Related papers: Quantum Decomposition Algorithm For Master Equatio…
This article consists of a short introduction to the quantum approximation optimisation algorithm (QAOA). The mathematical structure of the QAOA, as well as its basic properties, are described. The implementation of the QAOA on MaxCut…
Quantum adiabatic optimization seeks to solve combinatorial problems using quantum dynamics, requiring the Hamiltonian of the system to align with the problem of interest. However, these Hamiltonians are often incompatible with the native…
Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…
Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to…
Quantum error correction is a key challenge for the development of practical quantum computers, a direction in which significant experimental progress has been made in recent years. In solid-state qubits, one of the leading information loss…
Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…
Combinatorial optimization problems are typically formulated using Quadratic Unconstrained Binary Optimization (QUBO), where constraints are enforced through penalty terms that introduce auxiliary variables and rapidly increase Hamiltonian…
Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising…
Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and…
A new method for stochastic unraveling of general time-local quantum master equations (QME) which involve the reduced density operator at time t only is proposed. The present kind of jump algorithm enables a numerically efficient treatment…
Using the methods of quantum trajectories we investigate the effects of dissipative decoherence in a quantum computer algorithm simulating dynamics in various regimes of quantum chaos including dynamical localization, quantum ergodic regime…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
The quantum marginal problem consists in deciding whether a given set of marginal reductions is compatible with the existence of a global quantum state or not. In this work, we formulate the problem from the perspective of dynamical systems…
The variational quantum power method (VQPM), which adapts the classical power iteration algorithm for quantum settings, has shown promise for eigenvector estimation and optimization on quantum hardware. In this work, we provide a…
The simulation of many industrially relevant physical processes can be executed up to exponentially faster using quantum algorithms. However, this speedup can only be leveraged if the data input and output of the simulation can be…
Extracting the Hamiltonian of interacting quantum-information processing systems is a keystone problem in the realization of complex phenomena and large-scale quantum computers. The remarkable growth of the field increasingly requires…
Quantum data encoding (QDE) enables faster com-putations than classical algorithms through superposition and en-tanglement. Circuit cutting and knitting are effective techniques for ameliorating current noisy quantum processing unit (QPUs)…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
Recent advances in quantum computing and the increasing availability of quantum hardware have substantially enhanced the practical relevance of quantum approaches to discrete optimization. Among these, the Quadratic Unconstrained Binary…