基于超绝热捷径技术快速制备超导三量子比特Greenberger-Horne-Zeilinger态

本文提出了一个基于超绝热捷径技术快速制备超导三量子比特Greenberger-Horne-Zeilinger态的理论方案.该方案首先在量子Zeno动力学的帮助下得到系统的有效哈密顿量,之后通过引入与有效哈密顿量具有相同形式的反向导热哈密顿量来构建绝热捷径,加速了整个系统的演化过程.该方案不需要初态和目标态之间的直接耦合,在实验上也更容易实现.数值模拟结果表明该方案对超导量子比特的自发辐射、波导谐振腔的泄漏以及超导量子比特的退相位是鲁棒的.     

Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor

Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N.J. Cerf for Grover's search [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch-Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh's algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order N (where N=2(n) and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.     

Nonadiabatic Quantum Search Algorithm with Analytical Success Rate

In nonadiabatic quantum search algorithm, it is difficult to calculate the success rate analytically. We develop the nonadiabatic quantum search algorithm by adding a counterdiabatic driving term to the original time-dependent Hamiltonian. The Hamiltonian we structured is diagonal in eigen picture and the time-independent Schrödinger equation is solved analytically. Then, we get an accurate analytical expression of success rate in nonadiabatic quantum search algorithm. Utilizing this expression, a sufficient condition, which can ensure the success rate be one with arbitrary evolution time, was found. Moreover, we can choose the better parameters by calculating the precise success rate according to the expression.

     

Quantum Adiabatic Evolution for Pattern Recognition Problem

Quantum pattern recognition algorithm for two-qubit systems has been implemented by quantum adiabatic evolution.We will estimate required running time for this algorithm by means of an analytical solution of timedependent Hamiltonian since the time complexity of adiabatic quantum evolution is a limitation on the quantum computing.These results can be useful for experimental implementation.     

基于绝热捷径快速实现远距离的四维纠缠态的制备

作为量子信息处理的载体,量子纠缠态一直以来都是量子信息领域的研究热点.相比于低维纠缠态,高维纠缠态使得量子通信具有更快的传输速度、更强的安全性、更高的噪声容忍阈值等特点.另外,绝热技术因其对实验参数起伏不敏感而被广泛应用于纠缠态的制备,然而绝热过程需要相当长的演化时间,因此绝热捷径应运而生.本文提出了一种采用无跃迁量子驱动构建绝热捷径实现快速制备两个原子的四维纠缠态的理论方案,该系统中的两个原子分别被囚禁在两个由光纤连接的双模腔中.为了获得一个技术上可操作的物理系统,本方案采用能级失谐设计出一个可精确驱动系统沿着某一个系统的瞬时本征态演化的哈密顿.该方案所采用的无跃迁量子驱动构建绝热捷径不仅大大缩短了演化时间,而且在实验上也比较容易实现.本文还数值模拟了消相干因素对四维纠缠态保真度的影响,结果表明,只要脉冲参数选取在一定范围内,光纤耗散、腔场耗散和原子自发辐射等不利因素都会被大大抑制.     

Partial evolution based local adiabatic quantum search

Recently, Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution, which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger than one. Later, they found that the above two adiabatic search algorithms had the same time complexity when there is only one marked item in the database. In the present paper, following the idea of Roland and Cerf [Roland J and Cerf N J 2002 Phys. Rev. A 65 042308], if within the small symmetric evolution interval defined by Zhang et al., a local adiabatic evolution is performed instead of the original “global” one, this “new” algorithm exhibits slightly better performance, although they are progressively equivalent with M increasing. In addition, the proof of the optimality for this partial evolution based local adiabatic search when M=1 is also presented. Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search, which are found to have the same phenomenon above, are also discussed.     

A quantum search algorithm based on partial adiabatic evolution

This paper presents and implements a specified partial adiabatic search algorithm on a quantum circuit. It studies the minimum energy gap between the first excited state and the ground state of the system Hamiltonian and it finds that,in the case of M = 1,the algorithm has the same performance as the local adiabatic algorithm. However,the algorithm evolves globally only within a small interval,which implies that it keeps the advantages of global adiabatic algorithms without losing the speedup of the local adiabatic search algorithm.     

