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Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical variational algorithm that produces an upper-bound estimate of the ground-state energy of a Hamiltonian. As quantum computers become more powerful and go beyond the…
We report on two major hybrid applications of quantum computing, namely, the quantum approximate optimisation algorithm (QAOA) and the variational quantum eigensolver (VQE). Both are hybrid quantum classical algorithms as they require…
Hybrid algorithms that combine quantum and classical resources have become commonplace in quantum computing. The variational quantum eigensolver (VQE) is routinely used to solve prototype problems. Currently, hybrid algorithms use no more…
Variational quantum algorithms (VQAs) utilize a hybrid quantum-classical architecture to recast problems of high-dimensional linear algebra as ones of stochastic optimization. Despite the promise of leveraging near- to intermediate-term…
Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
Variational algorithms have particular relevance for near-term quantum computers but require non-trivial parameter optimisations. Here we propose Analytic Descent: Given that the energy landscape must have a certain simple form in the local…
While quantum computers are a very promising tool for the far future, in their current state of the art they remain limited both in size and quality. This has given rise to hybrid quantum-classical algorithms, where the quantum device…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There…
Variational quantum algorithms (VQAs) are a modern family of quantum algorithms designed to solve optimization problems using a quantum computer. Typically VQAs rely on a feedback loop between the quantum device and a classical optimization…
We propose a variational quantum eigensolver (VQE) for the simulation of strongly-correlated quantum matter based on a multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimization. This MERA quantum eigensolver can…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
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…
Gradient-based optimizers have been proposed for training variational quantum circuits in settings such as quantum neural networks (QNNs). The task of gradient estimation, however, has proven to be challenging, primarily due to distinctive…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
Variational quantum eigensolver (VQE) optimizes parameterized eigenstates of a Hamiltonian on a quantum processor by updating parameters with a classical computer. Such a hybrid quantum-classical optimization serves as a practical way to…
The variational quantum eigensolver (VQE), a type of variational quantum algorithm, is a hybrid quantum-classical algorithm to find the lowest-energy eigenstate of a particular Hamiltonian. We investigate ways to optimize the VQE solving…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…
Quantum Variational Circuits (QVCs) are often claimed as one of the most potent uses of both near term and long term quantum hardware. The standard approaches to optimizing these circuits rely on a classical system to compute the new…