We propose a new class of unconventional geometric gates involving nonzero dynamic phases, and elucidate that geometric quantum computation can be implemented by using these gates. Comparing with the conventional geometric gate operation, in which the dynamic phase shift must be removed or avoided, the gates proposed here may be operated more simply. We illustrate in detail that unconventional nontrivial two-qubit geometric gates with built-in fault tolerant geometric features can be implemented in real physical systems.PACS numbers: 03.67. Lx, 03.65.Vf, 03.67.Pp Quantum computation takes its power from superposition and entanglement, which are two main features distinguishing the quantum world from the classical world. But they are also very fragile and may be destroyed easily by a process called decoherence. The suppression of these decoherence effects in a large-scalable quantum computer is essential for construction of workable quantum logical devices. Quantum error-correcting codes [1] enable quantum computers to operate despite some degree of decoherence and may make quantum computers experimentally realizable, provided that the noise in individual quantum gates is below a certain constant threshold. The recently estimated threshold is that the individual gate infidelity should be of the order 10. In order for this precision to be possible, quantum gates must be operated in a built-in fault tolerant manner.Apart from a decoherence-free scheme [3], a promising approach to achieve built-in fault tolerant quantum gates is based on geometric phase shifts [4][5][6]. A universal set of quantum gates [7] may be realized using geometric phase shifts when the Hamiltonian of the qubit system changes along suitable loops in a control space [8][9][10][11][12][13][14][15]. A quantum gate is expressed by a unitary evolution operator U ({γ}), where the set {γ} are phases acquired in a particular evolution in realization of the gate, and usually these phases consist of both geometric (γ g ) and a dynamic (γ d ) components [4][5][6]. U ({γ}) is specified as a geometric gate if the phase γ in the gate-operation is a pure geometric one(i.e., with zero dynamic phase in the evolution), and quantum computation implemented in this way is referred to as geometric quantum computation (GQC) in a general sense [8][9][10][11][12][13][14][15]. GQC demands that logical gates in computing are realized by using geometric phase shifts, so that it may have the inherently fault-tolerant advantage due to the fact that the geometric phases depend only on some global geometric features. Although this property was doubted by some numerical calculations with * zwang@hkucc.hku.hk certain decohering mechanisms [16], an analytical result showed that geometric phases may be robust against dephasing [17]. Several basic ideas of adiabatic GQC by using NMR [9], superconducting nanocircuits [10], trapped ions [11], or semiconductor nanostructure [12] were proposed, and the generalization to nonadiabatic case was also suggested [13][14][15].According ...

We propose a large-scale quantum computer architecture by stabilizing a single large linear ion chain in a very simple trap geometry. By confining ions in an anharmonic linear trap with nearly uniform spacing between ions, we show that high-fidelity quantum gates can be realized in large linear ion crystals under the Doppler temperature based on coupling to a near-continuum of transverse motional modes with simple shaped laser pulses.PACS numbers: 03.67. Lx, 32.80.Qk, 03.67.Pp Trapped atomic ions remain one of the most attractive candidates for the realization of a quantum computer, owing to their long-lived internal qubit coherence and strong laser-mediated Coulomb interaction [1,2,3,4]. Various quantum gate protocols have been proposed [1,5,6,7,8,9] and many have been demonstrated with small numbers of ions [4,10,11,12,13,14]. The central challenge now is to scale up the number of trapped ion qubits to a level where the quantum behavior of the system cannot be efficiently modeled through classical means [4]. The linear rf (Paul) trap has been the workhorse for ion trap quantum computing, with atomic ions laser-cooled and confined in 1D crystals [1,2,3,4] (although there are proposals for the use of 2D crystals in a Penning trap [15] or array of microtraps [6]). However, scaling the linear ion trap to interesting numbers of ions poses significant difficulties [2,4]. As more ions are added to a harmonic axial potential, a structural instability causes the linear chain to buckle near the middle into a zigzag shape [16], and the resulting low-frequency transverse modes and the off-axis rf micromotion of the ions makes gate operation unreliable and noisy. Even in a linear chain, the complex motional mode spectrum of many ions makes it difficult to resolve individual modes for quantum gate operations, and to sufficiently laser cool many low-frequency modes. One promising approach is to operate with small linear ion chains and multiplex the system by shuttling ions between multiple chains through a maze of trapping zones, but this requires complicated electrode structures and exquisite control of ion trajectories [2,17].In this paper, we propose a new approach to ion quantum computation in a large linear architecture that circumvents the above difficulties. This scheme is based on combination of several ideas. First, an anharmonic axial trap provided by static electrode potentials can stabilize a single linear crystal containing a large number of ions. Second, tightly-confined and closely-spaced transverse phonon modes can mediate quantum gate operations in a large architecture [18], while eliminating the need for single-mode resolution and multimode sideband cooling. Third, gate operations on the large ion array exploit the local character of the laser-induced dipole interaction that is dominated by nearby ions only. As a result, the complexity of the quantum gate does not increase with the size of the system.The proposed ion architecture is illustrated in Fig. 1. It is a large linear array where the strong confi...

Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible mechanism for realizing robust QST via topologically protected edge states in superconducting qubit chains. Using superconducting Xmon qubits with tunable couplings, we construct generalized Su-Schrieffer-Heeger models and analytically derive the wave functions of topological edge states. We find that such edge states can be employed as a quantum channel to realize robust QST between remote qubits. With a numerical simulation, we show that both single-qubit states and two-qubit entangled states can be robustly transferred in the presence of sizable imperfections in the qubit couplings. The transfer fidelity demonstrates a wide plateau at the value of unity in the imperfection magnitude. This approach is general and can be implemented in a variety of quantum computing platforms.

A quantum memory, for storing and retrieving flying photonic quantum states, is a key interface for realizing long-distance quantum communication and large-scale quantum computation. While many experimental schemes of high storage-retrieval efficiency have been performed with weak coherent light pulses, all quantum memories for true single photons achieved so far have efficiencies far below 50%, a threshold value for practical applications. Here, we report the demonstration of a quantum memory for single-photon polarization qubits with an efficiency of >85% and a fidelity of >99%, basing on balanced two-channel electromagnetically induced transparency in laser-cooled rubidium atoms. For the singlechannel quantum memory, the optimized efficiency for storing and retrieving single-photon temporal waveforms can be as high as 90.6%. Our result pushes the photonic quantum memory closer to its practical applications in quantum information processing.

We propose a scheme to implement arbitrary-speed quantum entangling gates on two trapped ions immersed in a large linear crystal of ions, with minimal control of laser beams. For gate speeds slower than the oscillation frequencies in the trap, a single appropriately-detuned laser pulse is sufficient for high-fidelity gates. For gate speeds comparable to or faster than the local ion oscillation frequency, we discover a fivepulse protocol that exploits only the local phonon modes. This points to a method for efficiently scaling the ion trap quantum computer without shuttling ions.Significant advances have been made towards trapped ion quantum computation in the last decade [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Many ingredients of quantum computing have been demonstrated experimentally with this system [7][8][9][10][11][12][13][14][15][16][17]; and different versions of quantum gate schemes have been proposed, each offering particular advantages [2][3][4][5][6][18][19][20]. In conventional approaches to trapped ion quantum gates, the interaction between the ions is mediated by a particular phonon mode (PM) in the ion crystal through the sideband addressing with laser beams. In these types of gates, the control of the laser beams is relatively simple, requiring only a continuous-wave beam with an appropriate detuning; but to resolve individual motional sidebands, the gate speed must be much smaller than the ion trap oscillation frequencies. More recently, fast quantum gates have also been proposed, which can operate with a speed comparable with or greater than the trap frequencies [19,20]. These types of gates involve simultaneous excitation of all PMs [17][18][19][20] and require more complicated control of either the pulse shape [19] and/or the timing of a fast pulse sequence [19,20].In this paper, we develop a gate scheme that combines the desirable features of the above two types of gates. A conditional phase gate with arbitrary speed is constructed in a large ion array by optimization of few relevant experimental parameters. As a result, first we show that with simple control of the detuning of a continuous-wave laser beam, one can achieve a high fidelity gate with the gate speed approaching the ion trap frequency. This result is a bit surprising as many PMs are excited during the gate. However, with control of just one experimental parameter (the detuning), each of the modes becomes nearly disentangled with the ion internal states at the end of the gate. Secondly, we show that as the gate speed becomes larger than the local ion oscillation frequency (specified below and see also Ref.[20]), only "local" PMs will be primarily excited during the gate. This yields a scaling method for trapped ion quantum computation: a significant scaling obstacle to trapped ion quantum computation is that due to the long range Coulomb interaction, any collective gate on two ions is necessarily influenced by all the other ions in the architecture, which makes the gate control increasingly difficu...

