Related papers: Large time-step discretisation of adiabatic quantu…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
We show that by a suitable choice of a time dependent Hamiltonian, Deutsch's algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both…
We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to…
Trotter decomposition is the basis of the digital quantum simulation. Asymmetric and symmetric decompositions are used in our GPU demonstration of the digital adiabatic quantum simulations of $2+1$ dimensional quantum $\mathbb{Z}_2$ lattice…
Adiabatic elimination is a perturbative model reduction technique based on timescale separation and often used to simplify the description of composite quantum systems. We here analyze a quantum experiment where the perturbative expansion…
We propose a new adiabatic algorithm for the unsorted database search problem. This algorithm saves two thirds of qubits than Grover's algorithm in realizations. Meanwhile, we analyze the time complexity of the algorithm by both…
A new and intuitive perturbative approach to time-dependent quantum mechanics problems is presented, which is useful in situations where the evolution of the Hamiltonian is slow. The state of a system which starts in an instantaneous…
Adiabatic elimination is a standard tool in quantum optics, which produces an effective Hamiltonian for a relevant subspace of states, incorporating effects of its coupling to states with much higher unperturbed energy. It shares with…
At present, several models for quantum computation have been proposed. Adiabatic quantum computation scheme particularly offers this possibility and is based on a slow enough time evolution of the system, where no transitions take place. In…
Adiabatic quantum computing and optimization have garnered much attention recently as possible models for achieving a quantum advantage over classical approaches to optimization and other special purpose computations. Both techniques are…
Adiabatic quantum algorithms represent a promising approach to universal quantum computation. Whilst in a closed system these algorithms are limited by avoided level crossings, where the gap becomes exponentially small in the system size,…
A typical goal of a quantum simulation is to find the energy levels and eigenstates of a given Hamiltonian. This can be realized by adiabatically varying the system control parameters to steer an initial eigenstate into the eigenstate of…
Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols…
We report on a detailed analysis of generalization of the local adiabatic search algorithm. Instead of evolving directly from an initial ground state Hamiltonian to a solution Hamiltonian a different evolution path is introduced and is…
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as…
Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand…
The state of an open quantum system undergoing an adiabatic process evolves by following the instantaneous stationary state of its time-dependent generator. This observation allows one to characterize, for a generic adiabatic evolution, the…
The cost and the error of the adiabatic theorem for preparing the final eigenstate are discussed in terms of path length. Previous studies in terms of the norm of the Hamiltonian and its derivatives with the spectral gap are limited in…
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an…
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this…