Effect of local minima on adiabatic quantum optimization

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that, for problems that have an exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation.     

Role of coherence in adiabatic search algorithms

We systematically investigate the role of coherence in adiabatic search algorithms by using the relative entropy measure of coherence. Both in the ideal case (adiabatic evolution) and the non-ideal case (nonadiabatic evolution), the success probability increases with the decreases of coherence. In addition, the coherence depletion in global adiabatic search algorithm, local adiabatic search algorithm and an adiabatic search algorithm with constant evolution time was discussed. The results show that the coherence decreases faster in more efficient algorithm and an exponential decaying of coherence is necessary to achieve fast search (constant evolution time) in the adiabatic search algorithm. More importantly, we demonstrate that the efficiency of adiabatic search algorithm can be improved by utilizing appropriate method to speed up the coherence depletion.     

Adiabatic theorems and applications to the quantum hall effect

We study an adiabatic evolution that approximates the physical dynamics and describes a natural parallel transport in spectral subspaces. Using this we prove two folk theorems about the adiabatic limit of quantum mechanics: 1. For slow time variation of the Hamiltonian, the time evolution reduces to spectral subspaces bordered by gaps. 2. The eventual tunneling out of such spectral subspaces is smaller than any inverse power of the time scale if the Hamiltonian varies infinitly smoothly over a finite interval. Except for the existence of gaps, no assumptions are made on the nature of the spectrum. We apply these results to charge transport in quantum Hall Hamiltonians and prove that the flux averaged charge transport is an integer in the adiabatic limit.     

Quantum-Classical Correspondence for Adiabatic Shortcut in Two- and Three-Level Atoms

The methods of quickly achieving the adiabatic effect through a non-adiabatic process has recently drawn widely attention both in quantum and classical regime. In this work ,we study the classical adiabatic shortcut for two- and three-Level atoms by transforming the quantum version into classical one via quantum-classical corresponding theory. The results shows that, the additional couplings between the oscillators can be used to speed up the adiabatic evolution of coupled oscillators. Furthermore, we find that the quantum-classical correspondence theory still holds for the couter-adiabatic driving Hamiltonian for the TQD. This means that, we can obtain the counter-adiabatic driving Hamiltonian for a classical system by averaging over its quantum correspondence in a quantum system. This provides a feasible way to study the classical adiabatic shortcut and the simulation for the quantum adiabatic shortcut in a classical system.

     

On the Role of Prior Probability in Adiabatic Quantum Algorithms

In this paper, we study the role of prior probability on the efficiency of quantum local adiabatic search algorithm. The following aspects for prior probability are found here: firstly, only the probabilities of marked states affect the running time of the adiabatic evolution; secondly, the prior probability can be used for improving the efficiency of the adiabatic algorithm; thirdly, like the usual quantum adiabatic evolution, the running time for the case of multiple solution states where the number of marked elements are smaller enough than the size of the set assigned that contains them can be significantly bigger than that of the case where the assigned set only contains all the marked states.     

Highly efficient charging and discharging of three-level quantum batteries through shortcuts to adiabaticity

Quantum batteries are energy storage devices that satisfy quantum mechanical principles. How to improve the battery’s performance such as stored energy and power is a crucial element in the quantum battery. Here, we investigate the charging and discharging dynamics of a three-level counterdiabatic stimulated Raman adiabatic passage quantum battery via shortcuts to adiabaticity, which can compensate for undesired transitions to realize a fast adiabatic evolution through the application of an additional control field to an initial Hamiltonian. The scheme can significantly speed up the charging and discharging processes of a three-level quantum battery and obtain more stored energy and higher power compared with the original stimulated Raman adiabatic passage. We explore the effect of both the amplitude and the delay time of driving fields on the performances of the quantum battery. Possible experimental implementation in superconducting circuit and nitrogen–vacancy center is also discussed.     

