Related papers: More period finding with adiabatic quantum computa…
Quantum annealing (QA) is a promising approach for not only solving combinatorial optimization problems but also simulating quantum many-body systems such as those in condensed matter physics. However, non-adiabatic transitions constitute a…
We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem of finding a marked item inside of unsorted database. We show that the…
We investigate the connection between local minima in the problem Hamiltonian and first order quantum phase transitions during an adiabatic quantum computation. We demonstrate how some properties of the local minima can lead to an extremely…
We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. We continue with a description of quantum…
In quantum adiabatic algorithm, as the adiabatic parameter $s(t)$ changes slowly from zero to one with finite rate, a transition to excited states inevitably occurs and this induces an intrinsic computational error. We show that this…
Quantum computation by the adiabatic theorem requires a slowly varying Hamiltonian with respect to the spectral gap. We show that the Landau-Zener-St\"uckelberg oscillation phenomenon, that naturally occurs in quantum two level systems…
We present a technique that dramatically improves the accuracy of adiabatic state transfer for a broad class of realistic Hamiltonians. For some systems, the total error scaling can be quadratically reduced at a fixed maximum transfer rate.…
Exploring the ground state properties of many-body quantum systems conventionally involves adiabatic processes, alongside exact diagonalization, in the context of quantum annealing or adiabatic quantum computation. Shortcuts to adiabaticity…
In Amin and Choi \cite{AC09}, we show that an adiabatic quantum algorithm for the NP-hard maximum independent set (MIS) problem on a set of special family of graphs in which there are exponentially many local maxima would have the…
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes…
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…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
A computational model of adiabatic evolutionary quantum system (or AEQS, pronounced "eeh-ks") was introduced in [Yamakami,2022] as a sort of quantum annealing and its underlying input-driven Hamiltonians are generated…
We solve a model that has basic features that are desired for quantum annealing computations: entanglement in the ground state, controllable annealing speed, ground state energy separated by a gap during the whole evolution, and a…
We consider various iterative algorithms for solving the linear equation $ax=b$ using a quantum computer operating on the principle of quantum annealing. Assuming that the computer's output is described by the Boltzmann distribution, it is…
In the computational model of quantum annealing, the size of the minimum gap between the ground state and the first excited state of the system is of particular importance, since it is inversely proportional to the running time of the…
Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorization. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the…
We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the…
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…
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…