Universal fault-tolerant quantum computation on decoherence-free subspaces

A general scheme to perform universal, fault-tolerant quantum computation within decoherence-free subspaces (DFSs) is presented. At most two-qubit interactions are required, and the system remains within the DFS throughout the entire implementation of a quantum gate. We show explicitly how to perform universal computation on clusters of the four-qubit DFS encoding one logical qubit each under spatially symmetric (collective) decoherence. Our results have immediate relevance to quantum computer implementations in which quantum logic is implemented through exchange interactions, such as the recently proposed spin-spin coupled quantum dot arrays and donor-atom arrays.     

Long Distance Quantum Communication Over a Noisy Channel

The creation of a quantum network is an important goal of quantum intormation processing. Long distance quantum communication with high fidelity is the main obstacle in achieving this goal. A scheme to transmit qubits without fidelity decrease over the noisy channel is presented. Using the idea of ＂ time-bin entanglement＂ , the scheme works without any auxiliary particles and there is no resources increase with the length of the channel. The scheme is feasible with the current experimental technology.     

Universal quantum computation with spin-1/2 pairs and Heisenberg exchange

An efficient and intuitive framework for universal quantum computation is presented that uses pairs of spin-1/2 particles to form logical qubits and a single physical interaction, Heisenberg exchange, to produce all gate operations. Only two Heisenberg gate operations are required to produce a controlled pi-phase shift, compared to nineteen for exchange-only proposals employing three spins. Evolved from well-studied decoherence-free subspaces, this architecture inherits immunity from collective decoherence mechanisms. The simplicity and adaptability of this approach should make it attractive for spin-based quantum computing architectures.     

Scalable quantum computing in decoherence-free subspaces with Cooper-pair box qubits

We theoretically propose a feasible scheme to perform quantum computing in decoherence-free subspaces (DFSs) with Cooper-pair box (CPB) qubits arrayed in a circuit QED architecture. Based on the cavity-bus assisted interaction, the selective and controllable interqubit couplings occur only by adjusting the individual gate pulses, by which we obtain the scalable DFS-encoded universal quantum gates to resist certain collective noises. Further analysis shows the protocol may implement the scalable fault-tolerant quantum computing with current experimental means.     

Universal quantum computation through control of spin-orbit coupling

We propose a method for quantum computation which uses control of spin-orbit coupling in a linear array of single electron quantum dots. Quantum gates are carried out by pulsing the exchange interaction between neighboring electron spins, including the anisotropic corrections due to spin-orbit coupling. Control over these corrections, even if limited, is sufficient for universal quantum computation over qubits encoded into pairs of electron spins. The number of voltage pulses required to carry out either single-qubit rotations or controlled-Not gates scales as the inverse of a dimensionless measure of the degree of control of spin-orbit coupling.     

Double-occupancy probability and entanglement of two holes in double Ge/Si quantum dots

We have calculated the exchange energy, double occupation probability of the lowest singlet state, and degree of entanglement of two holes in vertically coupled double Ge/Si quantum dots. We determined the conditions on which the exchange coupling is large enough for a fast swap operation in quantum computation and the double-occupancy probability is still low, thus maximizing the entanglement for a small computation error. We found that both the degree of entanglement and double-occupancy probability for quantum dots with different dot size collapse onto universal, size independent curves when plotted as a function of singlet-triplet splitting.     

Heisenberg方程的保结构计算

出了Heishenberg方程的保等时交换关系-辛格式,为Heishenberg图景下计算量子系统(特别是时间相关外场中的原子)的时间演化提供了保结构的算法,用这种算法计算了一个非线性谐振子,结果显示保等时交换关系-辛格式对求解Heishenberg方程是精确和有效的.     

Swap action in a solid-state controllable anisotropic Heisenberg model

Correct swap action can be realized via the control of the anisotropic Heisenberg interaction in solid-state quantum systems. The conditions of performing a swap are derived by the dynamics of arbitrary bipartite pure state. It is found that swap errors can be eliminated in the presence of symmetric anisotropy. In realistic quantum computers with unavoidable fluctuations, the gate fidelity of swap action is estimated. The scheme of quantum computation via the anisotropic Heisenberg interaction is implemented in a one-dimensional quantum dots. The slanting and static magnetic field can be used to adjust the anisotropy.     

Robust Quantum Gates in Decoherence-Free Subspaces with Josephson Charge Qubits

We propose a new and feasible scheme to implement quantum gates in decoherence-free subspaces (DFSs) with Josephson charge qubits situated in a circuit QED architecture. Based on the resonator-assisted interaction, the controllable interqubit couplings occur only by tuning the individual flux biases, by which we obtain the DFS-encoded universal quantum gates. Compared with the non-DFS situation, we numerically consider the robustness of the DFS-encoded scheme that can be insensitive to the collective noises. Thus the protocol may perform the fault-tolerant quantum computing with Josephson charge qubits.     

Quantum computing with spin cluster qubits

We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) antiferromagnetic exchange interaction with uniform and nonuniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and intercluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decoherence times and short gate operation times of single spins. Control of single spins is hence not necessary for the realization of universal quantum gates.     

Dressed qubits

Inherent gate errors can arise in quantum computation when the actual system Hamiltonian or Hilbert space deviates from the desired one. Two important examples we address are spin-coupled quantum dots in the presence of spin-orbit perturbations to the Heisenberg exchange interaction, and off-resonant transitions of a qubit embedded in a multilevel Hilbert space. We propose a "dressed qubit" transformation for dealing with such inherent errors. Unlike quantum error correction, the dressed qubit method does not require additional operations or encoding redundancy, is insensitive to error magnitude, and imposes no new experimental constraints.     

Practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not, are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. We present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this result for systems of arbitrary finite dimension has been provided by Brylinski and Brylinski; however, their proof relies on a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical.     

Realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions

Quantum computers are in hot-spot with the potential to handle more complex problems than classical computers can.Realizing the quantum computation requires the universal quantum gate set {T,H,CNOT} so as to perform any unitary transformation with arbitrary accuracy.Here we first briefly review the Majorana fermions and then propose the realization of arbitrary two-qubit quantum gates based on chiral Majorana fermions.Elementary cells consist of a quantum anomalous Hall insulator surrounded by a topological superconductor with electric gates and quantum-dot structures,which enable the braiding operation and the partial exchange operation.After defining a qubit by four chiral Majorana fermions,the singlequbit T and H quantum gates are realized via one partial exchange operation and three braiding operations,respectively.The entangled CNOT quantum gate is performed by braiding six chiral Majorana fermions.Besides,we design a powerful device with which arbitrary two-qubit quantum gates can be realized and take the quantum Fourier transform as an example to show that several quantum operations can be performed with this space-limited device.Thus,our proposal could inspire further utilization of mobile chiral Majorana edge states for faster quantum computation.     

Creation of cluster state of four ions in ion-trap system by individual addressing

The cluster state is a special, highly entangled quantum state that forms the universal resource, on which measurement-based quantum computation can be performed. In this study, a new scheme is presented for creating four-ions cluster state in ion-trap system. This scheme is based on resonant sideband excitation in which the population is transferred to target states by precise control of pulse area. Meanwhile, the scheme is consist of combination of elementary stages belonging to a universal set whereby cluster state has been created in five interaction stages by individually addressed ions with red- or blue-sideband resonance laser pulses. The paper studies the population transfer of the system by numerical solutions of the master equation, considering the effect of decoherence channels due to dissipation in the phonon modes. The presented scheme does not require control of the turn-off ratio and time delay among pulses.     

Quantum chaos and random matrix theory for fidelity decay in quantum computations with static imperfections

We determine the universal law for fidelity decay in quantum computations of complex dynamics in presence of internal static imperfections in a quantum computer. Our approach is based on random matrix theory applied to quantum computations in presence of imperfections. The theoretical predictions are tested and confirmed in extensive numerical simulations of a quantum algorithm for quantum chaos in the dynamical tent map with up to 18 qubits. The theory developed determines the time scales for reliable quantum computations in absence of the quantum error correction codes. These time scales are related to the Heisenberg time, the Thouless time, and the decay time given by Fermis golden rule which are well-known in the context of mesoscopic systems. The comparison is presented for static imperfection effects and random errors in quantum gates. A new convenient method for the quantum computation of the coarse-grained Wigner function is also proposed.Received: 13 December 2003, Published online: 18 March 2004PACS: 03.67.Lx Quantum computation - 05.45.Pq Numerical simulations of chaotic systems - 05.45.Mt Quantum chaos; semiclassical methods     

Quantum Breathers in an Anisotropic Ferromagnetic Heisenberg Chain with Biquadratic Exchange Interaction

Based on the Hartree approximation and the semidiscrete multiple-scale method, quantum breathers in an anisotropic ferromagnetic Heisenberg chain with biquadratic exchange interaction are predicted analytically. The existence condition of quantum breathers is obtained, and the properties of quantum breathers are analyzed. Moreover, it is shown that the energy of such quantum breathers is quantized.     

Quantum Heat Engines with Complex Working Media,Complete Otto Cycles and Heuristics

Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.     

几何量子计算

实现可集成的量子计算的关键步骤是实现保真度足够高的一组普适量子逻辑门，最近几年发展的几何量子计算使用几何位相来实现量子逻辑门，其特点是利用几何位相的整体几何性质来避免某些局域的无规噪声的影响，从而实现较高保真度的量子门，文章先简要介绍常规几何量子逻辑门的概念，然后重点介绍最近提出的非常规几何量子计算：量子计算中使用的逻辑门的总位相既包含有几何位相，又包含有动力学位相，但它仅依赖于一些几何特征，而且，对于任意的量子位输入态，在量子门操作过程中积累的位相要么是零，要么是仅依赖几何特征的位相。     

海森堡XYZ自旋链系统的热纠缠与局域量子不确定性研究

研究了热平衡温度，自旋交换相互作用，Dzyaloshinskii-Moriya(DM)相互作用及外加非一致性磁场对两比特海森堡XYZ自旋链量子系统的热纠缠与局域量子不确定度的影响，对比分析了并发度量子纠缠与局域量子不确定度描述自旋链系统量子关联的差别.结果表明自旋链系统的量子纠缠在热平衡温度，DM相互作用及外加磁场的非一致性参数的变化情况下均会出现纠缠突然死亡的再生现象，而自旋链系统的局域量子不确定度随着这些参数呈连续变化现象.并且，自旋交换相互作用，DM相互作用及外加横向磁场作用强度较小时，他们的变化对自旋链系统的量子纠缠与局域量子不确定度的影响有着明显的差别.     

Quantum anisotropic Heisenberg triangular antiferromagnet: application to CsCuCl3

Triangular anisotropic Heisenberg antiferromagnet shares with the triangular planar antiferromagnet the rich phenomenology found in presence of an external magnetic field. The physical interest in the triangular Heisenberg model is obvious because the planar model has not the quantum analogous one and, more seriously, it does not allow out-of-plane fluctuations so that it provides a very rough representation of actual magnetic insulators. Indeed, we show that magnetic resonance data on CsCuCl₃ are satisfactorily understood on the basis of the properties of the quantum triangular Heisenberg antiferromagnet with easy-plane exchange anisotropy.