Showing papers on "Quantum computer published in 2006"
TL;DR: In this paper, the relevant hamiltonians for spin lattice models can be systematically engineered with polar molecules stored in optical lattices, where the spin is represented by a single-valence electron of a heteronuclear molecule.
Abstract: There is growing interest in states of matter with topological order. These are characterized by highly stable ground states robust to perturbations that preserve the topology, and which support excitations with so-called anyonic statistics. Topologically ordered states can arise in two-dimensional lattice-spin models, which were proposed as the basis for a new class of quantum computation. Here, we show that the relevant hamiltonians for such spin lattice models can be systematically engineered with polar molecules stored in optical lattices, where the spin is represented by a single-valence electron of a heteronuclear molecule. The combination of microwave excitation with dipole–dipole interactions and spin–rotation couplings enables building a complete toolbox for effective two-spin interactions with designable range, spatial anisotropy and coupling strengths significantly larger than relevant decoherence rates. Finally, we illustrate two models: one with an energy gap providing for error-resilient qubit encoding, and another leading to topologically protected quantum memory.
897 citations
TL;DR: In this article, a system of polaritons held in an array of resonant optical cavities, which could be realized using photonic crystals or toroidal microresonators, was shown to form a strongly interacting many-body system showing quantum phase transitions, where individual particles can be controlled and measured.
Abstract: Observing quantum phenomena in strongly correlated many-particle systems is difficult because of the short length- and timescales involved. Exerting control over the state of individual elements within such a system is even more so, and represents a hurdle in the realization of quantum computing devices. Substantial progress has been achieved with arrays of Josephson junctions and cold atoms in optical lattices, where detailed control over collective properties is feasible, but addressing individual sites remains a challenge. Here we show that a system of polaritons held in an array of resonant optical cavities—which could be realized using photonic crystals or toroidal microresonators—can form a strongly interacting many-body system showing quantum phase transitions, where individual particles can be controlled and measured. The system also offers the possibility to generate attractive on-site potentials yielding highly entangled states and a phase with particles much more delocalized than in superfluids.
775 citations
TL;DR: A generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection, is described.
Abstract: We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multimode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.
653 citations
TL;DR: In this article, a single pair of strongly coupled spins in diamond, associated with a nitrogen-vacancy defect and a nitrogen atom, respectively, can be optically initialized and read out at room temperature.
Abstract: Coherent coupling between single quantum objects is at the very heart of modern quantum physics. When the coupling is strong enough to prevail over decoherence, it can be used to engineer quantum entangled states. Entangled states have attracted widespread attention because of applications to quantum computing and long-distance quantum communication. For such applications, solid-state hosts are preferred for scalability reasons, and spins are the preferred quantum system in solids because they offer long coherence times. Here we show that a single pair of strongly coupled spins in diamond, associated with a nitrogen-vacancy defect and a nitrogen atom, respectively, can be optically initialized and read out at room temperature. To effect this strong coupling, close proximity of the two spins is required, but large distances from other spins are needed to avoid deleterious decoherence. These requirements were reconciled by implanting molecular nitrogen into high-purity diamond.
604 citations
TL;DR: The teleportation of a quantum state between two single material particles (trapped ions) has now also been achieved and is demonstrated between objects of a different nature—light and matter, which respectively represent ‘flying’ and ‘stationary’ media.
Abstract: Quantum teleportation is an important ingredient in distributed quantum networks, and can also serve as an elementary operation in quantum computers. Teleportation was first demonstrated as a transfer of a quantum state of light onto another light beam; later developments used optical relays and demonstrated entanglement swapping for continuous variables. The teleportation of a quantum state between two single material particles (trapped ions) has now also been achieved. Here we demonstrate teleportation between objects of a different nature--light and matter, which respectively represent 'flying' and 'stationary' media. A quantum state encoded in a light pulse is teleported onto a macroscopic object (an atomic ensemble containing 10 caesium atoms). Deterministic teleportation is achieved for sets of coherent states with mean photon number (n) up to a few hundred. The fidelities are 0.58 +/- 0.02 for n = 20 and 0.60 +/- 0.02 for n = 5--higher than any classical state transfer can possibly achieve. Besides being of fundamental interest, teleportation using a macroscopic atomic ensemble is relevant for the practical implementation of a quantum repeater. An important factor for the implementation of quantum networks is the teleportation distance between transmitter and receiver; this is 0.5 metres in the present experiment. As our experiment uses propagating light to achieve the entanglement of light and atoms required for teleportation, the present approach should be scalable to longer distances.
594 citations
TL;DR: These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits, which allows them to extend their application also to quantum teleportation, dense coding, and computation with magic states.
Abstract: We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits. This allows us to extend their application also to quantum teleportation, dense coding, and computation with magic states.
580 citations
TL;DR: Efficient quantum-logic circuits that perform two tasks are discussed: 1) implementing generic quantum computations, and 2) initializing quantum registers that are asymptotically optimal for respective tasks.
Abstract: The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits (Proc. R. Soc. Lond. A, Math. Phys. Sci., vol. 425, p. 73, 1989) to the attention of the electronic design automation community (Proc. 40th ACM/IEEE Design Automation Conf., 2003), (Phys. Rev. A, At. Mol. Opt. Phy., vol. 68, p. 012318, 2003), (Proc. 41st Design Automation Conf., 2004), (Proc. 39th Design Automation Conf., 2002), (Proc. Design, Automation, and Test Eur., 2004), (Phys. Rev. A, At. Mol. Opt. Phy., vol. 69, p. 062321, 2004), (IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 22, p. 710, 2003). Efficient quantum-logic circuits that perform two tasks are discussed: 1) implementing generic quantum computations, and 2) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state space of an n-qubit register is not finite and contains exponential superpositions of classical bitstrings. The proposed circuits are asymptotically optimal for respective tasks and improve earlier published results by at least a factor of 2. The circuits for generic quantum computation constructed by the algorithms are the most efficient known today in terms of the number of most expensive gates [quantum controlled-NOTs (CNOTs)]. They are based on an analog of the Shannon decomposition of Boolean functions and a new circuit block, called quantum multiplexor (QMUX), which generalizes several known constructions. A theoretical lower bound implies that the circuits cannot be improved by more than a factor of 2. It is additionally shown how to accommodate the severe architectural limitation of using only nearest neighbor gates, which is representative of current implementation technologies. This increases the number of gates by almost an order of magnitude, but preserves the asymptotic optimality of gate counts
545 citations
TL;DR: The complexity of the 2-locHam problem has been shown to be Ω(n 2 )-complete for any n ≥ 3 in the complexity class QMA as discussed by the authors.
Abstract: The $k$-{\locHam} problem is a natural complete problem for the complexity class $\QMA$, the quantum analogue of $\NP$. It is similar in spirit to {\sc MAX-$k$-SAT}, which is $\NP$-complete for $k\geq 2$. It was known that the problem is $\QMA$-complete for any $k \geq 3$. On the other hand, 1-{\locHam} is in {\P} and hence not believed to be $\QMA$-complete. The complexity of the 2-{\locHam} problem has long been outstanding. Here we settle the question and show that it is $\QMA$-complete. We provide two independent proofs; our first proof uses only elementary linear algebra. Our second proof uses a powerful technique for analyzing the sum of two Hamiltonians; this technique is based on perturbation theory and we believe that it might prove useful elsewhere. Using our techniques we also show that adiabatic computation with 2-local interactions on qubits is equivalent to standard quantum computation.
526 citations
TL;DR: It is shown how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree.
Abstract: We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.
500 citations
TL;DR: It is shown that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry, recasting the problem of finding quantum circuits as a geometric problem.
Abstract: Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.
494 citations
TL;DR: In this article, the optical transition between ground and excited electronic states allows coupling of spin degrees of freedom to the state of the electromagnetic field, such coupling gives access to spin state read-out via spin-selective scattering of photons.
