The dc SQUID qubit can be viewed as a single current biased Josephson junction attached to an inductive isolation network. Excellent broadband isolation is possible and is adjustable in situ. The isolation network increases the effective shunt resistance due to the lead impedance allowing for long energy dissipation times T₁. We present data on Rabi oscillations, and macroscopic quantum tunneling as isolation from the bias leads is varied.

This paper discusses the use of continuous weak measurement and quantum feedback for the rapid purification of the quantum state of a model solid state qubit: a superconducting Cooper pair box. The feedback algorithm uses Jacobs' rapid purification protocol, which starts with a completely mixed state and applies controls to rotate the qubit Bloch vector onto the plane orthogonal to the measurement axis. This rotation maximises the rate of increase of the average purity of the state but can require large changes in the control fields to produce the required rotation. Since solid state qubits have finite controls and feedback channels have limited bandwidth, such rotations may not be practical. This paper applies Jacobs' protocol to the Cooper pair box with realistic control fields.

A quantum lattice algorithm is developed for the solution of the coupled Gross-Pitaevskii equations, which are just the nonlinear Schrodinger equations with an external potential. In the language of solitons, a sufficiently strong external potential can localize the solitons and even the radiation in the case of Manikov solitons. For non-integrable potential cases the radiation is no longer localized and one can also lose the soliton structures themselves. One also finds locked mode structures if the systems is close to being integrable.

Properties of the stability diagram and exchange energy of a few-electron laterally coupled quantum dots in magnetic fields are investigated. The calculations are performed by numerically exact diagonalization of the many-body Schroedinger equation. We show variations of the energy separation between the single-particle ground and first excited states, and the exchange energy with biases on the two dots at different magnetic fields. Two-dimensional single-particle wavefunction and electron density profiles show electron localization with magnetic fields. From the extracted double-triple point separation on the stability diagram, we also show that the coupling strength decrease as the magnetic field increases.

A unified theory is given of dynamically modified decay and decoherence of field-driven multilevel multipartite entangled states that are weakly coupled to zero-temperature baths. The theory allows for arbitrary local differences in their coupling to the environment. Due to such differences, the optimal driving-field modulation to ensure maximal fidelity is found to substantially differ from conventional π-phase flips of the single-qubit evolution.

We survey results on the decay of multiqubit entanglement due to internal interactions between qubits. Dipole-dipole interaction induces decoherence of strongly entangled nuclear spins. The dynamics of spin clusters can be described as quantum decoherence due to an effective composite bath consisting of fully correlated and uncorrelated parts. The rate of decoherence scales up as a square root of the number of entangled spins, resulting in linear scaling of a measure of quantum noise. Our theory is consistent with a recent experiment.

Two photon states entangled in polarization and momentum, hyper-entangled, have been generated by using linear optics and a single Type I nonlinear crystal. These states have been completely characterized and their nonlocal behaviour have been verified by independent Bell's inequalities tests performed in the two degrees of freedom of entanglement and by an "all versus nothing" test of local realism. The manipulation of these states may represent a useful control in quantum state engineering and Bell state measurements and, more in general, in Quantum Information applications.

The recent developments in the experimental realization of quasi-one-dimensional (1D) systems exhibit many interesting features. These include current quantization which has the potential application for a current standard as well as quantum information and security schemes. In this paper, we investigate the effect of spin-orbit interaction (SOI) on the energy levels of electrons confined to quantum dots on the surface of nanotubes. The radius of a nanotube is a few nanometers and is quasi-1D. The energy levels play a crucial role in determining the electron transport properties.The SOI may arise from the electrostatic confining potential due to gates applied perpendicular to the axis of the nanotube. The quantum computation scheme which we are suggesting consists of a nano-circuit of nanotubes on which electrons are confined within dots. The qubit operation is based on the exchange interaction between a pair of spins occupying states within the quantum dots. We employ a simple model for the electron confinement to obtain the energy eigenstates. Our simplified calculation was able to show that the SOI splits the energy levels which are then used to obtain the exchange energy of a pair of spins with the s-wave Heitler-London approach. We calculate the exchange energy of the entangled electrons on a pair of coaxial and parallel nanotubes as a function of separation between the nanotubes and show that the SOI enhances the entanglement.

Coherent control of quantum dynamics by phase-manipulation of the driving fields, has long been established as an essential tool for state-selective preparation of systems. On the other hand, the basic manipulations of qubits in most physical realizations of quantum-computation devices use Rabi pulses that operate on the Bloch sphere, particularly for weakly-coupled, slow-decoherent systems. In this work we analyze the role of phase-control and phase-dependence of Rabi pulses that prepare Bell states in a system of distinguishable qubits interacting in a harmonic trap. We show that the population dynamics and the properties of the entanglement exhibit a strong dependence to the relative phase. For coherent phonon distributions, collapse and full revival of entanglement occur, while for thermal distributions, except for a few "protected" phases, decoherence with partial revivals are observed.

We study a new approach to the control of a quantum system S, which uses the coupling of S with a quantum probe P. The external control affects only P, and the accessibility and controllability properties describe to what extent it is possible to drive the state of S by varying the initial state of P and using the interaction between the two systems. In particular, we study the case of two-dimensional system and probe. Two situations are considered: either the total system S + P is a closed one, or it is surrounded by a bath of decoupled harmonic oscillators. We give results on the controllability and accessibility properties of this scheme, and we discuss the relation of these properties with the entangling capability of the interaction between S and P. In particular, we show that the SWAP operator plays a special role.

The operation of a polarization-based quantum key distribution (QKD) testbed system is described. The system was developed for the Army Research Laboratory (ARL) by the Johns Hopkins University Applied Physics Laboratory under the DARPA Quantum Information Science and Technology program. Recent developments include upgrading the testbed system for operation at 830 nm wavelength. We describe the system architecture, control software, diagnostic and operational modes. The cryptosystem was tested in a point-to-point configuration with transmitter and receiver separated by a distance of 1.5 km, and using in-ground single-mode telecommunications optical fiber for the quantum channel.

Following a review of the measure of Renyi information gain and its optimization, the quantum circuits and designs are reviewed of optimized entangling probes for attacking the BB84 protocol of quantum key distribution (QKD), extracting maximum Renyi information on the pre-privacy amplified key. Probe photon polarization states become optimally entangled with the signal states on their way between the legitimate transmitter and receiver. Standard symmetric von Neumann projective measurements of the probe yield maximum information on the pre-privacy amplified key.

Quantum cryptography systems can operate over relatively long distances in standard telecommunications fiber by taking advantage of the low transmission losses in these fibers at 1.3 or 1.5 microns. Although there has been much progress toward the development of highly efficient and low-noise detectors for these wavelengths, silicon avalanche photodiodes currently offer superior single photon counting performance, but only at visible and near IR wavelengths where the fiber transmission is poor. For ranges typical of local area networks, it is possible that a quantum key distribution (QKD) system operating below 850nm could be optimal, even though standard telecommunications fiber supports multiple optical modes at these wavelengths. We have recently developed an optical mode filter that allows efficient higher order mode rejection from standard telecommunications fiber near 830nm. We have used this type of filter to launch and recover QKD signals from a polarization-based system implementing the BB84 quantum cryptography protocol. Here we present results from testing and operation in installed fiber links ranging up to 3km. These results demonstrate that the filters can attenuate the higher order modes over 35dB while having a minimal (<1dB) impact on the fundamental mode carrying the QKD signal.

Quantum cryptography asserts that shared secrets can be established over public channels in such a way that the total information of an eavesdropper can be made arbitrarily small with probability arbitrarily close to 1. As we will show below, the current state of affairs, especially as it pertains to engineering issues, leaves something to be desired.

Quantum cryptography applies the uncertainty principle and the no-cloning theorem to allow to parties to share a secret key over an ultra-secure link. Present quantum cryptography technologies provide encryption key distribution only between two users. However, practical implementations of encryption key distribution schemes require establishing secure quantum communications amongst multiple users. This paper looks at some of the advantages and drawbacks of some common network topologies that could be used in sending cryptographic keys across a network consisting of multiple users. These topologies are the star, ring, and bus networks. Their performances are compared and analyzed using quantum bit error rate analysis. The paper also presents an experimental demonstration of a six-user quantum key distribution network implemented on a bus topology.

In the simplest problems of quantum communication, Alice transmits one of two quantum states, with equal probabilities, to Bob's receiver, modeled by a positive-operator-valued measure (POVM); one seeks the POVM that is optimal according to one or another criterion. We discuss four such criteria, the first three of which lead to distinctive types of POVM. By introducing a reciprocal basis for the state vectors, we shorten the derivations of known results for the two most popular criteria. A new optimization problem defined by a third criterion, intermediate between the first two, is formulated and solved. Then we turn to a fourth criterion, that of minimizing Bob's Renyi entropy for an arbitrary order α. Depending on the value of α and the separation of Alice's states, the POVM that minimizes Bob's entropy can be any of the preceding three types.

The efficiency of spontaneous parametric down conversion is calculated and measured for several nonlinear crystals and waveguides in single spatial mode regime. Efficiency of waveguide sources is found to be far superior compared to the bulk crystal sources.

NIST has developed a high-speed quantum key distribution (QKD) test bed incorporating both free-space and fiber systems. These systems demonstrate a major increase in the attainable rate of QKD systems: over two orders of magnitude faster than other systems. NIST's approach to high-speed QKD is based on a synchronous model with hardware support. Practical one-time pad encryption requires high key generation rates since one bit of key is needed for each bit of data to be encrypted. A one-time pad encrypted surveillance video application was developed and serves as a demonstration of the speed, robustness and sustainability of the NIST QKD systems. We discuss our infrastructure, both hardware and software, its operation and performance along with our migration to quantum networks.

If an eavesdropper Eve is equipped with quantum computers, she can easily break the public key exchange protocols used today. In this paper we will discuss the post-quantum Diffie-Hellman key exchange and private key exchange protocols.

We report "plug & play" and free-space implementations of continuous-variable (CV) quantum key distribution (QKD). In a CV QKD system, a homodyne detector is used to detect a weak signal light by superposing the signal with a local oscillator (LO) whose intensity is much stronger than the signal. In conventional "plug & play" (or auto compensating) systems, two pulses traverse an identical optical path and the intensities of them become equal. In our experiment we use an acousto-optic modulator and have successfully controlled the intensities of the signal and the LO. For free-space implementation of CV QKD the stability of the double interferometer is a crucial problem. We have separated the signal and LO in time longer than the coherence time of the pulse by exploiting the birefringence of EOM crystals. In this setup the signal and LO traverse along the same ray path, so the stability of the interferometer is greatly improved.

A complete fiber-based polarization encoding quantum key distribution (QKD) system based on the BB84 protocol has been developed at National Institute of Standard and Technology (NIST). The system can be operated at a sifted key rate of more than 4 Mbit/s over optical fiber of length 1 km and mean photon number 0.1. The quantum channel uses 850 nm photons from attenuated high speed VCSELs and the classical channel uses 1550 nm light from normal commercial coarse wavelength division multiplexing devices. Sifted-key rates and quantum error rates at different transmission rates are measured as a function of distance (fiber length). A polarization auto-compensation module has been developed and utilized to recover the polarization state and to compensate for temporal drift. An automatic timing alignment device has also been developed to quickly handle the initial configuration of quantum channels so that detection events fall into the correct timing window. These automated functions make the system more practical for integration into existing optical local area networks.

