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Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…

Variational quantum algorithms (VQAs) represent a promising approach to utilizing current quantum computing infrastructures. VQAs are based on a parameterized quantum circuit optimized in a closed loop via a classical algorithm. This hybrid…

The variational approach is a cornerstone of computational physics, considering both conventional and quantum computing computational platforms. The variational quantum eigensolver (VQE) algorithm aims to prepare the ground state of a…

We explore a non-variational quantum state preparation approach combined with the ADAPT operator selection strategy in the application of preparing the ground state of a desired target Hamiltonian. In this algorithm, energy gradient…

We compare recently proposed methods to compute the electronic state energies of the water molecule on a quantum computer. The methods include the phase estimation algorithm based on Trotter decomposition, the phase estimation algorithm…

We present a comparative study of two implementations of a variational quantum algorithm aimed at minimizing the energy of a complex quantum system. In one implementation, we extract the information of the energy gradient by projective…

Gradient-based optimization is a key ingredient of variational quantum algorithms, with applications ranging from quantum machine learning to quantum chemistry and simulation. The parameter-shift rule provides a hardware-friendly method for…

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…

Preparing low energy states is a central challenge in quantum computing and quantum complexity theory. Several known approaches to prepare low energy states often get stuck in suboptimal states, such as high energy eigenstates (or low…

Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost…

We present a detailed numerical study of an alternative approach, named Quantum Non-Demolition Measurement (QNDM), to efficiently estimate the gradients or the Hessians of a quantum observable. This is a key step and a resource-demanding…

Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those…

Sampling from a probability distribution is a core task in many quantum and classical algorithms. Variational quantum circuits provide a natural approach to generating such distributions, as measurement outcomes directly define the…

We propose a method for constructing $\texttt{PREPARE}$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The…

Variational hybrid quantum-classical algorithms are some of the most promising workloads for near-term quantum computers without error correction. The aim of these variational algorithms is to guide the quantum system to a target state that…

We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…

We present superconducting quantum circuits which exhibit atomic energy spectrum and selection rules as ladder and lambda three-level configurations designed by means of genetic algorithms. These heuristic optimization techniques are…

Alternative computing paradigms open the door to exploiting recent innovations in computational hardware to probe the fundamental thermodynamic limits of information processing. One such paradigm employs superconducting quantum interference…

Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…

The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence…