Quantum computing with trapped ions

Quantum computers hold the promise of solving certain computational tasks much more efficiently than classical computers. We review recent experimental advances towards a quantum computer with trapped ions. In particular, various implementations of qubits, quantum gates and some key experiments are discussed. Furthermore, we review some implementations of quantum algorithms such as a deterministic teleportation of quantum information and an error correction scheme.     

Realization of Three-Qubit Controlled-Phase Gate Operation with Atoms in Cavity QED System

We propose a scheme for realization of three-qubit controlled-phase gate via passing two three-level atoms through a high-Q optical cavity in a cavity QED system. In the presented protocol, the two stable ground states of the atoms act as the two controlling qubits and the zero- and one-photon Fock states of the cavity-field form the target qubit, and no auxiliary state or any measurement is required. The numerical simulation shows that the gate fidelities remain at a high level under the influence of the atomic spontaneous emission, the decay of the cavity mode and deviation of the coupling strength. The experimental feasibility of our proposal is also discussed.     

Scheme for Implementing an N-Qubit Phase Gate via Selective Atom--Field Interaction with Cavity Quantum Electrodynamics

A scheme for implementing a two-qubit phase gate with atoms sent through a high-Q optical cavity is proposed by choosing nonidentical coupling constants between the atoms and cavity. The atomic spontaneous emission can be suppressed due to the large atom-field detuning. Moreover, the scheme can be generalized to implement an N-qubit phase gate and the gating time does not change with an increase of the number of qubits.     

Realization of a Multiqubit Conditional Phase Gate by Virtue of a Weak Coherent Light Field

We propose a scalable scheme to generate a multiqubit conditional phase gate by using a basic building block, i.e., a weak coherent optical pulse ｜α〉 reflected successively from a cavity with trapped atoms. In the scheme, we use a coherent state of light instead of a single photon source, homodyne measurement on a coherent light field instead of single photon detection, which reduces the complexity of the practical experiment. The outcomes of these measurements indicate either completion of the gate or the presence of the original qubits such that the operation can be repeated until it is successful.     

A Scheme for Atomic Entangled States and Quantum Gate Operations in Cavity QED

We propose a scheme for controllably entangling the ground states of five-state W-type atoms confined in a cavity and realizing swap gate and phase gate operations. In this scheme the cavity is only virtually excited and the atomic excited states are almost not occupied, so the produced entangled states and quantum logic operations are very robust against the cavity decay and atomic spontaneous emission.     

Quantum State Transfer in Trapped-Ion-Cavity Systems

We study the information transfer and entanglement transfer in a system consisting of single trapped ions in cavities by the three-mode cross-Kerr-like interaction among the cavity field （photons）, the centre-of-mass motion （phonons） and the internal state of the trapped ion in the Lamb-Dicke and large detuning regime.     

Intrinsic quantum computation

We introduce ways to measure information storage in quantum systems, using a recently introduced computation-theoretic model that accounts for measurement effects. The first, the quantum excess entropy, quantifies the shared information between a quantum process's past and its future. The second, the quantum transient information, determines the difficulty with which an observer comes to know the internal state of a quantum process through measurements. We contrast these with von Neumann entropy and quantum entropy rate and provide a closed-form expression for the latter for the class of deterministic quantum processes.     

fficient Scheme for Implementing a Fredkin Gate via Resonant Interaction with Two-Mode Cavity Quantum Electrodynamics

A scheme for implementing a Fredkin gate with an atom sent through a microwave cavity is proposed. The scheme is based on the resonant atom-cavity interaction so that the gating time is sharply short, which is important in view of decoherence.     

Research on Quantum Searching Algorithms Based on Phase Shifts

One iterative in Grover＇s original quantum search algorithm consists of two Hadamard-Walsh transformations, a selective amplitude inversion and a diffusion amplitude inversion. We concentrate on the relation among the probability of success of the algorithm, the phase shifts, the number of target items and the number of iterations via replacing the two amplitude inversions by phase shifts of an arbitrary φ = ψ（0 ≤, ψ≤ 27r）. Then, according to the relation we find out the optimal phase shifts when the number of iterations is given. We present a new quantum search algorithm based on the optimal phase shifts of 1.018 after 0.57π√M/N iterations. The new algorithm can obtain either a single target item or multiple target items in the search space with the probability of success at least 93.43%     

Quantum Partial Searching Algorithm of a Database with Several Target Items

Choi and Korepin [Quantum Information Processing 6（2007）243] presented a quantum partial search algorithm of a database with several target items which can find a target block quickly when each target block contains the same number of target items. Actually, the number of target items in each target block is arbitrary. Aiming at this case, we give a condition to guarantee performance of the partial search algorithm to be performed and the number of queries to oracle of the algorithm to be minimized. In addition, by further numerical computing we come to the conclusion that the more uniform the distribution of target items, the smaller the number of queries.     

