Related papers: Corrections to adiabatic behavior for long paths

Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the…

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…

We present a bound on the length of the path defined by the ground states of a continuous family of Hamiltonians in terms of the spectral gap G. We use this bound to obtain a significant improvement over the cost of recently proposed…

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…

Recent work argued that the scaling of a dimensionless quantity $Q_D$ with path length is a better proxy for quantifying the scaling of the computational cost of maintaining adiabaticity than the timescale. It also conjectured that…

The adiabatic theorem in quantum mechanics implies that if a system is in a discrete eigenstate of a Hamiltonian and the Hamiltonian evolves in time arbitrarily slowly, the system will remain in the corresponding eigenstate of the evolved…

Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…

The preparation of a given quantum state on a quantum computing register is a typically demanding operation, requiring a number of elementary gates that scales exponentially with the size of the problem. Using the adiabatic theorem for…

A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply…

We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is…

We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time…

Adiabatic quantum computing is a powerful framework for state preparation, while its evolution time often scales quadratically in the inverse Hamiltonian spectral gap, leading to sub-optimal computational complexity. In this work, we…

Consider a path of non-degenerate eigenstates of unitary operators or Hamiltonians with minimum eigenvalue gap G. The eigenpath traversal problem is to transform one or more copies of the initial to the final eigenstate. Solutions to this…

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that for problems that have exponentially large number of…

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…

The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables,…

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…

Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…

The time or cost of simulating a quantum circuit by adiabatic evolution is determined by the spectral gap of the Hamiltonians involved in the simulation. In "standard" constructions based on Feynman's Hamiltonian, such a gap decreases…

The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the…