Showing papers on "Qubit published in 2000"
TL;DR: Experimental evidence is presented that a superconducting quantum interference device (SQUID) can be put into a superposition of two magnetic-flux states: one corresponding to a few microamperes of current flowing clockwise, the other corresponding to the same amount ofCurrent flowing anticlockwise.
Abstract: In 1935, Schrodinger attempted to demonstrate the limitations of quantum mechanics using a thought experiment in which a cat is put in a quantum superposition of alive and dead states. The idea remained an academic curiosity until the 1980s when it was proposed that, under suitable conditions, a macroscopic object with many microscopic degrees of freedom could behave quantum mechanically, provided that it was sufficiently decoupled from its environment. Although much progress has been made in demonstrating the macroscopic quantum behaviour of various systems such as superconductors, nanoscale magnets, laser-cooled trapped ions, photons in a microwave cavity and C60 molecules, there has been no experimental demonstration of a quantum superposition of truly macroscopically distinct states. Here we present experimental evidence that a superconducting quantum interference device (SQUID) can be put into a superposition of two magnetic-flux states: one corresponding to a few microamperes of current flowing clockwise, the other corresponding to the same amount of current flowing anticlockwise.
1,066 citations
TL;DR: It is shown that parametric down-conversion offers enhanced performance compared to its weak coherent pulse counterpart and existing experimental schemes (based on weak pulses) currently do not offer unconditional security for the reported distances and signal strength.
Abstract: We provide limits to practical quantum key distribution, taking into account channel losses, a realistic detection process, and imperfections in the ``qubits'' sent from the sender to the receiver. As we show, even quantum key distribution with perfect qubits might not be achievable over long distances when the other imperfections are taken into account. Furthermore, existing experimental schemes (based on weak pulses) currently do not offer unconditional security for the reported distances and signal strength. Finally we show that parametric down-conversion offers enhanced performance compared to its weak coherent pulse counterpart.
1,020 citations
TL;DR: In this paper, the full power of modern electronic band-structure engineering and epitaxial heterostructures was applied to design a transistor that can sense and control a single-donor electron spin.
Abstract: We apply the full power of modern electronic band-structure engineering and epitaxial heterostructures to design a transistor that can sense and control a single-donor electron spin. Spin-resonance transistors may form the technological basis for quantum information processing. One- and two-qubit operations are performed by applying a gate bias. The bias electric field pulls the electron wave function away from the dopant ion into layers of different alloy composition. Owing to the variation of the g factor (Si: g1.998,Ge:g1.563), this displacement changes the spin Zeeman energy, allowing single-qubit operations. By displacing the electron even further, the overlap with neighboring qubits is affected, which allows two-qubit operations. Certain silicon-germanium alloys allow a qubit spacing as large as 200 nm, which is well within the capabilities of current lithographic techniques. We discuss manufacturing limitations and issues regarding scaling up to a large size computer.
722 citations
16 Jul 2000
TL;DR: The results show that GQA is superior to other genetic algorithms using penalty functions, repair methods and decoders and can represent a linear superposition of solutions due to its probabilistic representation.
Abstract: This paper proposes a novel evolutionary computing method called a genetic quantum algorithm (GQA). GQA is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting qubit chromosome as a representation GQA can represent a linear superposition of solutions due to its probabilistic representation. As genetic operators, quantum gates are employed for the search of the best solution. Rapid convergence and good global search capability characterize the performance of GQA. The effectiveness and the applicability of GQA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that GQA is superior to other genetic algorithms using penalty functions, repair methods and decoders.
622 citations
TL;DR: In this article, it was shown that a qubit chosen from equatorial or polar great circles on a Bloch sphere can be remotely prepared with one cbit from Alice to Bob if they share one ebit of entanglement.
Abstract: We show that a qubit chosen from equatorial or polar great circles on a Bloch sphere can be remotely prepared with one cbit from Alice to Bob if they share one ebit of entanglement. Also we show that any single-particle measurement on an arbitrary qubit can be remotely simulated with one ebit of shared entanglement and communication of one cbit.
572 citations
TL;DR: The experimental results demonstrate the possibility of delayed determination of particlelike or wavelike behavior via quantum entanglement, and the which-path or both-path information of a quantum can be marked or erased by its entangled twin even after the registration of the quantum.
Abstract: We report a delayed "choice" quantum eraser experiment of the type proposed by Scully and Druhl (where the "choice" is made randomly by a photon at a beam splitter). The experimental results demonstrate the possibility of delayed determination of particlelike or wavelike behavior via quantum entanglement. The which-path or both-path information of a quantum can be marked or erased by its entangled twin even after the registration of the quantum.