Abstract: Quantum computing is an attractive and multidisciplinary field, which became a focus for experimental and theoretical research during the last decade. Among other systems, such as ions in traps and superconducting circuits, solid state based qubits are considered to be promising candidates for use in first experimental tests of quantum hardware. Here we report recent progress in quantum information processing with point defects in diamond. Qubits are defined as single spin states (electron or nuclear). This allows exploration of long coherence times (up to seconds for nuclear spins at cryogenic temperatures). In addition, the optical transition between ground and excited electronic states allows coupling of spin degrees of freedom to the state of the electromagnetic field. Such coupling gives access to spin state read-out via spin-selective scattering of photons. This also allows the use of spin states as robust memory for flying qubits (photons).
Book•
01 Jan 2006
TL;DR: In this paper, the authors introduce quantum mechanics, quantum cryptography, quantum computing, entanglement, quantum teleportation, and quantum information processing, including poisson statistics and quantum number states.
Abstract: PART I: INTRODUCTION AND BACKGROUND 1. Introduction 2. Classical optics 3. Quantum mechanics 4. Radiative transitions in atoms PART II: PHOTONS 5. Photon statistics 6. Photon antibunching 7. Coherent states and squeezed light 8. Photon number states PART III: ATOM-PHOTON INTERACTIONS 9. Resonant light-atom interactions 10. Atoms in cavities 11. Cold atoms PART IV: QUANTUM INFORMATION PROCESSING 12. Quantum cryptography 13. Quantum computing 14. Entangled states and quantum teleportation APPENDICES A. Poisson statistics B. Parametric amplification C. The density of states D. Low dimensional semiconductor structures E. Nuclear magnetic resonance F. Bose-Einstein condensation
TL;DR: It is shown that highly reliable swap and entangling gates are achievable and exactly study the stability of these gates in the presence of imperfections in coupling strengths and interaction times and prove them to be robust.
Abstract: We investigate the possibility of realizing effective quantum gates between two atoms in distant cavities coupled by an optical fiber. We show that highly reliable swap and entangling gates are achievable. We exactly study the stability of these gates in the presence of imperfections in coupling strengths and interaction times and prove them to be robust. Moreover, we analyze the effect of spontaneous emission and losses and show that such gates are very promising in view of the high level of coherent control currently achievable in optical cavities.
TL;DR: In this paper, the spectral theory of quantum graphs is discussed and exact trace formulae for the spectrum and the quantum-to-classical correspondence are discussed, as well as its application to quantum chaos.
Abstract: During the last few years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wavefunction statistics. In the first part of this review we give a detailed introduction to the spectral theory of quantum graphs and discuss exact trace formulae for the spectrum and the quantum-to-classical correspondence. The second part of this review is devoted to the spectral statistics of quantum graphs as an application to quantum chaos. In particular, we summarize recent developments on the spectral statistics of generic large quantum graphs based on two approaches: the periodic-orbit approach and the supersymmetry approach. The latter provides a condition and a proof for universal spectral statistics as predicted by random-matrix theory.
Book•
01 Jan 2006
TL;DR: In this article, Lloyd showed how the universe itself is a giant computer and every atom and elementary particle stores these bits, and every collision between those atoms and particles flips the bits into a new arrangement and effortlessly spins out beautiful and complex systems.
Abstract: IN THE BEGINNING WAS THE BIT...The universe is made of bits of information and it has been known for more than a century that every piece of the the universe - every electron, atom and molecule - registers these bits and that information. It is only in the last years, however, with the discovery and development of quantum computers, that scientists have gained a fundamental understanding of just how that information is registered and processed. Building on recent breakthroughs in quantum computation, Seth Lloyd shows how the universe itself is a giant computer. Every atom and elementary particle stores these bits, and every collision between those atoms and particles flips the bits into a new arrangement and effortlessly spins out beautiful and complex systems, including galaxies, planets and life itself. But every computer needs a program, the set of instructions that tell it what patterns to create. Where did the bits come from that tell the universe to create its magnificent complexity? Who - or what - is programming the universe?
TL;DR: A fault-tolerant one-way quantum computer on cluster states in three dimensions using methods of topological error correction resulting from a link between cluster states and surface codes is described.
TL;DR: The detection efficiency and the entanglement fidelity are high enough to allow in a next step the generation of entangled atoms at large distances, ready for a final loophole-free Bell experiment.