Heisenberg's uncertainty principle has been understood to set a limitation on measurements, whereas the long standing mathematical formulation does not allow such an interpretation. Recently, a new relation was found by the present author to give a universally valid relation between noise and disturbance in general quantum measurements, and it has become clear that the new relation plays a role of the first principle to derive various quantum limits on measurement and information processing. Here, we discuss the state-dependent notion of precise measurements of a given observable, and consider a perfect distance such that zero distance implies the perfect correlation. Then, we shall show that even in the perfect error notions both the position measuring noise and the momentum disturbance can be arbitrarily small. We also show that it is possible to generalize the new noise-disturbance uncertainty relation to perfect error distances.

If operations in a quantum computer were conditioned on the results of a subsequent post-selection measurement, then NP-complete problems could be solved in polynomial time. Using the natural connection between post-selection and NP, we show that this result is un-physical by considering constraints on new kinds of measurements which depend on the future post-selection in a non-trivial way. We review practical quantum information advantages of post-selection.

Irrespective of the underlying technology used to implement a large-scale quantum architecture system, one of the central challenges of accurately modeling the architecture is the ability to map and schedule a quantum application onto a physical grid while taking into account the cost of communication, the classical resources, and the maximum exploitable parallelism. In this paper we introduce and evaluate a physical operations scheduler for arbitrary quantum circuits. Our scheduler accepts a description of a circuit together with a description of a specific physical layout and outputs a sequence of operations that expose the required communication and available parallelism in the circuit. The output of the scheduler is a quantum assembly language file that can directly be simulated on a set of available tools.

We demonstrate a method of constructing L-shape cluster states by exploiting equivalence class properties of graph states. The L-shape cluster state is a primitive which can be used to construct cluster states capable of supporting universal quantum computation. The method is device independent but is shown to be considerably more efficient than previously proposed approaches for photonic cluster construction. Two-dimensional photonic cluster states can be efficiently built via local unitaries and type-I fusion only. To allow for a complete calculation of the cost of two-dimensional photonic cluster-state construction, we also provide a recursion relation relating the length of a photonic cluster chain to the average resources required.

In the paper, the foundation requirement of a quantum key distribution network is described. According to the requirement, a kind of star topology quantum key distribution network is introduced. The core of this quantum network is a "router" which is composed of less than N wavelength division multiplexers. Based on the "router", a four nodes quantum key distribution network has been set up, the measurement results shown us that it is suitable for simple purpose of quantum key distribution over many users and the crosstalk is weak enough.

We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups.

In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of the form e^2πi/k. This description is given with two objectives in mind. The first is to describe the algorithm in such a way as to make explicit the underlying and inherent control structure. The second is to make this algorithm accessible to a larger audience.

In this paper we review the content of the Quantum Computer Condition, which is a rigorously specified criterion that provides a set of mathematical constraints that must be satisfied by a physical system if we intend to use that system as a quantum computing machine, and we discuss an important consequence of it known as the Quantum Computing No-Go Theorem, which establishes a bound for decoherence and dissipation beyond which quantum computation is not possible. In connection with this theorem, we explicitly calculate a universal critical damping value for fault-tolerant quantum computation. We also discuss a relevant class of time-dependent generalizations of the Lindblad equation.

We formulate an expression for the accessible information in mirror-symmetric ensembles of real qubit states. This expression is used to make a detailed study of optimum quantum measurements for extracting the accessible information in three-state, mirror-symmetric ensembles. Distinct measurement regimes are identified for these ensembles with optimal measurement strategies involving different numbers of measurement operators, similar to results found for minimum error discrimination. Our results generalize known results for the accessible information in two pure states and in the trine ensemble.

The scaling of NMR ensemble computers is currently one of the main obstacles to building larger-scale quantum computing devices. To achieve scalability, one needs a large number of highly polarized spins in liquid nuclear-spin systems at finite temperature. In quantum computing terminology, such spin-half states are (almost) pure qubit states. Producing highly polarized spins (almost pure qubit states) out of non-polarized spins (non-pure qubit states) is sometimes called "purification". From a thermodynamic point of view, purification can be viewed as cooling spins to a very low temperature. In this preliminary work, we study the optimality of purification as a tradeoff between the number of cooled spins and the closeness of their quantum state to the ideal pure state.