507 citations
01 Mar 2000
TL;DR: In this article, a superconducting qubit that has circulating currents of opposite sign as its two states is presented. But the circuit consists of three nanoscale aluminum Josephson junctions connected in a super-conducting loop and controlled by magnetic fields.
Abstract: We present the design of a superconducting qubit that has circulating currents of opposite sign as its two states. The circuit consists of three nanoscale aluminum Josephson junctions connected in a superconducting loop and controlled by magnetic fields. The advantages of this qubit are that it can be made insensitive to background charges in the substrate, the flux in the two states can be detected with a superconducting quantum interference device, and the states can be manipulated with magnetic fields. Coupled systems of qubits are also discussed as well as sources of decoherence. @S0163-1829~99!00746-8#
465 citations
TL;DR: It is shown that violations of local realism are stronger for two maximally entangled quNits than for two qubits and that they increase with N.
Abstract: Tests of local realism versus quantum mechanics based on Bell's inequality employ two entangled qubits. We investigate the general case of two entangled quantum systems defined in N-dimensional Hilbert spaces, or " quNits." Via a numerical linear optimization method we show that violations of local realism are stronger for two maximally entangled quNits ( 3
452 citations
TL;DR: In this paper, the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form.
Abstract: We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.
344 citations
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TL;DR: In this article, a ring of N qubits in a translationally invariant quantum state is considered, and it is shown that the ground state of an antiferromagnetic ring consisting of an even number of spin-1/2 particles can achieve the maximum possible nearest-neighbor entanglement.
Abstract: Consider a ring of N qubits in a translationally invariant quantum state We ask to what extent each pair of nearest neighbors can be entangled Under certain assumptions about the form of the state, we find a formula for the maximum possible nearest-neighbor entanglement We then compare this maximum with the entanglement achieved by the ground state of an antiferromagnetic ring consisting of an even number of spin-1/2 particles We find that, though the antiferromagnetic ground state does not maximize the nearest-neighbor entanglement relative to all other states, it does so relative to other states having zero z-component of spin
304 citations
TL;DR: In this article, the authors describe two schemes to manipulate the electronic qubit states of trapped ions independent of the collective vibrational state of the ions, which enables simulation of nonlinear quantum systems including systems that exhibit phase transitions, and other semiclassical bifurcations.
Abstract: We describe two schemes to manipulate the electronic qubit states of trapped ions independent of the collective vibrational state of the ions. The first scheme uses an adiabatic method, and thus is intrinsically slow. The second scheme takes the opposite approach and uses fast pulses to produce an effective direct coupling between the electronic qubits. This last scheme enables the simulation of a number of nonlinear quantum systems including systems that exhibit phase transitions, and other semiclassical bifurcations. Quantum tunnelling and entangled states occur in such systems.
TL;DR: In this paper, the authors present two optimal methods of teleporting an unknown qubit using any pure entangled state and discuss how such methods can also have successful application in quantum secret sharing with pure multipartite entangled states.
Abstract: We present two optimal methods of teleporting an unknown qubit using any pure entangled state. We also discuss how such methods can also have successful application in quantum secret sharing with pure multipartite entangled states.
TL;DR: In this paper, it was shown that the linearity of quantum theory does not allow us to delete a copy of an arbitrary quantum state perfectly, even irreversibly, with quantum information.
Abstract: A photon in an arbitrary polarization state cannot be cloned perfectly. But suppose that at our disposal we have several copies of a photon in an unknown state. Is it possible to delete the information content of one or more of these photons by a physical process? Specifically, if two photons are in the same initial polarization state, is there a mechanism that produces one photon in the same initial state and the other in some standard polarization state? If this could be done, then one would create a standard blank state onto which one could copy an unknown state approximately, by deterministic cloning or exactly, by probabilistic cloning. This could in principle be useful in quantum computation, where one could store new information in an already computed state by deleting the old information. Here we show, however, that the linearity of quantum theory does not allow us to delete a copy of an arbitrary quantum state perfectly. Though in a classical computer information can be deleted (reversibly) against a copy, the analogous task cannot be accomplished, even irreversibly, with quantum information.
TL;DR: An experimental realization of an algorithmic benchmark using an NMR technique that involves coherent manipulation of seven qubits is reported, which can be used as a reliable and efficient method for creating a standard pseudopure state, the first step for implementing traditional quantum algorithms in liquid state NMR systems.