Abstract: We report the observation of entanglement between a single trapped atom and a single photon at a wavelength suitable for low-loss communication over large distances, thereby achieving a crucial step towards long range quantum networks. To verify the entanglement, we introduce a single atom state analysis. This technique is used for full state tomography of the atom-photon qubit pair. The detection efficiency and the entanglement fidelity are high enough to allow in a next step the generation of entangled atoms at large distances, ready for a final loophole-free Bell experiment.
TL;DR: The quantum interference of two single photons emitted by two independently trapped single atoms is demonstrated, bridging the gap towards the simultaneous emission of many indistinguishable single photons by different emitters.
Abstract: When two indistinguishable single photons are fed into the two input ports of a beam splitter, the photons will coalesce and leave together from the same output port. This is a quantum interference effect, which occurs because two possible paths-in which the photons leave by different output ports-interfere destructively. This effect was first observed in parametric downconversion (in which a nonlinear crystal splits a single photon into two photons of lower energy), then from two separate downconversion crystals, as well as with single photons produced one after the other by the same quantum emitter. With the recent developments in quantum information research, much attention has been devoted to this interference effect as a resource for quantum data processing using linear optics techniques. To ensure the scalability of schemes based on these ideas, it is crucial that indistinguishable photons are emitted by a collection of synchronized, but otherwise independent sources. Here we demonstrate the quantum interference of two single photons emitted by two independently trapped single atoms, bridging the gap towards the simultaneous emission of many indistinguishable single photons by different emitters. Our data analysis shows that the observed coalescence is mainly limited by wavefront matching of the light emitted by the two atoms, and to a lesser extent by the motion of each atom in its own trap.
TL;DR: A novel protocol for a quantum repeater that enables long-distance quantum communication through realistic, lossy photonic channels by incorporating active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station.
Abstract: We describe a novel protocol for a quantum repeater that enables long-distance quantum communication through realistic, lossy photonic channels. Contrary to previous proposals, our protocol incorporates active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station. Because of these minimal physical requirements, the present protocol can be realized in simple physical systems such as solid-state single photon emitters. As an example, we show how nitrogen-vacancy color centers in diamond can be used to implement the protocol, using the nuclear and electronic spin to form the two qubits.
TL;DR: A review of theoretical and experimental aspects of multiphoton quantum optics can be found in this paper, where the authors focus on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms that are relevant for the conceptual investigations and for the practical applications of modern quantum mechanics.
TL;DR: In this article, a short introduction to and review of the cluster-state model of quantum computation is presented, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum state known as a cluster state.
TL;DR: By combining the spin and orbital degrees of freedom of the electron, an effective quantum two-level (qubit) system is defined that can be coherently manipulated by the voltage applied to the gate electrodes, without the need for an external time-dependent magnetic field or spin-orbit coupling.
Abstract: We consider a single electron in a 1D quantum dot with a static slanting Zeeman field. By combining the spin and orbital degrees of freedom of the electron, an effective quantum two-level (qubit) system is defined. This pseudospin can be coherently manipulated by the voltage applied to the gate electrodes, without the need for an external time-dependent magnetic field or spin-orbit coupling. Single-qubit rotations and the controlled-NOT operation can be realized. We estimated the relaxation (T1) and coherence (T2) times and the (tunable) quality factor. This scheme implies important experimental advantages for single electron spin control.
TL;DR: In this article, a 2D donor electron spin quantum computer architecture is proposed, which addresses major technical issues in the original Kane design, including spatial oscillations in the exchange coupling strength and cross-talk in gate control, and the introduction of nonlocality in qubit interaction will significantly improve the scaling fault-tolerant threshold over the nearest-neighbor linear array.
Abstract: Through the introduction of a new electron spin transport mechanism, a 2D donor electron spin quantum computer architecture is proposed. This design addresses major technical issues in the original Kane design, including spatial oscillations in the exchange coupling strength and cross-talk in gate control. It is also expected that the introduction of nonlocality in qubit interaction will significantly improve the scaling fault-tolerant threshold over the nearest-neighbor linear array.
TL;DR: In this paper, the authors show how ultracold polar molecules, suggested as a new platform for quantum computation, can be manipulated to switch ''on'' and ''off'' their strong dipole-dipole interactions.
