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For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution…

Applying low-depth quantum neural networks (QNNs), variational quantum algorithms (VQAs) are both promising and challenging in the noisy intermediate-scale quantum (NISQ) era: Despite its remarkable progress, criticisms on the efficiency…

Quantum Physics · Physics 2023-07-11 Huan-Yu Liu , Zhao-Yun Chen , Tai-Ping Sun , Cheng Xue , Yu-Chun Wu , Guo-Ping Guo

Variational quantum algorithms (VQAs) are among the most promising algorithms in the era of Noisy Intermediate Scale Quantum Devices. Such algorithms are constructed using a parameterization U($\pmb{\theta}$) with a classical optimizer that…

Quantum Physics · Physics 2022-10-21 Lucas Friedrich , Jonas Maziero

Variational quantum algorithms are promising algorithms for achieving quantum advantage on near-term devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is…

Quantum Physics · Physics 2022-07-01 Stefan H. Sack , Raimel A. Medina , Alexios A. Michailidis , Richard Kueng , Maksym Serbyn

The barren plateau phenomenon, where the gradients of parametrized quantum circuits become vanishingly small, poses a significant challenge in quantum machine learning. While previous studies attempted to explain the barren plateau…

Quantum Physics · Physics 2026-02-06 Yuhan Yao , Yoshihiko Hasegawa

Variational quantum algorithms (VQAs) are hybrid quantum-classical approaches used for tackling a wide range of problems on noisy intermediate-scale quantum (NISQ) devices. Testing these algorithms on relevant hardware is crucial to…

Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, quantum entropies, the Bures fidelity and the quantum Fisher information of mixed quantum states are developed. In addition,…

Quantum Physics · Physics 2021-09-17 Kok Chuan Tan , Tyler Volkoff

Variational Quantum Algorithms (VQAs), such as the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA), are widely studied as candidates for near-term quantum advantage. Recent work has shown that…

Quantum Physics · Physics 2025-04-01 Georgios Korpas , Vyacheslav Kungurtsev , Jakub Mareček

Two main challenges preventing efficient training of variational quantum algorithms and quantum machine learning models are local minima and barren plateaus. Typically, barren plateaus are associated with deep circuits, while shallow…

Quantum Physics · Physics 2025-02-10 Nikita A. Nemkov , Evgeniy O. Kiktenko , Aleksey K. Fedorov

Variational quantum algorithms (VQAs) are promising methods that leverage noisy quantum computers and classical computing techniques for practical applications. In VQAs, the classical optimizers such as gradient-based optimizers are…

Quantum Physics · Physics 2021-06-22 Yudai Suzuki , Hiroshi Yano , Rudy Raymond , Naoki Yamamoto

Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is…

Variational quantum circuits are used in quantum machine learning and variational quantum simulation tasks. Designing good variational circuits or predicting how well they perform for given learning or optimization tasks is still unclear.…

Quantum Physics · Physics 2022-08-18 Junyu Liu , Francesco Tacchino , Jennifer R. Glick , Liang Jiang , Antonio Mezzacapo

We present a new optimization method for small-to-intermediate scale variational algorithms on noisy near-term quantum processors which uses a Gaussian process surrogate model equipped with a classically-evaluated quantum kernel.…

Quantum Physics · Physics 2023-08-16 Alistair W. R. Smith , A. J. Paige , M. S. Kim

Variational quantum algorithms (VQAs) have recently received significant attention from the research community due to their promising performance in Noisy Intermediate-Scale Quantum computers (NISQ). However, VQAs run on parameterized…

Quantum Physics · Physics 2022-05-06 Zeyi Tao , Jindi Wu , Qi Xia , Qun Li

Variational quantum algorithms are expected to demonstrate the advantage of quantum computing on near-term noisy quantum computers. However, training such variational quantum algorithms suffers from gradient vanishing as the size of the…

Quantum Physics · Physics 2021-11-29 Anbang Wu , Gushu Li , Yufei Ding , Yuan Xie

Quantum compilation provides a method to translate quantum algorithms at a high level of abstraction into their implementations as quantum circuits on real hardware. One approach to quantum compiling is to design a parameterised circuit and…

Quantum Physics · Physics 2022-10-18 Niall F. Robertson , Albert Akhriev , Jiri Vala , Sergiy Zhuk

Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data. But this excitement has been tempered by the existence of exponentially vanishing gradients, known as barren plateau…

Quantum Physics · Physics 2021-11-02 Arthur Pesah , M. Cerezo , Samson Wang , Tyler Volkoff , Andrew T. Sornborger , Patrick J. Coles

Quantum machine learning -- and specifically Variational Quantum Algorithms (VQAs) -- offers a powerful, flexible paradigm for programming near-term quantum computers, with applications in chemistry, metrology, materials science, data…

Quantum Physics · Physics 2024-03-15 M. Bilkis , M. Cerezo , Guillaume Verdon , Patrick J. Coles , Lukasz Cincio

Variational quantum algorithms (VQAs) are prominent candidates for near-term quantum advantage but lack rigorous guarantees of convergence and generalization. By contrast, quantum phase estimation (QPE) provides provable performance under…

Quantum Physics · Physics 2025-10-09 Tuyen Nguyen , Mária Kieferová

In quantum computing, the variational quantum algorithms (VQAs) are well suited for finding optimal combinations of things in specific applications ranging from chemistry all the way to finance. The training of VQAs with gradient descent…

Quantum Physics · Physics 2022-04-06 Pinaki Sen , Amandeep Singh Bhatia , Kamalpreet Singh Bhangu , Ahmed Elbeltagi