相关论文: On the Power of Quantum Algorithms for Vector Valu…

Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…

This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…

Quantum Kernels are projected to provide early-stage usefulness for quantum machine learning. However, highly sophisticated classical models are hard to surpass without losing interpretability, particularly when vast datasets can be…

We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…

Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed…

Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum…

Benchmarking models via classical simulations is one of the main ways to judge ideas in quantum machine learning before noise-free hardware is available. However, the huge impact of the experimental design on the results, the small scales…

The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…

Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…

Classical simulation is important because it sets a benchmark for quantum computer performance. Classical simulation is currently the only way to exercise larger numbers of qubits. To achieve larger simulations, sparse matrix processing is…

The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…

Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…

Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…

In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern…

Traditional algorithms for simulating quantum computers on classical ones require an exponentially large amount of memory, and so typically cannot simulate general quantum circuits with more than about 30 or so qubits on a typical PC-scale…

Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the…

In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly-powerful classical computing model, called "stochastic ensemble machine (SEnM)," is considered. The SEnM runs with an ensemble…

In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…

Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…