Abstract: Quantum information processing offers potentially great advantages over classical information processing, both for efficient algorithms1,2 and for secure communication3,4. Therefore, it is important to establish that scalable control of a large number of quantum bits (qubits) can be achieved in practice. There are a rapidly growing number of proposed device technologies5,6,7,8,9,10,11 for quantum information processing. Of these technologies, those exploiting nuclear magnetic resonance (NMR) have been the first to demonstrate non-trivial quantum algorithms with small numbers of qubits12,13,14,15,16. To compare different physical realizations of quantum information processors, it is necessary to establish benchmark experiments that are independent of the underlying physical system, and that demonstrate reliable and coherent control of a reasonable number of qubits. Here we report an experimental realization of an algorithmic benchmark using an NMR technique that involves coherent manipulation of seven qubits. Moreover, our experimental procedure can be used as a reliable and efficient method for creating a standard pseudopure state, the first step for implementing traditional quantum algorithms in liquid state NMR systems. The benchmark and the techniques can be adapted for use with other proposed quantum devices.
TL;DR: In this paper, the authors introduce the basic background for understanding applications of NMR to quantum information processing and explain their current successes, limitations and potential, and sketch one direction leading towards a scalable quantum computer using spin 1/2 particles.
Abstract: Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. We sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step of which is a solid state NMR-based QIP capable of reaching 10-30 qubits.
TL;DR: In this article, a quantum Cramer-Rao inequality was proposed for estimating the state of a large but finite number of identical quantum systems, where the only relevant measure of the quality of estimation becomes the mean quadratic error matrix.
Abstract: We consider the problem of estimating the state of a large but finite numberN of identical quantum systems. As N becomes large the problem simplifies dramatically. The only relevant measure of the quality of estimation becomes the mean quadratic error matrix. Here we present a bound on this quantity: a quantum Cramer-Rao inequality. This bound succinctly expresses how in the quantum case one can trade information about one parameter for information about another. The bound holds for arbitrary measurements on pure states, but only for separable measurements on mixed states—a striking example of nonlocality without entanglement for mixed but not for pure states. Cramer-Rao bounds are generally only derived for unbiased estimators. Here we give a version of our bound for biased estimators, and a simple asymptotic version for large N. Finally we prove that when the unknown state belongs to a two-dimensional Hilbert space our quantum Cramer-Rao bound can always be attained, and we provide an explicit measurement strategy that attains it. Thus we have a complete solution to the problem of estimating as efficiently as possible the unknown state of a large ensemble of qubits in the same pure state. The same is true for qubits in the same mixed state if one restricts oneself to separable measurements, but nonseparable measurements allow dramatic increase of efficiency. Exactly how much increase is possible is a major open problem.
TL;DR: A family of asymmetric quantum cloning machines is introduced that produce two approximate copies of a single quantum bit, each copy emerging from a Pauli channel, and a no-cloning inequality is derived.
Abstract: A family of asymmetric quantum cloning machines is introduced that produce two approximate copies of a single quantum bit, each copy emerging from a Pauli channel. A no-cloning inequality is derived, describing the balance between the quality of the copies. The Pauli cloning machine is also shown to put a limit on the quantum capacity of Pauli channels.
TL;DR: In this article, a set of real polynomials of the entries of the density matrix of a two-qubit unitary system is presented, which are invariant under local unitary transformations.
Abstract: Entanglement of two parts of a quantum system is a non-local property unaffected by local manipulations of these parts. It is described by quantities invariant under local unitary transformations. Here we present, for a system of two qubits, a set of invariants which provides a complete description of non-local properties. The set contains 18 real polynomials of the entries of the density matrix. We prove that one of two mixed states can be transformed into the other by single-bit operations if and only if these states have equal values of all 18 invariants. Corresponding local operations can be found efficiently. Without any of these 18 invariants the set is incomplete.
Similarly, non-local, entangling properties of two-qubit unitary gates are invariant under single-bit operations. We present a complete set of 3 real polynomial invariants of unitary gates. Our results are useful for optimization of quantum computations since they provide an effective tool to verify if and how a given two-qubit operation can be performed using exactly one elementary two-qubit gate, implemented by a basic physical manipulation (and arbitrarily many single-bit gates).
TL;DR: This work describes in detail a set of ideas for implementing qubits, quantum gates, and quantum gate networks in a semiconductor heterostructure device based on an extension of the technology used for surface acoustic wave based single-electron transport devices.