On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms

In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.     

A Necessary Condition for Quantum Adiabaticity Applied to the Adiabatic Grover Search

Numerous sufficient conditions for adiabaticity of the evolution of a driven quantum system have been known for quite a long time. In contrast, necessary adiabatic conditions are scarce. Recently a practicable necessary condition well suited for many-body systems has been proved. Here we tailor this condition for estimating run times of adiabatic quantum algorithms. As an illustration, the condition is applied to the adiabatic algorithm for searching in an unstructured database (adiabatic Grover search algorithm). We find that the thus obtained lower bound on the run time of this algorithm reproduces \( \sqrt{N} \) scaling (with N being the number of database entries) of the explicitly known optimum run time. This is in contrast to the poor performance of the known sufficient adiabatic conditions, which guarantee adiabaticity only for a run time on the order of O(N), which does not constitute any speedup over the classical database search. This observation highlights the merits of the new adiabatic condition and its potential relevance to adiabatic quantum computing.     

Fast Implementation of Quantum Phase Gates and Creation of Cluster States via Transitionless Quantum Driving

In this paper, combining transitionless quantum driving and quantum Zeno dynamics, we propose an efficient scheme to fast implement a two-qubit quantum phase gate which can be used to generate cluster state of atoms trapped in distant cavities. The influence of various of various error sources including spontaneous emission and photon loss on the fidelity is analyzed via numerical simulation. The results show that this scheme not only takes less time than adiabatic scheme but also is not sensitive to both error sources. Additionally, a creation of N-atom cluster states is put forward as a typical example of the applications of the phase gates.     

Does adiabatic quantum optimization fail for NP-complete problems?

It has been recently argued that adiabatic quantum optimization would fail in solving NP-complete problems because of the occurrence of exponentially small gaps due to crossing of local minima of the final Hamiltonian with its global minimum near the end of the adiabatic evolution. Using perturbation expansion, we analytically show that for the NP-hard problem known as maximum independent set, there always exist adiabatic paths along which no such crossings occur. Therefore, in order to prove that adiabatic quantum optimization fails for any NP-complete problem, one must prove that it is impossible to find any such path in polynomial time.     

Exact Equivalence between Quantum Adiabatic Algorithm and Quantum Circuit Algorithm

We present a rigorous proof that quantum circuit algorithm can be transformed into quantum adiabatic algorithm with the exact same time complexity. This means that from a quantum circuit algorithm of L gates we can construct a quantum adiabatic algorithm with time complexity of O(L). Additionally, our construction shows that one may exponentially speed up some quantum adiabatic algorithms by properly choosing an evolution path.     

Adiabatic evolution under quantum control

One difficulty with adiabatic quantum computation is the limit on the computation time. Here we propose two schemes to speed-up the adiabatic evolution. To apply this controlled adiabatic evolution to adiabatic quantum computation, we design one of the schemes without any explicit knowledge of the instantaneous eigenstates of the final Hamiltonian. Whereas in another scheme, we assume that the ground state of the Hamiltonian is known, and this information can be used to design the control. By these techniques, a linear speed-up proportional to the nonlinearity can be predicted. As an illustration, we study a two-level system driven by a time-dependent magnetic field under the control. The problem of finding an item in an unsorted database by adiabatic evolution is also examined. The physics behind the control scheme is interpreted.     

远距离三原子量子纠缠特性与其应用

三原子分别被束缚在用光纤环形连接单侧泄漏微光学腔场中,在微腔中输入激光驱动场和施加局域激光场,利用输入-输出技术及绝热近似理论,推导出一维Ising链模型的有效哈密顿量,该哈密顿量表明该系统会诱导出三原子中的任意两原子纠缠及三原子纠缠,用伴随数(concurrence)度量两原子纠缠,用内禀纠缠度量三原子纠缠,通过数值计算,给出两原子和三原子纠缠随时间演化曲线,通过适当调控激光驱动场和局域激光场,在远距离三原子中任意两原子实现未知量子态的隐形传送。