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Variational quantum eigensolvers (VQEs) are a promising class of quantum algorithms for preparing approximate ground states in near-term quantum devices. Minimizing the error in such an approximation requires designing ansatzes using…
By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is…
This work presents steps toward the design of Majorana zero modes (MZM) in InAsP quantum dots (QD) embedded in an InP semiconducting nanowire in contact with a p-type superconductor described by the Kitaev Hamiltonian. The single particle…
In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground and excited state estimation on near-term hardware. We derive the theoretical ground on which the…
The adaptive derivative-assembled pseudo-trotter variational quantum eigensolver (ADAPT-VQE) is a promising hybrid quantum-classical algorithm for molecular ground state energy calculation, yet its practical scalability is hampered by…
Approximating the ground states of strongly interacting electron systems in quantum chemistry and condensed matter physics is expected to be one of the earliest applications of quantum computers. In this paper, we prepare highly accurate…
Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained…
Recently, an adaptive variational algorithm termed Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) has been proposed by Grimsley et al. (Nat. Commun. 10, 3007) while the number of measurements…
The wave function Ansatze are crucial in the context of the Variational Quantum Eigensolver (VQE). In the Noisy Intermediate-Scale Quantum era, the design of low-depth wave function Ansatze is of great importance for executing quantum…
The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of IBM's Eagle-processor quantum computers. A new algorithm to prepare the ground state of a gapped translationally-invariant system on a quantum computer is…
The Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (ADAPT-VQE) has emerged as a pivotal promising approach for electronic structure challenges in quantum chemistry with noisy quantum devices. Nevertheless, to…
The Variational Quantum Eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers. However, the circuit depth is expected to grow significantly with problem…
ADAPT-VQE is a robust algorithm for hybrid quantum-classical simulations of quantum chemical systems on near-term quantum computers. While its iterative process systematically reaches the ground state energy, ADAPT-VQE is sensitive to local…
We propose a co-designed variant of ADAPT-VQE (Co-ADAPT-VQE) where the quantum hardware is taken into account in the construction of the ansatz. This framework can be readily used to optimize state preparation circuits for any device,…
The variational quantum eigensolver (VQE) is an attracting possible application of near-term quantum computers. Originally, the aim of the VQE is to find a ground state for a given specific Hamiltonian. It is achieved by minimizing the…
We introduce Majorana Propagation, an algorithmic framework for the classical simulation of Fermionic circuits. Inspired by Pauli Propagation, Majorana Propagation operates by applying successive truncations throughout the Heisenberg…
Quantum simulation, one of the most promising applications of a quantum computer, is currently being explored intensely using the variational quantum eigensolver. The feasibility and performance of this algorithm depend critically on the…
The matrix product state (MPS) ansatz offers a promising approach for finding the ground state of molecular Hamiltonians and solving quantum chemistry problems. Building on this concept, the proposed technique of quantum circuit MPS (QCMPS)…
An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near-term quantum computers. It is based on McLachlan's…
Classical simulation of molecular systems is limited by exponential scaling, a hurdle quantum algorithms like Variational Quantum Eigensolvers (VQEs) aim to overcome. Although ADAPT-VQE enhances VQEs by dynamically building ans\"atze, it…