Dissipative decoherence in the Grover algorithm

Using the methods of quantum trajectories we study effects of dissipative decoherence on the accuracy of the Grover quantum search algorithm. The dependence on the number of qubits and dissipation rate are determined and tested numerically with up to 16 qubits. As a result, our numerical and analytical studies give the universal law for decay of fidelity and probability of searched state which are induced by dissipative decoherence effects. This law is in agreement with the results obtained previously for quantum chaos algorithms.     

Quantum phase estimation algorithm in presence of static imperfections

We study numerically the effects of static imperfections and residual couplings between qubits for the quantum phase estimation algorithm with two qubits. We show that the success probability of the algorithm is affected significantly more by static imperfections than by random noise errors in quantum gates. An improvement of the algorithm accuracy can be reached by application of the Pauli-random-error-correction method (PAREC).     

Performance of equal phase-shift search for one iteration

Grover presented the phase-shift search by replacing the selective inversions by selective phase shifts of π/3. In this paper, we investigate the phase-shift search with general equal phase shifts. We show that for small uncertainties, the failure probability of the phase-π/3 search is smaller than the general phase-shift search and for large uncertainties, the success probability of the large phase-shift search is larger than the phase-π/3 search. Therefore, the large phase-shift search is suitable for large-size of databases.     

基于超导量子比特网络的Grover搜索算法实现方案

首先,提出了一个改进超导电路结构,此结构能实现任意两个量子比特的相互作用而非近邻作用,长程作用是实现量子计算所必需的,此结构能用目前的技术制作。其次,基于此结构提出了Grover搜索算法实现的物理方案。由于能实现任意两量子比特之间的控制相位门,所以多比特Grover搜索算法也能实现,以满足各种量子计算的需要。此方案是一个基于电流控制的超导电荷比特网络结构的可扩展及易实现的Grover搜索算法实现方案。     

Eigenstates of an operating quantum computer: hypersensitivity to static imperfections

We study the properties of eigenstates of an operating quantum computer which simulates the dynamical evolution in the regime of quantum chaos. Even if the quantum algorithm is polynomial in number of qubits n_q, it is shown that the ideal eigenstates become mixed and strongly modified by static imperfections above a certain threshold which drops exponentially with n_q. Above this threshold the quantum eigenstate entropy grows linearly with n_q but the computation remains reliable during a time scale which is polynomial in the imperfection strength and in n_q. Received 7 March 2002/ Received in final form 3 May 2002 Published online 19 July 2002     

Resilient quantum computation in correlated environments: a quantum phase transition perspective

We analyze the problem of a quantum computer in a correlated environment protected from decoherence by quantum error correction using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of the computer and the scaling dimension of the correlations. For an irrelevant flow, the error probability is reduced to a stochastic form for a long time and/or a large number of qubits; thus, the traditional derivation of the threshold theorem holds for these error models. In this way, the "threshold theorem" of quantum computing is rephrased as a dimensional criterion.     

Arbitrary state controlled-unitary gate between two remote atomic qubits via adiabatic passage

We generalize the scheme of Lacour et al. [X. Lacour, N. Sangouard, S. Guerin, H.R. Jauslin, Phys. Rev. A 73 (2006) 042321] to the case of nonlocal qubits, which makes the resultant gate suitable for distributed quantum computation. In our scheme, two remote atomic qubits are separately trapped in two distant cavities connected by an optical fiber. Based on adiabatic passage, our scheme is immune to the decoherence due to spontaneous emission and to photon decay from the cavity modes and the fiber mode. Moreover, our scheme can work robustly beyond the Lamb–Dicke limit. It is shown that the minimum fidelity of the resultant gate operation for an arbitrary input state could be over 0.98.     

Multi-particle and high-dimension controlled order rearrangement encryption protocols

Based on controlled order rearrange encryption (CORE) for quantum key distribution using EPR pairs [Fu.G. Deng, G.L. Long, Phys. Rev. A 68, 042315 (2003)], we propose generalized controlled order rearrangement encryption (GCORE) protocols of N qubits and N qutrits, and concretely display them in cases using 3-qubit, 2-qutrit maximally entangled basis states. We further show that our protocols will become safer with an increase in dimensions and number of particles. Moreover, we carry out the security analysis using quantum covariant cloning machine. Although the applications of the generalized scheme need to be further studied, GCORE has many distinct features such as large capacity and high efficiency.     

Collective quantum decoherence induced by qubit-electron interaction

We investigate a model of quantum register composed of N qubits coupling with itinerant electrons by adopting the Born-Markov master equation. Decoherence induced by this coupling is studied for various initial states. By solving the master equation for N=4 with the numerical integration, we obtain time evolution of fidelity and linear entropy of the register. The decoherence rate of this model is proportional to ²|J^′| with J^′ being the exchange coupling strength of electrons and qubits. We also investigate the decoherence free subspace which provides a possible routine of applications in quantum computation.     

Stability investigation on quantum correlations of coupled qubits in non-Markovian process

Utilizing the concurrence and the quantum discord as the measure method, in this paper we compare and investigate the dynamic evolution features of quantum correlations of coupled qubits in non-Markovian process. We focus attention on decoherence effect influences the stability of quantum correlations. The investigation results show that because of the decoherence influence between the system and environment, the concurrence always evolves with time in oscillation form in the way of deaths and survivals, however, the quantum discord time evolution does not appear the deaths and survivals. The quantum discord survives obviously longer than concurrence, which indicates that quantum discord has a stronger ability to resist decoherence than entanglement. Through regulating and controlling the purity and entanglement of the initial quantum state, we can effectively suppress the decay of the quantum correlations, which is advantaged to complete the quantum information processing.     