We are interested in finding quantum algorithms for problems in the area of computation geometry. Many of the problems we study have already polynomial time algorithms. Bounded error quantum algorithms can actually have sublinear running time.

Using Computer Algebra Software (Mathematica and Maple), the recently introduced topic of Yang- Baxterization applied to quantum computing, is explored from the mathematical and computational views. Some algorithms of computer algebra were elaborated with the aim to make the calculations to obtain some of results that were originally presented in the paper by Shang-Kauffman-Ge. Also certain new results about computational Yang-baxterization are presented. We obtain some Hamiltonians for hypothetical physical systems which can be realized within the domain of spin chains and certain diffusion process. We conclude that it is possible to have real physical systems on which implement, via Yang-baxterization, the standard quantum gates with topological protection. Finally some lines for future research are deligned.

We consider the problem of generalizing some quantum algorithms so that they will work on input domains whose cardinalities are not necessarily powers of two. When analyzing the algorithms we assume that generating superpositions of arbitrary subsets of basis states whose cardinalities are not necessarily powers of two perfectly is possible. We have taken Ballhysa's model as a template and have extended it to Chi, Kim and Lee's generalizations of the Deutsch-Jozsa algorithm and to Simon's algorithm. With perfectly equal superpositions of input sets of arbitrary size, Chi, Kim and Lee's generalized Deutsch-Jozsa algorithms, both for evenly-distributed and evenly-balanced functions, worked with one-sided error property. For Simon's algorithm the success probability of the generalized algorithm is the same as that of the original for input sets of arbitrary cardinalities with equiprobable superpositions, since the property that the measured strings are all those which have dot product zero with the string we search, for the case where the function is 2-to-1, is not lost.

We have studied the performance of a geometric phase gate with a quantized driving field numerically, and developed an analytical approximation that yields some preliminary insight on the way the qubit becomes entangled with the driving field.

The engineering of practical quantum computers requires dealing with the so-called "temperature mismatch problem". More specifically, analysis of quantum logic using ensembles of quantum systems typically assumes very low temperatures, kT<< E, where T is the temperature, k is the Boltzmann's constant, and E is the energy separation used to represent the two different states of the qubits. On the other hand, in practice the electronics necessary to control these quantum gates will almost certainly have to operate at much higher temperatures. One solution to this problem is to construct electronic components that are able to work at very low temperatures, but the practical engineering of these devices continues to face many difficult challenges. Another proposed solution is to study the behavior of quantum gates devices continues to face many difficult challenges. Another proposed solution is to study the behavior of quantum gates different from the T=0 case, where collective interactions and stochastic phenomena are not taken into consideration. In this paper we discuss several aspects of quantum logic at finite temperature. In particular, we present analysis of the behavior of quantum systems undergoing a specified computation performed by quantum gates at nonzero temperature. Our main interest is the effect of temperature on the practical implementation of quantum computers to solve potentially large and time-consuming computations.

Single-electron transistors (SETs) are attractive candidates for spin qubits. An AlGaAs/GaAs SET consists of a confined two-dimensional droplet of electrons, called an artificial atom or quantum dot, coupled by tunnel barriers to two conducting leads. Controlling the voltages on the lithographic gates that define the quantum dot allows us to confine a single electron in the dot, as well as to adjust the tunnel barriers to the leads. By applying a magnetic field, we can split the spin-up and spin-down states of the electron by an energy |g|μ_BB; the goal is to utilize coherent superpositions of these spin states to construct a qubit. We will discuss our attempts to observe electron spin resonance (ESR) in this system by applying magnetic fields at microwave frequencies. Observation of ESR would demonstrate that we can manipulate a single spin and allow us to measure the decoherence time T₂*.