Accurate control of a quantum system is a fundamental requirement in many areas of modern science ranging from quantum information processing to high-precision measurements. A significantly important goal in quantum control is preparing a desired state as fast as possible, with sufficiently high fidelity allowed by available resources and experimental constraints. Stimulated Raman adiabatic passage (STIRAP) is a robust way to realize high-fidelity state transfer but it requires a sufficiently long operation time to satisfy the adiabatic criteria. Here we theoretically propose and then experimentally demonstrate a shortcut-to-adiabatic protocol to speed-up the STIRAP. By modifying the shapes of the Raman pulses, we experimentally realize a fast and high-fidelity stimulated Raman shortcut-to-adiabatic passage that is robust against control parameter variations. The all-optical, robust and fast protocol demonstrated here provides an efficient and practical way to control quantum systems.

We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.

The realistic application of geometric quantum computation is crucially dependent on an unproved robustness conjecture, claiming that geometric quantum gates are more resilient against random noise than dynamic gates. We propose a suitable model that allows a direct and fair comparison between geometrical and dynamical operations. In the presence of stochastic control errors we find that the maximum of gate fidelity corresponds to quantum gates with a vanishing dynamical phase. This is a clear evidence for the robustness of nonadiabatic geometric quantum computation. The predictions here presented can be experimentally tested in almost all of the already existing quantum computer candidates.An essential prerequisite for quantum computation ͑QC͒ is the ability to maintain quantum coherence and quantum entanglement in an information-processing system ͓1͔. Unfortunately, since both these properties are very fragile against control errors as well as against unwanted couplings with environment, this goal is extremely hard to achieve. To this end several strategies have been developed, most notably quantum error correction ͓2͔, decoherence-free subspace ͓3͔, and bang-bang techniques ͑dynamical suppression of decoherence͒ ͓4͔.Quantum computation implemented by geometric phases ͓5͔ is believed to be another approach that can be used to overcome certain kinds of errors ͓6-10͔. However, the statement that quantum gates ͑QGs͒ achieved by this way may have built-in fault-tolerant features ͑due to the fact that geometric phases depend only on some global geometric properties͒ has still the status of a debated conjecture. Indeed this alleged resilience against errors of geometrical gates has been doubted by some numerical calculations including certain decohering mechanisms ͓11,12͔. On the other hand, analytical results show that the adiabatic Berry's phase itself may be robust against dephasing ͓13͔ and stochastic fluctuations of control parameters ͓14͔. These latter provide a sort of indirect evidence for the robustness of adiabatic geometric QC, but a more direct and convincing evidence is still missing. Since any realistic application of geometric QC is crucially dependent on this robustenss conjecture, to prove or to reject it unavoidably becomes one of the key tasks in the field of geometric QC.In this paper we analyze a scheme for QC that is suitable to distinguish the difference between geometric QGs and dynamic gates and then provide a clear-cut evidence for the robustness of nonadiabatic geometric QC. The main points we are going to make are the following:͑i͒ The main difficulty in proving or rejecting the robustness conjecture is that one does not have a suitable model that allows a direct and fair comparison between geometrical and dynamical operations. The difficulty is overcome by the model analyzed here. The model is, in a sense, a hybrid between the purely geometric QG and the standard dynamic one; by tuning the parameters, the QGs can be continuously changed from one kind to theother. Thus, studying the change...