
The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $\zeta(3)$ to $d$ decimal digits have time complexity $O(M(d) \log^2 d)$ and space complexity of $O(d \log d)$ or $O(d)$. Following work…
We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing…
The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…