Adiabatic Quantum Gates

We discuss the logic implementation of quantum gates in the framework of the quantum adiabatic method, which uses the language of ground states, spectral gaps and Hamiltonians instead of the standard unitary transformation language.     

Unstructured Adiabatic Quantum Search

In the adiabatic quantum computation model, a computational procedure is described by the continuous time evolution of a time dependent Hamiltonian. We apply this method to the Grover's problem, i.e., searching a marked item in an unstructured database. Classically, the problem can be solved only in a running time of order O(N) (where N is the number of items in the database), whereas in the quantum model a speed up of order has been obtained. We show that in the adiabatic quantum model, by a suitable choice of the time-dependent Hamiltonian, it is possible to do the calculation in constant time, independent of the the number of items in the database. However, in this case the initial time-complexity of is replaced by the complexity of implementing the driving Hamiltonian.     

Quantum Algorithm for Hilbert's Tenth Problem

We explore in the framework of Quantum Computation the notion of Computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to the Turing halting problem and is known to be mathematically noncomputable, is proposed where quantum continuous variables and quantum adiabatic evolution are employed. If this algorithm could be physically implemented, as much as it is valid in principle—that is, if certain Hamiltonian and its ground state can be physically constructed according to the proposal—quantum computability would surpass classical computability as delimited by the Church—Turing thesis. It is thus argued that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles.     

Stark-Chirped Rapid Adiabatic Passage in Presence of Dissipation for Quantum Computation

Stark-chirped rapid adiabatic passage （SCRAP） is an important technique used for coherent quantum controls. In this paper we investigate how the practically-existing dissipation of the system influences on the efficiency of the passage, and thus the fidelities of the SCRAP-based quantum gates. With flux-biased Josephson qubits as a specifical example, our results show clearly that the efficiency of the logic gates implemented by SCRAP are robust against the weak dissipation. The influence due to the non-adiabtic transitions between the adiabatic passages is comparatively significantly small. Therefore, the SCRAP-based logic gates should be feasible for the realistic physical systems with noises.     

A Parallel Quantum Algorithm for the Satisfiability Problem

In this paper we present a classical parallel quantum algorithm for the satisfiability problem. We have exploited the classical parallelism of quantum algorithms developed in [G.L. Long and L. Xiao, Phys. Rev. A 69 （2004） 052303], so that additional acceleration can be gained by using classical parallelism. The quantum algorithm first estimates the number of solutions using the quantum counting algorithm, and then by using the quantum searching algorithm, the explicit solutions are found.     

Quantum Hamiltonian for the Rigid Rotator

An excess term exists when using hermitian form of Cartesian momentum p _i (i = 1,2,3) in usual kinetic energy 1/(2) p ² _i for the rigid rotator, and the correct kinetic energy turns to be 1/(2) (1/f _i ) p _i f _i p _i where f _i are dummy factors in classical mechanics and nontrivial in quantum mechanics.     

Quantum Density Peak Clustering Algorithm

A widely used clustering algorithm, density peak clustering (DPC), assigns different attribute values to data points through the distance between data points, and then determines the number and range of clustering by attribute values. However, DPC is inefficient when dealing with scenes with a large amount of data, and the range of parameters is not easy to determine. To fix these problems, we propose a quantum DPC (QDPC) algorithm based on a quantum DistCalc circuit and a Grover circuit. The time complexity is reduced to O(log(N2)+6N+N), whereas that of the traditional algorithm is O(N2). The space complexity is also decreased from O(N·⌈logN⌉) to O(⌈logN⌉).     

Maximum Speed of Quantum Evolution

In this paper, we discuss the question of the minimum time needed for any state of a given quantum system to evolve into a distinct (orthogonal) state. This problem is relevant to deriving physical limits in quantum computation and quantum information processing. Here, we consider both cases of nonadiabatic and adiabatic evolution and we derive the Hamiltonians corresponding to the minimum time evolution predicted by the Margolus–Levitin theorem.     

On a Nonlinear Model in Adiabatic Evolutions

In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using.     

Quantum Phase Gates for Trapped Ions via Adiabatic Passage

We propose a scheme to produce quantum phase gates for trapped ions. Taking advantage of the adiabatic evolution, the operation is insensitive to small fluctuations of experimental parameters. Furthermore, the spontaneous emission is suppressed since the ions have no probability of being populated in the electronic excited states.     

