arXiv subjects
Publications and source records attributed to Seth Lloyd.
A universal quantum computer can be constructed using abelian anyons. Two qubit quantum logic gates such as controlled-NOT operations are performed using topological effects. Single-anyon operations such as hopping from site to site on a lattice suffice to perform all quantum logic operations. Quantum computation using abelian anyons shares some but not all of the robustness of quantum computation using non-abelian anyons.
This paper investigates a variety of unconventional quantum computation devices, including fermionic quantum computers and computers that exploit nonlinear quantum mechanics. It is shown that unconventional quantum computing devices can in principle compute some quantities more rapidly than `conventional' quantum computers.
Off-resonant effects are a significant source of error in quantum computation. This paper presents a group theoretic proof that off-resonant transitions to the higher levels of a multilevel qubit can be completely prevented in principle. This result can be generalized to prevent unwanted transitions due to qubit-qubit interactions. A simple scheme exploiting dynamic pulse control techniques is presented that can cancel transitions to higher states to arbitrary accuracy.
We present control schemes for open quantum systems that combine decoupling and universal control methods with coding procedures. By exploiting a general algebraic approach, we show how appropriate encodings of quantum states result in obtaining universal control over dynamically-generated noise-protected subsystems with limited control resources. In particular, we provide an efficient scheme for performing universal encoded quantum computation in a wide class of systems subjected to linear non-Markovian quantum noise and supporting Heisenberg-type internal Hamiltonians.
Computers are physical systems: what they can and cannot do is dictated by the laws of physics. In particular, the speed with which a physical device can process information is limited by its energy and the amount of information that it can process is limited by the number of degrees of freedom it possesses. This paper explores the physical limits of computation as determined by the speed of light $c$, the quantum scale $\hbar$ and the gravitational constant $G$. As an example, quantitative bounds are put to the computational power of an `ultimate laptop' with a mass of one kilogram confined to a volume of one liter.
Arrays of weakly-coupled quantum systems can be made to compute by subjecting them to a sequence of electromagnetic pulses of well-defined frequency and length. Such pulsed arrays are true quantum computers: bits can be placed in superpositions of 0 and 1, logical operations take place coherently, and dissipation is required only for error correction. Programming such computers is accomplished by selecting the proper sequence of pulses.
This paper shows that universal quantum computers possess decoherent histories in which complex adaptive systems evolve with high probability.
Simulation of quantum systems that provide intrinsically fault-tolerant quantum computation is shown to preserve fault tolerance. Errors committed in the course of simulation are eliminated by the natural error-correcting features of the systems simulated. Two examples are explored, toric codes and non-abelian anyons. The latter is shown to provide universal robust quantum computation via simulation.
The problem of feedback control of quantum systems by means of weak measurements is investigated in detail. When weak measurements are made on a set of identical quantum systems, the single-system density matrix can be determined to a high degree of accuracy while affecting each system only slightly. If this information is fed back into the systems by coherent operations, the single-system density matrix can be made to undergo an arbitrary nonlinear dynamics, including for example a dynamics governed by a nonlinear Schrödinger equation. We investigate the implications of such nonlinear quantum dynamics for various problems in quantum control and quantum information theory, including quantum computation. The nonlinear dynamics induced by weak quantum feedback could be used to create a novel form of quantum chaos in which the time evolution of the single-system wave function depends sensitively on initial conditions.
We present the design of a superconducting qubit that has circulating currents of opposite sign as its two states. The circuit consists of three nano-scale 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 SQUID, and the states can be manipulated with magnetic fields. Coupled systems of qubits are also discussed as well as sources of decoherence.
It is shown that if one can perform a restricted set of fast manipulations on a quantum system, one can implement a large class of dynamical evolutions by effectively removing or introducing selected Hamiltonians. The procedure can be used to achieve universal noise-tolerant control based on purely unitary open-loop transformations of the dynamics. As a result, it is in principle possible to perform noise-protected universal quantum computation using no extra space resources.
The quantum Fourier transform (QFT) has been implemented on a three bit nuclear magnetic resonance (NMR) quantum computer, providing a first step towards the realization of Shor's factoring and other quantum algorithms. Implementation of the QFT is presented with fidelity measures, and state tomography. Experimentally realizing the QFT is a clear demonstration of NMR's ability to control quantum systems.
Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation required by open-loop control. In addition, an information-theoretic analysis of closed-loop control shows feedback control to be essentially a zero sum game: each bit of information gathered directly from a dynamical systems by a control device can serve to decrease the entropy of that system by at most one bit additional to the reduction of entropy attainable without such information (open-loop control). Consequences for the control of discrete binary systems and chaotic systems are discussed.
The Greenberger-Horne-Zeilinger (GHZ) effect provides an example of quantum correlations that cannot be explained by classical local hidden variables. This paper reports on the experimental realization of GHZ correlations using nuclear magnetic resonance (NMR). The NMR experiment differs from the originally proposed GHZ experiment in several ways: it is performed on mixed states rather than pure states; and instead of being widely separated, the spins on which it is performed are all located in the same molecule. As a result, the NMR version of the GHZ experiment cannot entirely rule out classical local hidden variables. It nonetheless provides an unambiguous demonstration of the "paradoxical" GHZ correlations, and shows that any classical hidden variables must communicate by non-standard and previously undetected forces. The NMR demonstration of GHZ correlations shows the power of NMR quantum information processing techniques for demonstrating fundamental effects in quantum mechanics.
Entanglement of quantum variables is usually thought to be a prerequisite for obtaining quantum speed-ups of information processing tasks such as searching databases. This paper presents methods for quantum search that give a speed-up over classical methods, but that do not require entanglement. These methods rely instead on interference to provide a speed-up. Search without entanglement comes at a cost: although they outperform analogous classical devices, the quantum devices that perform the search are not universal quantum computers and require exponentially greater overhead than a quantum computer that operates using entanglement. Quantum search without entanglement is compared to classical search using waves.
We propose a novel dynamical method for beating decoherence and dissipation in open quantum systems. We demonstrate the possibility of filtering out the effects of unwanted (not necessarily known) system-environment interactions and show that the noise-suppression procedure can be combined with the capability of retaining control over the effective dynamical evolution of the open quantum system. Implications for quantum information processing are discussed.
This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam-splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform `quantum floating point' computations. Problems of noise, finite precision, and error correction are discussed.
We explore a strategy for protecting the evolution of a qubit against the effects of environmental noise based on the application of controlled time-dependent perturbations. In the case of a purely decohering coupling, an explicit sequence of control operations is designed, able to average out the decoherence of the qubit with high efficiency. We argue that, in principle, the effects of arbitrary qubit-environment interactions can be removed through suitable decoupling perturbations acting on the system dynamics over time scales comparable to the correlation time of the environment.