Abstract: We show how ultracold polar molecules, suggested as a new platform for quantum computation, can be manipulated to switch ``on'' and ``off'' their strong dipole-dipole interactions. This can be accomplished through selective excitation of states with considerably different dipole moments. We discuss different schemes for quantum gates using real molecules: CO, LiH, and CaF, as examples of polar molecules which are being experimentally studied at ultracold temperatures. These schemes can be realized in several recently proposed architectures.
TL;DR: This work reduces the cost of addition dramatically with only a slight increase in the number of required qubits, and can be used within current modularmultiplication circuits to reduce substantially the run-time of Shor's algorithm.
Abstract: We present an efficient addition circuit, borrowing techniques from classical carry-lookahead arithmetic. Our quantum carry-lookahead (QCLA) adder accepts two n-bitnumbers and adds them in O(log n) depth using O(n) ancillary qubits. We present bothin-place and out-of-place versions, as well as versions that add modulo 2n and modulo2n - 1. Previously, the linear-depth ripple-carry addition circuit has been the methodof choice. Our work reduces the cost of addition dramatically with only a slight increasein the number of required qubits. The QCLA adder can be used within current modularmultiplication circuits to reduce substantially the run-time of Shor's algorithm.
TL;DR: In this paper, the authors highlight the role of Lie algebras and noncommutativity in the design of a compensating pulse sequence and investigate three common dispersions in NMR spectroscopy, namely the Larmor dispersion, rf inhomogeneity and strength of couplings between the spins.
Abstract: Finding control fields (pulse sequences) that can compensate for the dispersion in the parameters governing the evolution of a quantum system is an important problem in coherent spectroscopy and quantum information processing. The use of composite pulses for compensating dispersion in system dynamics is widely known and applied. In this paper, we make explicit the key aspects of the dynamics that makes such a compensation possible. We highlight the role of Lie algebras and noncommutativity in the design of a compensating pulse sequence. Finally, we investigate three common dispersions in NMR spectroscopy, namely the Larmor dispersion, rf inhomogeneity, and strength of couplings between the spins.
TL;DR: In this article, a method for efficient storage and recall of arbitrary nonstationary light fields, such as single photon time-bin qubits or intense fields, in optically dense atomic ensembles is proposed.
Abstract: We propose a method for efficient storage and recall of arbitrary nonstationary light fields, such as, for instance, single photon time-bin qubits or intense fields, in optically dense atomic ensembles. Our approach to quantum memory is based on controlled, reversible, inhomogeneous broadening and relies on a hidden time-reversal symmetry of the optical Bloch equations describing the propagation of the light field. We briefly discuss experimental realizations of our proposal.
TL;DR: In this article, the authors considered topological quantum computation with a particular class of anyons that are believed to exist in the fractional quantum Hall effect state at Landau-level filling fraction v = 5/2.
Abstract: We consider topological quantum computation (TQC) with a particular class of anyons that are believed to exist in the fractional quantum Hall effect state at Landau-level filling fraction v =5/2. Since the braid group representation describing the statistics of these anyons is not computationally universal, one cannot directly apply the standard TQC technique. We propose to use very noisy nontopological operations such as direct short-range interactions between anyons to simulate a universal set of gates. Assuming that all TQC operations are implemented perfectly, we prove that the threshold error rate for nontopological operations is above 14%. The total number of nontopological computational elements that one needs to simulate a quantum circuit with L gates scales as L(ln L)to the 3rd.
TL;DR: A new design concept is introduced in which the capacitive element is explicitly separate from the Josephson tunnel junction for improved qubit performance and the number of two-level systems that couple to the qubit is reduced and the measurement fidelity improves to 90%.
Abstract: We introduce a new design concept for superconducting phase quantum bits (qubits) in which we explicitly separate the capacitive element from the Josephson tunnel junction for improved qubit performance. The number of two-level systems that couple to the qubit is thereby reduced by an order of magnitude and the measurement fidelity improves to 90%. This improved design enables the first demonstration of quantum state tomography with superconducting qubits using single-shot measurements.
TL;DR: It is shown that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r(D).
Abstract: We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts collectively on pairs of qubits and on the environment, and we show that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r^D.