Related papers: Error Reduction in Quantum Annealing using Boundar…
Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of…
Transition amplitudes between instantaneous eigenstates of quantum two-level system are evaluated analytically on the basis of a new parametrization of its evolution operator, which has recently been proposed to construct exact solutions.…
Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic…
The adiabatic approximation in quantum mechanics is considered in the case where the self-adjoint hamiltonian $H_0(t)$, satisfying the usual spectral gap assumption in this context, is perturbed by a term of the form $\epsilon H_1(t)$. Here…
A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a…
We derive a nearly optimal upper bound on the running time in the adiabatic theorem for a switching family of Hamiltonians. We assume the switching Hamiltonian is in the Gevrey class $G^\alpha$ as a function of time, and we show that the…
We study a simple system described by a 2x2 Hamiltonian and the evolution of the quantum states under the influence of a perturbation. More precisely, when the initial Hamiltonian is not degenerate,we check analytically the validity of the…
Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps…
It has been recently reported that classical systems have speed limit for state evolution, although such a concept of speed limit had been considered to be unique to quantum systems. Owing to the speed limit for classical system, the lower…
The time-evolution operator for an explicitly time-dependent Hamiltonian is expressed as the product of a sequence of unitary operators. These are obtained by successive time-dependent unitary transformations of the Hilbert space followed…
By introducing a temporal change timescale $\tau_{\text{A}}(t)$ for the time-dependent system Hamiltonian, a general formulation of the Markovian quantum master equation is given to go well beyond the adiabatic regime. In appropriate…
In the conventional quantum mechanics (i.e., hermitian QM) the adia- batic theorem for systems subjected to time periodic fields holds only for bound systems and not for open ones (where ionization and dissociation take place) [D. W. Hone,…
Trotter errors in digitized quantum dynamics arise from approximating time-ordered evolution under noncommuting Hamiltonian terms with a product formula. In the adiabatic regime, such errors are known to exhibit long-time self-healing…
We introduce a simple framework for estimating lower bounds on the runtime of a broad class of adiabatic quantum algorithms. The central formula consists of calculating the variance of the final Hamiltonian with respect to the initial…
In adiabatic quantum annealing, the speed with which an anneal can be run, while still achieving a high final ground state fidelity, is dictated by the size of the minimum gap that appears between the ground and first excited state in the…
Adiabatic quantum computing is a general framework for preparing eigenstates of Hamiltonians on quantum devices. However, its digital implementation requires an efficient Hamiltonian simulation subroutine, which may introduce extra…
We study the Ising Hamiltonian with a transverse field term to simulate the quantum annealing. Using shortcuts to adiabaticity, we design the time dependence of the Hamiltonian. The dynamical invariant is obtained by the mean-field ansatz,…
The propagation of errors severely compromises the reliability of quantum computations. The quantum adiabatic algorithm is a physically motivated method to prepare ground states of classical and quantum Hamiltonians. Here, we analyze the…
We consider a time-dependent small quantum system weakly coupled to an environnement, whose effective dynamics we address by means of a Lindblad equation. We assume the Hamiltonian part of the Lindbladian is slowly varying in time and the…
Quantum annealing is a generic name of quantum algorithms to use quantum-mechanical fluctuations to search for the solution of optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum…