Related papers: An anatomy of a quantum adiabatic algorithm that t…
We concentrate on the geometric potential in the invariant perturbation theory of quantum adiabatic process which is presented in our recent papers. It is found out to be related to the geodesic curvature of the spherical curve in…
In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an…
The majorization theory has been applied to analyze the mathematical structure of quantum algorithms. An empirical conclusion by numerical simulations obtained in the previous literature indicates that step-by-step majorization seems to…
We study an architecture for implementing adiabatic quantum computation with trapped neutral atoms. Ground state atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism, thereby providing the requisite…
Quantum algorithms are prominent in the pursuit of achieving quantum advantage in various computational tasks. However, addressing challenges, such as limited qubit coherence and high error rate in near-term devices, requires extensive…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
Quantum computation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantum computer design that performs universal quantum computation within a single…
We clarify that the nonadiabatic scheme based on a parallel extension of the adiabatic scenario cannot realize the desired goal of quantum computation.
The problem Hamiltonian of the adiabatic quantum algorithm for the maximum-weight independent set problem (MIS) that is based on the reduction to the Ising problem (as described in [Choi08]) has flexible parameters. We show that by choosing…
We import the tools of Morse theory to study quantum adiabatic evolution, the core mechanism in adiabatic quantum computations (AQC). AQC is computationally equivalent to the (pre-eminent paradigm) of the Gate model but less error-prone, so…
We introduce an algorithm to perform an optimal adiabatic evolution that operates without an apriori knowledge of the system spectrum. By probing the system gap locally, the algorithm maximizes the evolution speed, thus minimizing the total…
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
We give a careful proof that a parallelized version of adiabatic quantum computation can efficiently simulate universal gate model quantum computation. The proof specifies an explicit parameter-dependent Hamiltonian $H({\lambda})$ that is…
The quantum adiabatic theorem is fundamental to time dependent quantum systems, but being able to characterize quantitatively an adiabatic evolution in many-body systems can be a challenge. This work demonstrates that the use of appropriate…
We demonstrate provable (sub)exponential quantum speedups in both discrete and continuous optimization, achieved through simple and natural quantum optimization algorithms, namely the quantum adiabatic algorithm for discrete optimization…
The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation…
The goal of this paper is to introduce building blocks for adiabatic quantum algorithms. Adiabatic quantum computing uses the principle of quantum annealing, which implies that a carefully controlled energy solution is optimal and…
Recent work at Fraunhofer FKIE shows that Morefield's method for multiple target data association can in theory be solved on an adiabatic quantum computer. The present paper validates the theory and examines the significant limitations of…
Farhi and others have introduced the notion of solving NP problems using adiabatic quantum com- puters. We discuss an application of this idea to the problem of integer factorization, together with a technique we call gluing which can be…
Adiabatic quantum computation for performing quantum computations such as Shor's algorithm is protected against thermal errors by an energy gap of size $O(1/n)$, where $n$ is the length of the computation to be performed.