Related papers: Quantum Singular Value Transformation for Solving …
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
This paper introduces a non-variational quantum algorithm designed to solve a wide range of combinatorial optimisation problems, including constrained and non-binary problems. The algorithm leverages an engineered interference process…
This paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing…
Quantum Fourier Transform (QFT) plays a principal role in the development of efficient quantum algorithms. Since the number of quantum bits that can currently built is limited, while many quantum technologies are inherently three- (or more)…
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 solving of linear systems provides a rich area to investigate the use of nearer-term, noisy, intermediate-scale quantum computers. In this work, we discuss hybrid quantum-classical algorithms for skewed linear systems for…
The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
Variational Quantum algorithms, especially Quantum Approximate Optimization and Variational Quantum Eigensolver (VQE) have established their potential to provide computational advantage in the realm of combinatorial optimization. However,…
We construct quantum circuits for solving one-dimensional Schr\"odinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight…
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT),…
Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE)…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
Quantum simulation is a cornerstone application for quantum computing, yet standard methods face a trade-off between circuit depth and accuracy: Trotterization depth scales with the number of Hamiltonian terms $L$, while sampling-based…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given…
We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is…
This work develops simulation methods that enable the application of the variational quantum linear solver (VQLS) to simulate quantum transport in nanoscale semiconductor devices. Most previous work on VQLS applications in semiconductor…
We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum table reads, to…
Solving systems of linear equations is one of the most important primitives in quantum computing that has the potential to provide a practical quantum advantage in many different areas, including in optimization, simulation, and machine…