Abstract: We describe in detail a set of ideas for implementing qubits, quantum gates, and quantum gate networks in a semiconductor heterostructure device. Our proposal is based on an extension of the technology used for surface acoustic wave (SAW) based single-electron transport devices. These devices allow single electrons to be captured from a two-dimensional electron gas in the potential minima of a SAW. We discuss how this technology can be adapted to allow the capture of electrons in pure spin states and how both single and two-qubit gates can be constructed using magnetic and nonmagnetic gate technology. We give designs for readout gates to allow the spin state of the electrons to be measured and discuss how combinations of gates can be connected to make multiqubit networks. Finally we consider decoherence and other sources of error, and how they can be minimized for our design.
TL;DR: In this article, a pure state of four qubits whose single-qubit density matrices are all maximally mixed and whose average entanglement as a system of two pairs of qubits appears to be maximal is described.
TL;DR: In this paper, the authors study the experimental realization of quantum teleportation as performed by Bouwmeester et al. and show that coincidences between photon pairs from parametric down-conversion automatically probe the non-Poissonian structure of these sources.
Abstract: We study the experimental realization of quantum teleportation as performed by Bouwmeester et al. [Nature (London) 390, 575 (1997)] and the adjustments to it suggested by Braunstein and Kimble [Nature (London) 394, 841 (1998)]. These suggestions include the employment of a detector cascade and a relative slow-down of one of the two down-converters. We show that coincidences between photon pairs from parametric down-conversion automatically probe the non-Poissonian structure of these sources. Furthermore, we find that detector cascading is of limited use, and that modifying the relative strengths of the down-conversion efficiencies will increase the time of the experiment to the order of weeks. Our analysis therefore points to the benefits of single-photon detectors in non post selected-type experiments, a technology currently requiring roughly 6 \ifmmode^\circ\else\textdegree\fi{}K operating conditions.
TL;DR: In this article, an all-optical implementation of quantum information processing in semiconductor quantum dots is proposed, where electron-hole excitations serve as the computational degrees of freedom (qubits).
Abstract: We propose an all-optical implementation of quantum-information processing in semiconductor quantum dots, where electron-hole excitations (excitons) serve as the computational degrees of freedom (qubits). We show that the strong dot confinement leads to an overall enhancement of Coulomb correlations and to a strong renormalization of the excitonic states, which can be exploited for performing conditional and unconditional qubit operations.
TL;DR: The results show that a broad parameter region does exist where the efficient operation of a quantum computer is possible, and that below the quantum chaos border an ideal state can survive for long times, and an be used for computation.
Abstract: We study the standard generic quantum computer model, which describes a realistic isolated quantum computer with fluctuations in individual qubit energies and residual short-range interqubit couplings. It is shown that in the limit where the fluctuations and couplings are small compared to the one-qubit energy spacing, the spectrum has a band structure, and a renormalized Hamiltonian is obtained which describes the eigenstate properties inside one band. Studies are concentrated on the central band of the computer (``core'') with the highest density of states. We show that above a critical interqubit coupling strength, quantum chaos sets in, leading to a quantum ergodicity of the computer eigenstates. In this regime the ideal qubit structure disappears, the eigenstates become complex, and the operability of the computer is quickly destroyed. We confirm that the quantum chaos border decreases only linearly with the number of qubits n, although the spacing between multiqubit states drops exponentially with n. The investigation of time evolution in the quantum computer shows that in the quantum chaos regime, an ideal (noninteracting) state quickly disappears, and exponentially many states become mixed after a short chaotic time scale for which the dependence on system parameters is determined. Below the quantum chaos border an ideal state can survive for long times, and an be used for computation. The results show that a broad parameter region does exist where the efficient operation of a quantum computer is possible.
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TL;DR: In this paper, the authors present a technique for protecting states against decoherence based on the engineering of pointer states, and apply this procedure to the vibrational motion of a trapped ion.
Abstract: We present a proposal for protecting states against decoherence, based on the engineering of pointer states. We apply this procedure to the vibrational motion of a trapped ion, and show how to protect qubits, squeezed states, approximate phase eigenstates and superpositions of coherent states.
TL;DR: It is demonstrated that a single pure qubit, together with a collection of log 2N qubits in an arbitrary mixed state, is sufficient to implement Shor's factorization algorithm efficiently.
Abstract: It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit, together with a collection of ${log}_{2}N$ qubits in an arbitrary mixed state, is sufficient to implement Shor's factorization algorithm efficiently.
