Related papers: Dynamics of quantum adiabatic evolution algorithm …
In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to…
Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…
Background: Solving nuclear many-body problems with an ab initio approach is widely recognized as a computationally challenging problem. Quantum computers offer a promising path to address this challenge. There are urgent needs to develop…
One of the difficulties in adiabatic quantum computation is the limit on the computation time. Here we propose two schemes to speed-up the adiabatic evolution. To apply this controlled adiabatic evolution to adiabatic quantum computation,…
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…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
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…
Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing…
We provide model reduction formulas for open quantum systems consisting of a target component which weakly interacts with a strongly dissipative environment. The time-scale separation between the uncoupled dynamics and the interaction…
We consider a composite open quantum system consisting of a fast subsystem coupled to a slow one. Using the time-scale separation, we develop an adiabatic elimination technique to derive at any order the reduced model describing the slow…
We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state.…
Presented is a quantum computing representation of Dirac particle dynamics. The approach employs an operator splitting method that is an analytically closed-form product decomposition of the unitary evolution operator. This allows the Dirac…
We introduce a quantum algorithm to efficiently prepare states with a small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width $\delta$. Given a local…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
Numerous sufficient conditions for adiabaticity of the evolution of a driven quantum system have been known for quite a long time. In contrast, necessary adiabatic conditions are scarce. A practicable necessary condition well-suited for…
Quantum adiabatic evolution, an important fundamental concept inphysics, describes the dynamical evolution arbitrarily close to the instantaneous eigenstate of a slowly driven Hamiltonian. In most systems undergoing spontaneous…
We systematically characterize the dynamical evolution of time-parity (PT )-symmetric two-level systems with spin-dependent dissipations. If the control parameters of the gap are linearly tuned with time, the dynamical evolution can be…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
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…
We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. This strengthens the superpolynomial separation recently proved by…