Computation in finitary stochastic and quantum processes

We introduce stochastic and quantum finite-state transducers as computation-theoretic models of classical stochastic and quantum finitary processes. Formal process languages, representing the distribution over a process’ behaviors, are recognized and generated by suitable specializations. We characterize and compare deterministic and nondeterministic versions, summarizing their relative computational power in a hierarchy of finitary process languages. Quantum finite-state transducers and generators are a first step toward a computation-theoretic analysis of individual, repeatedly measured quantum dynamical systems. They are explored via several physical systems, including an iterated-beam-splitter, an atom in a magnetic field, and atoms in an ion trap—a special case of which implements the Deutsch quantum algorithm. We show that these systems’ behaviors, and so their information processing capacity, depends sensitively on the measurement protocol.     

Engineering of Two Quantum States via Conditional Measurement on Two-Mode Squeezed State

We propose a scheme for the simultaneously preparation radiation-field modes of a single photon and a superposition of zero- and one-photon states, based on the coherent quantum state displacement and photon subtraction from two-mode squeezed state. It is shown that the single-photon and the superposition states can be obtained by only choosing the suitable parameter of displacements. The experimental feasibility to accomplish this scheme is also discussed.     

Multiparty Quantum Secret Sharing of Classical Message using Cavity Quantum Electrodynamic System

An experimental feasible scheme of multiparty secret sharing of classical messages is proposed, based on a cavity quantum electrodynamic system. The secret messages are imposed on atomic Bell states initially in the sender＇s possession by local unitary operations. By swapping quantum entanglement of atomic Bell states, the secret messages are split into several parts and each part is distributed to a separate party. In this case, any subset of the entire party group can not read out the secret message but the entirety via mutual cooperations. In this scheme, to discriminate atomic Bell states, additional classical fields are employed besides the same highlydetuned single-mode cavities used to prepare atomic Bell states. This scheme is insensitive to the cavity decay and the thermal field, and usual joint Bell-state measurements are unnecessary.     

One-Step Generation of Cluster States Assisted by a Strong Driving Classical Field in Cavity Quantum Electrodynamics

We propose a scheme for one-step generation of cluster states with atoms sent through a thermal cavity with strong classical driving field, based on the resonant atom-cavity interaction so that the operating time is sharply short, which is important in the view of decoherence.     

One Atom in an Optical Cavity： Entanglement and Applications to Quantum Computation

We propose a scheme to implement two-bit .quantum phase gates and one-bit unitary gates by using the two- mode two-photon Jaynes Cummings model. The entanglement between the atom and cavity is also investigated in the presence of phase decoherence. It is found that there is stationary entanglement that is sensitive with the detuning     

Possible Realization of Cluster States and Quantum Information Transfer in Cavity QED via Raman Transition

We present a scheme to generate cluster states with many scheme, no transfer of quantum information between the atoms in cavity QED via Raman transition. In this atoms and cavities is required, the cavity fields are only virtually excited and thus the cavity decay is suppressed during the generation of cluster states. The atoms are always populated in the two ground states. Therefore, the scheme is insensitive to the atomic spontaneous emission and cavity decay. We also show how to transfer quantum information from one atom to another.     

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.     

Quantum State Transfer between Charge and Flux Qubits in Circuit-QED

We propose a scheme to implement quantum state transfer in a hybrid circuit quantum electrodynarnics （QED） system which consists of a superconducting charge qubit, a flux qubit, and a transmission line resonator （TLR）. It is shown that quantum state transfer between the charge qubit and the flux qubit can be realized by using the TLR as the data bus.     

Quantum Nonlocality and Entanglement of Pair Cat States with Phase Decoherence

We investigate the entanglement of pair cat states in the phase damping channel by adopting the log-negativity and then study the possible violations of Bell＇s inequalities for the pair cat states in terms of the Wigner representation in phase space based upon parity measurement and displacement operation.     

Coherent coupling of a single <Superscript>40</Superscript>Ca<Superscript>+</Superscript> ion to a high-finesse optical cavity

We demonstrate coherent coupling of the quadrupole S_1/2D_5/2 optical transition of a single trapped ⁴⁰Ca⁺ ion to the standing wave field of a high-finesse cavity. The dependence of the coupling on temporal dynamics and spatial variations of the intracavity field is investigated in detail. By precisely controlling the position of the ion in the cavity standing wave field and by selectively exciting vibrational state-changing transitions the ion’s quantized vibration in the trap is deterministically coupled to the cavity mode. We confirm coherent interaction of ion and cavity field by exciting Rabi oscillations with short resonant laser pulses injected into the cavity, which is frequency-stabilized to the atomic transition. Received: 23 August 2002 / Published online: 8 January 2003 RID="*" ID="*"Corresponding author. E-mail: christoph.becher@uibk.ac.at RID="**" ID="**"Present address: Time and Frequency Division, National Institute of Standards and Technology, Boulder, CO 80305, USA