14 May 2000
TL;DR: It is shown that although unconditionally secure quantum bit commitment is impossible, it can be based upon any family of quantum one-way permutations and the resulting scheme is unconditionally concealing and computationally binding.
Abstract: We show that although unconditionally secure quantum bit commitment is impossible, it can be based upon any family of quantum one-way permutations. The resulting scheme is unconditionally concealing and computationally binding. Unlike the classical reduction of Naor, Ostrovski, Ventkatesen and Young, our protocol is non-interactive and has communication complexity O(n) qubits for n a security parameter.
TL;DR: In this article, the stabilizers in the group of local unitary transformations of spin-½ particles are classified by means of their stabilizers and shown that the stabilizer is generically discrete and that a larger stabilizer indicates a stationary value for some local invariant.
Abstract: Entanglement types of pure states of three spin-½ particles are classified by means of their stabilizers in the group of local unitary transformations. It is shown that the stabilizer is generically discrete, and that a larger stabilizer indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilizers.
TL;DR: In this article, entangled qubits are encoded as entangled coherent states of two-dimensional center-of-mass vibrational motion for two ions in an ion trap, and a proposal for entanglement transfer from the two vibrational modes to the electronic states of the two ions is introduced.
Abstract: We show how entangled qubits can be encoded as entangled coherent states of two-dimensional center-of-mass vibrational motion for two ions in an ion trap. The entangled qubit state is equivalent to the canonical Bell state, and we introduce a proposal for entanglement transfer from the two vibrational modes to the electronic states of the two ions in order for the Bell state to be detected by resonance fluorescence shelving methods.
TL;DR: In this paper, the fundamental unit of a two-qubit universal quantum gate is self-assembled based on two exchange coupled multilayered quantum dots, which can be wired using thiolated conjugated molecules as electrical connectors.
Abstract: Quantum computers promise vastly enhanced computational power and an uncanny ability to solve classically intractable problems. However, few proposals exist for robust, solid-state implementation of such computers where the quantum gates are sufficiently miniaturized to have nanometer-scale dimensions. Here I present a new approach whereby a complete computer with nanoscale gates might be self-assembled using chemical synthesis. Specifically, I demonstrate how to self-assemble the fundamental unit of this quantum computer---a two-qubit universal quantum gate---based on two exchange coupled multilayered quantum dots. Then I show how these gates can be wired using thiolated conjugated molecules as electrical connectors. Each quantum dot in this architecture consists of ferromagnet-semiconductor-ferromagnet layers. The ground state in the semiconductor layer is spin split because of the Rashba interaction and the spin-splitting energy can be varied by an external electrostatic potential applied to the dot. A spin polarized electron is injected into each dot from one of the ferromagnetic layers and trapped by Coulomb blockade. Its spin orientation encodes a qubit. Arbitrary qubit rotations are effected by bringing the spin-splitting energy in a target quantum dot in resonance with a global ac magnetic field by applying a potential pulse of appropriate amplitude and duration to the dot. The controlled dynamics of the universal two-qubit rotation operation can be realized by exploiting the exchange coupling with the nearest-neighboring dot. The qubit (spin orientation) is read via the current induced between the ferromagnetic layers under an applied potential. The ferromagnetic layers act as ``polarizers'' and ``analyzers'' for spin injection and detection. A complete prescription for initialization of the computer and data input/output operations is presented. This paradigm, to the best of our knowledge, draws together two great recent scientific advances: one in materials science (nanoscale self-assembly) and the other in information science (quantum computing).
TL;DR: In this article, the authors investigated the use of quantum bits (qubits) - semiconductor quantum dots containing one electron and each consisting of two tunnel-connected parts - as basic elements of the quantum computer and showed that in such structures the realization of a full set of basic logic operations, which are necessary for fulfillment of quantum computations, is possible.
Abstract: We investigated the use of quantum bits (qubits) - semiconductor quantum dots containing one electron and each consisting of two tunnel-connected parts - as basic elements of the quantum computer. The numerical solution of a Schrodinger equation taking account of the Coulomb field of adjacent electrons shows that in such structures the realization of a full set of basic logic operations, which are necessary for fulfillment of quantum computations, is possible. Durations of one- and two-qubit operations versus qubit geometry are obtained. Decoherence rates due to spontaneous emission of phonons and acoustic phonons (both piezoelectric and deformation) are evaluated. Analysis of these rates shows the proposed qubit to be coherent enough to work for an unlimited time.