Related papers: Distributed Variational Quantum Linear Solver
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
A distributed algorithm is described for solving a linear algebraic equation of the form $Ax=b$ assuming the equation has at least one solution. The equation is simultaneously solved by $m$ agents assuming each agent knows only a subset of…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
Near-term large quantum computers are not able to operate as a single processing unit. It is therefore required to partition a quantum circuit into smaller parts, and then each part is executed on a small unit. This approach is known as…
Quantum simulation is a promising pathway toward practical quantum advantage by simulating large-scale quantum systems. In this work, we propose communication-efficient distributed quantum simulation protocols by exploring three quantum…
The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over…
Noisy linear problems have been studied in various science and engineering disciplines. A class of "hard" noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector $\mathbf{b}$ constructed using a finite set…
Quantum machine learning is emerging as a promising application of quantum computing due to its distinct way of encoding and processing data. It is believed that large-scale quantum machine learning demonstrates substantial advantages over…
The Variational Quantum Linear Solver (VQLS), a hybrid quantum-classical algorithm for solving linear systems, faces a practical scalability bottleneck: the Linear Combination of Unitaries (LCU) decomposition requires O(L^2) circuit…
Variational quantum algorithms (VQAs) incorporate hybrid quantum-classical computation aimed at harnessing the power of noisy intermediate-scale quantum (NISQ) computers to solve challenging computational problems. In this thesis, three…
Variational quantum algorithms (VQAs) have emerged as a promising near-term technique to explore practical quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, the inefficient parameter training process due to the…
Variational Quantum Algorithms (VQAs) have emerged as promising methods for tackling complex problems on near-term quantum devices. Among these algorithms, the Variational Quantum Linear Solver (VQLS) addresses linear systems of the form…
Distributing quantum workloads over many Quantum Processing Units (QPUs) is a crucial step in scaling up quantum computers toward practical quantum advantage due to the limitations in size of a single QPU. In the absence of high-fidelity…
Quantum computing is presently undergoing rapid development to achieve a significant speedup promised in certain applications. Nonetheless, scaling quantum computers remains a formidable engineering challenge, prompting exploration of…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining…
Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current…