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Quantum algorithms based on parameterized quantum circuits (PQCs) have enabled a wide range of applications on near-term quantum devices. However, existing PQC architectures face several challenges, among which the ``barren plateaus"…
Variational quantum algorithms have been widely demonstrated in both experimental and theoretical contexts to have extensive applications in quantum simulation, optimization, and machine learning. However, the exponential growth in the…
Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized…
The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth quantum circuit to produce a parameter dependent state. For a given combinatorial optimization problem instance, the quantum expectation of the associated cost…
The Vehicle Routing Problem (VRP) is a fundamental combinatorial optimization challenge with broad applications in logistics and transportation. In this work, we present a quantum-assisted framework that integrates the Quantum Approximate…
Sampling noisy intermediate-scale quantum devices is a fundamental step that converts coherent quantum-circuit outputs to measurement data for running variational quantum algorithms that utilize gradient and Hessian methods in cost-function…
We study the performance and resource usage of the variational quantum factoring (VQF) algorithm for different instance sizes and optimization algorithms. Our simulations show better chance of finding the ground state when using VQE rather…
Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large…
The aircraft loading optimization problem is a computationally hard problem with the best known classical algorithm scaling exponentially with the number of objects. We propose a quantum approach based on a multi-angle variant of the QAOA…
The Quantum Alternating Operator Ansatz (QAOA) is a prominent variational quantum algorithm for solving combinatorial optimization problems. Its effectiveness depends on identifying input parameters that yield high-quality solutions.…
The training of a parameterized model largely depends on the landscape of the underlying loss function. In particular, vanishing gradients are a central bottleneck in the scalability of variational quantum algorithms (VQAs), and are known…
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,…
We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained combinatorial optimization problems (COPs). COPs are typically transformed into ground-state search problems of the Ising model on a…
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 algorithms are considered to be appealing applications of near-term quantum computers. However, it has been unclear whether they can outperform classical algorithms or not. To reveal their limitations, we must seek a…
Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as…
In machine learning, overparameterization is associated with qualitative changes in the empirical risk landscape, which can lead to more efficient training dynamics. For many parameterized models used in statistical learning, there exists a…
This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit…
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…
The Variational Quantum Eigensolver (VQE) is a promising candidate for quantum applications on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. Despite a lot of empirical studies and recent progress in theoretical understanding…