Related papers: Quantum adiabatic evolutions that can't be used to…
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 simple proof of quantum adiabatic theorem is provided. Quantum adiabatic approximation is divided into two kinds. For Hamiltonian H(t/T), a relation between the size of the error caused by quantum adiabatic approximation and the parameter…
The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic…
This paper is devoted to a generalisation of the quantum adiabatic theorem to a nonlinear setting. We consider a Hamiltonian operator which depends on the time variable and on a finite number of parameters and acts on a separable Hilbert…
We construct a set of instances of 3SAT which are not solved efficiently using the simplest quantum adiabatic algorithm. These instances are obtained by picking random clauses all consistent with two disparate planted solutions and then…
Transitionless quantum driving achieves adiabatic evolution in a hurry, using a counter-diabatic Hamiltonian to stifle non-adiabatic transitions. Here this strategy is cast in terms of a generator of adiabatic transport, leading to a…
A classical-kind phase-space formalism is developed to address the tiny intrinsic dynamical deviation from what is predicted by Wilczek-Zee theorem during quantum adiabatic evolution on degeneracy levels. In this formalism, the Hilbert…
Quantum computation promises to provide substantial speedups in many practical applications with a particularly exciting one being the simulation of quantum many-body systems. Adiabatic state preparation (ASP) is one way that quantum…
Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial…
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass…
Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to…
Controllable adiabatic evolution of a multi-qubit system can be used for adiabatic quantum computation (AQC). This evolution ends at a configuration where the Hamiltonian of the system encodes the solution of the problem to be solved. As a…
Adiabatic quantum computation (AQC), which is particularly useful for combinatorial optimization, becomes more powerful by using excited states, instead of ground states. However, the excited-state AQC is prone to errors due to dissipation.…
A new simple proof of the adiabatic theorem is given in the finite dimensional case for nondegenerate as well as degenerate states. The explicitly integrable two level system is considered as an example. It is demonstrated that the error…
Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the…
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in [E. Farhi, et al., arXiv:quant-ph/0208135]. The algorithm is applied to a random binary optimization problem (a version…
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…
The adiabatic theorem of quantum mechanics states that the error between an instantaneous eigenstate of a time-dependent Hamiltonian and the state given by quantum evolution of duration $\tau$ is upper bounded by $C/\tau$ for some positive…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
Despite its simplicity and strong theoretical guarantees, adiabatic state preparation has received considerably less interest than variational approaches for the preparation of low-energy electronic structure states. Two major reasons for…