A Quantum Protocol for Millionaire Problem with Continuous Variables

In this paper, a protocol for quantum millionaire problem with continuous variables is proposed. In the protocol, two participants can compare the values of their fortune with the assistance of a semi-trusted third party （STTP）. Only EPR states are exploited in our protocol while most other protocols exploited d-dimensional Bell states. Two participants are just required to perform single particle operations, which makes our protocol more efficiently. Our protocol can ensure fairness, correctness, security and high efficiency as well. In our protocol, only the two participants can deduce the results of comparisons, others include STTP will learn no information. Our protocol can resist various kinds of attacks from both the outside eavesdroppers and the inside participants, even the STTP.     

Symmetry-Protected Quantum Adiabatic Evolution in Spontaneous Symmetry-Breaking Transitions

Quantum adiabatic evolution describes the dynamical evolution of a slowly driven Hamiltonian. In most systems undergoing spontaneous symmetry-breaking transitions, the symmetry-protected quantum adiabatic evolution can still appear, even when the two lowest eigenstates become degenerate. Here, a general derivation to revisit the symmetry-dependent transition and the symmetry-dependent adiabatic condition (SDAC) is given. Further, based on the SDAC, an adiabatic-parameter-fixed sweeping scheme is used for achieving fast adiabatic evolution, which is more efficient than the linear sweeping scheme. In the limit of small adiabatic parameter, an analytic inequality is obtained for the ground state fidelity only dependent on the adiabatic parameter. The general statements are then demonstrated via two typical systems. Besides, the robustness of the symmetry-dependent adiabatic evolution against weak symmetry-breaking sources is studied. The findings can be tested via the techniques in quantum annealing and may provide promising applications in practical quantum technologies.     

Sufficient Condition for Validity of Quantum Adiabatic Theorem

In this paper,we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem.The new sufficient condition can clearly remove the inconsistency and the counterexample of the quantum adiabatic theorem pointed out by Marzlin and Sanders.     

Elementary Quantum Gates Based on Intrinsic Interaction Hamiltonian

A kind of new operators, the generalized pseudo-spin operators are introduced and a universal intrinsic Hamiltonian of two-qubit interaction is studied in terms of the generalized pseudo-spin operators. A fundamental quantum gate U(θ) is constructed based on the universal Hamiltonian and shown that the roles of the new quantum gate U(θ) is equivalent, functionally, to the joint operation of Hadamard and C-Not gates.     

Elementary Quantum Gates Based on Intrinsic Interaction Hamiltonian

A kind of new operators, the generalized pseudo-spin operators are introduced and a universad intrinsic Hamiltonian of two-qubit interaction is studied in terms of the generalized pseudo-spin operators. A fundamental quantum gate U（θ） is constructed based on the universal Hamiltonian and shown that the roles of the new quantum gate U （θ） is equivalent, functionally, to the joint operation of Hadamard and C-Not gates.     

绝热量子计算理论引介

本文引介绝热量子计算理论评述量子绝热定理最新的应用.基于量子绝热方法在最新的前沿领域量子计算中建立量子绝热算法.我们引介"局域量子绝热",并考虑了这一局域绝热概念对量子算法的可能应用.     

绝热量子计算理论引介

本文引介绝热量子计算理论评述量子绝热定理最新的应用。基于量子绝热方法在最新的前沿领域量子计算中建立量子绝热算法。我们引介"局域量子绝热",并考虑了这一局域绝热概念对量子算法的可能应用。     

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.     

Three-Dimensional Quantum State Transferring Between Two Remote Atoms by Adiabatic Passage under Dissipation

Recently, Zhou et al. [Phys. Rev. A 79 （2009） 044304] proposed a scheme for transferring three-dimensional quantum states between remote atomic qubits confined in cavities connected by fibers through adiabatic passage. In order to avoid the decoherence due to spontaneous emission, Zhou et al. utilized the large detuning atom-field interaction. In the present paper, we discuss the influence of dissipation on the scheme in both the resonant atom-field interaction case and the large detuning case. We numerically analyze the success probability and the transferring fidelity. It is shown that the resonant case is a preferable choice for the technique of the stimulated Raman adiabatic passage （STIRAP） due to the shorter operation time and the smaller probability of dissipation.