Quantum computing in decoherence-free subspaces with superconducting charge qubits

Taking into account the main noises in superconducting charge qubits (SCQs), we propose a feasible scheme to realize quantum computing (QC) in a specially-designed decoherence-free subspace (DFS). In our scheme two physical qubits are connected with a common inductance to form a strong coupling subsystem, which acts as a logical qubit. Benefiting from the well-designed DFS, our scheme is helpful to suppress certain decoherence effects.     

One-step implementation of the Toffoli gate via quantum Zeno dynamics

Based on the quantum Zeno dynamics, we present a scheme for one-step implementation of a Toffoli gate via manipulating three rf superconducting quantum interference device (SQUID) qubits to resonantly interact with a superconducting cavity. The effects of decoherence such as spontaneous emission and the loss of cavity are also considered.     

Scheme for Generating Cluster States with Charge Qubits in a Cavity

Based on superconducting charge qubits （SCCQs） coupled to a single-mode microwave cavity, we propose a scheme for generating charge cluster states. For all SCCQs, the controlled gate voltages are all in their degeneracy points, the quantum information is encoded in two logic states of charge basis. The generation of the multi-qubit cluster state can be achieved step by step on a pair of nearest-neighbor qubits. Considering effective long-rang coupling, we provide an efficient way to one-step generating of a highly entangled cluster state, in which the qubit-qubit coupling is mediated by the cavity mode. Our quantum operations are insensitive to the initial state of the cavity mode by removing the influence of the cavity mode via the periodical evolution of the system. Thus, our operation may be against the decoherence from the cavity.     

Remanent quantum correlations in dissipative qubits

Starting from the exact evolution of a Markovian dissipative quantum walk, a non-Markovian decoherence of two qubits interacting with a phonon thermal bath has been investigated analytically using quantum information tools. Concurrence and quantum discord are affected in a complex way, showing that entanglement decreases with dissipation. At the limit where dissipation dominates, quantum correlations survive in time as ∝t^−1/2$\propto t^{-1/2}$. Thus, even under the influence of dissipation, two qubits retain their quantumness for a long time. Quantum correlations could be therefore observed for a long time in related photonic experiments.     

Entanglement dynamics of a three-qubit system interacting with a quantum spin environment

We investigate the entanglement dynamics and decoherence of a three-qubit system under a quantum spin environment at a finite temperature in the thermodynamics limit. For the case under study, we find the evolution of pairwise entanglement depends not only on the initial states but also on the parameters related to the system and the spin environment. In addition, an undesirable entanglement sudden death occurs in the process of entanglement evolution, and this effect can be controlled by the coupling constant between two qubits, external magnetic field, and the interaction between the system and the environment.     

An all-silicon linear chain NMR quantum computer

An updated version of our all-silicon quantum computing scheme [T.D. Ladd, J.R. Goldman, F. Yamaguchi, Y. Yamamoto, E. Abe, K.M. Itoh, Phys. Rev. Lett. 89 (2002) 017901. [3]] and the experimental progress towards its realization are discussed. We emphasize the importance of revisiting a wide range of isotope effects which have been explored over the past several decades for the construction of solid-state silicon quantum computers. Using RF decoupling techniques [T.D. Ladd, D. Maryenko, Y. Yamamoto, E. Abe, K.M. Itoh, Phys. Rev. B. 71 (2005) 014401] phase decoherence times T₂=25 s of ²⁹Si nuclear spins in single-crystal Si have been obtained at room temperature. We show that a linear chain of ²⁹Si stable isotopes with nuclear spin I=1/2 embedded in a spin free ²⁸Si stable isotope matrix can form an ideal building block for solid-state quantum information processors, especially, in the form of a quantum memory which requires a large number of operations within T₂ for the continuous error correction.     

Entanglement-assisted quantum logic gates for two remote qubits

We propose a protocol to realize quantum logic gates for two remote qubits via entanglement swapping. According to the scheme of quantum repeater presented by H.-J. Briegel et al., we can complete long-distance communication and computation. Compared with previous schemes through noisy channels, our protocol can overcome the limitation that error probability scales exponentially with the length of the channel. We illustrate this protocol in cavity QED system, but the idea can also be realized in other physical systems.     

A New Quantum Secure Direct Communication Protocol Using Decoherence-Free Subspace

A new quantum secure direct communication （QSDC） protocol is proposed by using decoherence free subspace （DFS） to avoid insecurity of the present QSDC protocols in a quantum noise channel. This protocol makes it easily for Bob and Alice to find eavesdropping in channel because the collective dephasing noise disappears in DFS. The probability of successful attack by Eve in this protocol is smaller than in BB84 protocol. Thus this protocol realizes secure QSDC and is feasible with present-day technology.     

The two-qubit amplitude damping channel: Characterization using quantum stabilizer codes

A protocol based on quantum error correction based characterization of quantum dynamics (QECCD) is developed for quantum process tomography on a two-qubit system interacting dissipatively with a vacuum bath. The method uses a 5-qubit quantum error correcting code that corrects arbitrary errors on the first two qubits, and also saturates the quantum Hamming bound. The dissipative interaction with a vacuum bath allows for both correlated and independent noise on the two-qubit system. We study the dependence of the degree of the correlation of the noise on evolution time and inter-qubit separation.     

Universal quantum logic gates in a scalable Ising spin quantum computer

We consider the model of quantum computer, which is represented as a Ising spin lattice, where qubits (spin-half systems) are separated by the isolators (two spin-half systems). In the idle mode or at the single bit operations the total spin of isolators is 0. There are no need of complicated protocols for correcting the phase and probability errors due to permanent interaction between the qubits. We present protocols for implementation of universal quantum gates with the rectangular radio-frequency pulses.