Related papers: Sign Embedding Quantum Algorithms for Matrix Equat…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low…
The notorious sign problem severely limits the applicability of quantum Monte Carlo (QMC) simulations, as statistical errors grow exponentially with system size and inverse temperature. A recent proposal of a quantum-computing stochastic…
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
The matrix logarithm is one of the important matrix functions. Recently, a quantum algorithm that computes the state $|f\rangle$ corresponding to matrix-vector product $f(A)b$ is proposed in [Takahira, et al. Quantum algorithm for matrix…
We consider the problem of finding \textit{semi-matching} in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the…
Quantum eigenvalue transformation (QET) and its generalization, quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, which cover many of significant…
Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix…
Systems of correlated quantum matter can be a steep challenge to any would-be method of solution. Matrix-product state (MPS)-based methods can describe 1D systems quasiexactly, but often struggle to retain sufficient bipartite entanglement…
Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many…
We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…
Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…
The problem of Phase Estimation (or Amplitude Estimation) admits a quadratic quantum speedup. Wang, Higgott and Brierley [2019, Phys. Rev. Lett. 122 140504] have shown that there is a continuous trade-off between quantum speedup and circuit…
In the numerical linear algebra community, it was suggested that to obtain nearly optimal bounds for various problems such as rank computation, finding a maximal linearly independent subset of columns (a basis), regression, or low-rank…
We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…
The QED-C suite of Application-Oriented Benchmarks provides the ability to gauge performance characteristics of quantum computers as applied to real-world applications. Its benchmark programs sweep over a range of problem sizes and inputs,…