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Physical Review A

Realizing an adiabatic quantum search algorithm with shortcuts to adiabaticity in an ion-trap system

Jie Zhang, Feng‐Guang Li, Yi Xie, Chun-Wang Wu, Bao-Quan Ou, Wei Wu, Ping‐Xing Chen

Published Nov 19, 2018• 8 citations
Publisher

Abstract

Adiabatic quantum computing (AQC) is an approach for solving optimization problems and has advantages against environmental decoherence and certain kinds of random unitary perturbations; however, long coherence time of quantum systems is required to meet the adiabatic criteria for the implementation of AQC. To break the dilemma of evolution time in AQC, the method of shortcuts to adiabaticity (STA) is employed to speed up the evolution process and suppress the nonadiabatic transitions. In this work we demonstrate the application of STA in AQC by implementing a fast two-bit Grover's algorithm with STA in an ion trap system, and the method here is also applicable for realizing Grover's algorithm with more entries.

DOI
10.1103/physreva.98.052323

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Realizing an adiabatic quantum search algorithm with shortcuts to adiabaticity in an ion-trap system

Wei Wu, Jie Zhang

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text W. Wu and J. Zhang, "Realizing an adiabatic quantum search algorithm with shortcuts to adiabaticity in an ion-trap system," in Quantum Information and Measurement (QIM) V: Quantum Technologies, OSA Technical Digest (Optica Publishing Group, 2019), paper F5A.18. Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

Quantum Information and Measurement (QIM)•Jan 1, 2019•0 citations
Adiabatic quantum computing (AQC) is an approach for solving optimization problems and has advantages against environmental decoherence and certain kinds of random unitary perturbations; however, long coherence time of quantum systems is required to meet the adiabatic criteria for the implementation of AQC. To break the dilemma of evolution time in AQC, the method of shortcuts to adiabaticity (STA) is employed to speed up the evolution process and suppress the nonadiabatic transitions. In this work we demonstrate the application of STA in AQC by implementing a fast two-bit Grover's algorithm with STA in an ion trap system, and the method here is also applicable for realizing Grover's algorithm with more entries.
Adiabatic quantum computing~(AQC) is based on the adiabatic principle, where a quantum system remains in an instantaneous eigenstate of the driving Hamiltonian. The final state of the Hamiltonian encodes solution to the problem of interest. While AQC has distinct advantages, recent researches have shown that quantumness such as quantum coherence in adiabatic processes may be lost entirely due to the system-bath interaction when the evolution time is long, and consequently the expected quantum speedup dose not show up. Here we propose a fast-signal assisted adiabatic quantum algorithm. We find that by applying a sequence of fast random or regular signals during the evolution process, the runtime can be reduced greatly, yet advantages of the adiabatic algorithm remain intact. Significantly, we present a \emph{randomized} Trotter formula and show that the driving Hamiltonian and the sequence of fast signals can be implemented simultaneously. We apply the algorithm for solving the 333-bit exact cover problem~(EC333) and put forward an approach for implementing the problem with trapped ions.
Fast and robust quantum control protocols are often based on an idealized approximate description of the relevant quantum system.While this may provide a performance that is close to optimal, improvements can be made by incorporating elements of the full system representation.We propose a technique for such scenarios, called enhanced shortcuts to adiabaticity (eSTA).The eSTA method works for previously intractable Hamiltonians by providing an analytical correction to existing STA protocols.This correction can be easily calculated, and the resulting protocols are outside the class of STA schemes.We demonstrate the effectiveness of the method for three distinct cases: manipulation of an internal atomic state beyond the rotating-wave approximation, transport of a neutral atom in an optical Gaussian trap, and transport of two trapped ions in an anharmonic trap.
Shortcuts to adiabaticity (STA) are fast methods to realize the same final state evolution of quantum adiabatic process. We develop a general theory to construct a new kind of STA by solely sampling the points of the adiabatic path of the original adiabatic Hamiltonian. In contrast to previous methods, our approach does not require any additional control resources, has inherent robustness, and does not use any complicated unitary transformation. Based on path sampling, the resulting STA protocols are simple and can avoid points of adiabatic path that are challenging to implement. As applications of our theory, we demonstrate reduction of the effects of both dissipation and dephasing noise by a novel robust three-level control, as well as reliable and fast ground state evolution in an adiabatic quantum computing model. Our theory offers a new route to design robust and fast control methods for general quantum systems.
By definition, quantum adiabatic process means a slow process which allows the state to follow the instantaneous eigenstates of time-dependent Hamiltonian. For some reasons, for example, to avoid the decoherence effects, or to implement large-scale quantum information processing, we may want to speed up the adiabatic process, that is, to achieve the adiabatic-like control but in very short time. In this talk, we present new methods to speeded-up expansion and transport of cold atoms in a harmonic trap. Such shortcuts to adiabaticity provide the fast expansion or transport, in which the final atomic state is the same as in the adiabatic process, but in arbitrarily short time, keeping the same populations of vibrational levels in the initial and final trap. These methods can also be generalized to Bose-Einstein Condensates. Moreover, we present shortcuts to adiabatic passage from one internal atomic state to another in twoor three-level atoms. In detail, we can apply Berry’s transitionless quantum driving method and invariant-based inverse engineering method to accelerate the Rapid Adiabatic Passage (RAP) and Stimulated Raman Adiabatic Passage (STIRAP) in twoand three-level atomic systems, respectively. We also examine and compare the stability of different schemes concerning different types of noise and system errors. Finally, we show that the technique of shortcuts to adiabaticity in two-level system can be applied in fast and robust spin flip in a quantum dot, to avoid the decoherent effects.
Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text W. Wu and J. Zhang, "Realizing an adiabatic quantum search algorithm with shortcuts to adiabaticity in an ion-trap system," in Quantum Information and Measurement (QIM) V: Quantum Technologies, OSA Technical Digest (Optica Publishing Group, 2019), paper F5A.18. Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article