Resonant transition-based quantum computation

Abstract

In this article we assess a novel quantum computation paradigm based on the resonant transition (RT) phenomenon commonly associated with atomic and molecular systems. We thoroughly analyze the intimate connections between the RT-based quantum computation and the well-established adiabatic quantum computation (AQC). Both quantum computing frameworks encode solutions to computational problems in the spectral properties of a Hamiltonian and rely on the quantum dynamics to obtain the desired output state. We discuss how one can adapt any adiabatic quantum algorithm to a corresponding RT version and the two approaches are limited by different aspects of Hamiltonians' spectra. The RT approach provides a compelling alternative to the AQC under various circumstances. To better illustrate the usefulness of the novel framework, we analyze the time complexity of an algorithm for 3-SAT problems and discuss straightforward methods to fine tune its efficiency.

Quantum-Walk-Inspired Dynamic Adiabatic Local Search

“…As the simulation suggests, both modified CTQW-inspired approaches outperform the original adiabatic local search. When the N ≤ 2 21 , the H m2 (s) outperforms H m1 (s). When problem size N is larger then 2 21 , H m1 (s) is a better choice over H m2 (s).…”

“…When the N ≤ 2 21 , the H m2 (s) outperforms H m1 (s). When problem size N is larger then 2 21 , H m1 (s) is a better choice over H m2 (s).…”

“…Besides being search algorithms, CTQWs have been applied in fields such as quantum transport [ 8 , 9 , 10 , 11 ], state transfer [ 12 , 13 ], link prediction in complex networks [ 14 ] and the creation of Bell pairs in a random network [ 15 ]. Some other well known universal models include the quantum circuit model [ 16 , 17 , 18 ], topological quantum computation [ 19 ], adiabatic quantum computation (AQC) [ 20 ], resonant transition-based quantum computation [ 21 ] and measurement-based quantum computation [ 22 , 23 , 24 , 25 ]. Investigating relationships among the frameworks helps to identify violations when mapping frameworks and potential solutions.…”

Optimizing Quantum Walk Search on a Reduced Uniform Complete Multi-Partite Graph

“…(32) from Eqn. (6). In this section we translate the UCPG into the three extreme graphs; complete graph, bipartite graph and star graph, as demonstrated in [21] by simply choosing the right value for P and m 0 .…”

“…Various quantum computational frameworks, such as Quantum Circuit Model [20], Topological Quantum Computation [15], Adiabatic Quantum Computation (AQC) [13], Quantum Walk (QW) [1,14], Resonant Transition Based Quantum Computation (RTBQC) [6] and Measurement Based Quantum Computation (MBQC) [5] have been proposed to attack problems that are considered extremely difficult for classical computers. Notable successes include the inventions of Shor's factoring algorithm and Grover's search algorithm, which manifest indisputable enhancement over all known classical algorithms designed for the same purpose.…”