arXiv subjects

Seth Lloyd

Publications and source records attributed to Seth Lloyd.

262 records · Page 15Linked to original sources

arXiv1998

A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors

We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and chemistry problems) for which all known classical algorithms require exponential time. Applications of the algorithm to specific problems are considered, and we find that classically intractable and interesting problems from atomic physics may be solved with between 50 and 100 quantum bits.

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arXiv1998

Experimental realization of a quantum algorithm

Nuclear magnetic resonance techniques are used to realize a quantum algorithm experimentally. The algorithm allows a simple NMR quantum computer to determine global properties of an unknown function requiring fewer function ``calls'' than is possible using a classical computer.

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arXiv1998

Dynamical suppression of decoherence in two-state quantum systems

The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radiofrequency pulses that repetitively flip the state of the system, a technique that can be termed quantum "bang-bang" control after its classical analog. Decoherence introduced by the system's interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques.

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arXiv1998

Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems

If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting nonlinear quantum logic gates. It is argued that virtually any deterministic nonlinear quantum theory will include such gates, and the method is explicitly demonstrated using the Weinberg model of nonlinear quantum mechanics.

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arXiv1997

Analog quantum error correction

Quantum error-correction routines are developed for continuous quantum variables such as position and momentum. The result of such analog quantum error correction is the construction of composite continuous quantum variables that are largely immune to the effects of noise and decoherence.

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arXiv1997

A Greenberger-Horne-Zeilinger experiment for mixed states

This paper shows how the Greenberger-Horne-Zeilinger experiment, which demonstrates the nonlocal nature of quantum mechanics, can be performed using nuclear magnetic resonance on spins in molecules at finite temperature. The use of nuclear magnetic resonance techniques allows the experiment to uncover the nonlocality not just of special GHZ states, but of arbitrary three particle states.

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arXiv1997

Simulation of Many-Body Fermi Systems on a Universal Quantum Computer

We provide fast algorithms for simulating many body Fermi systems on a universal quantum computer. Both first and second quantized descriptions are considered, and the relative computational complexities are determined in each case. In order to accommodate fermions using a first quantized Hamiltonian, an efficient quantum algorithm for anti-symmetrization is given. Finally, a simulation of the Hubbard model is discussed in detail.

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arXiv1997

Quantum controllers for quantum systems

This paper discusses fully coherent quantum feedback control, in which the sensors, controller, and actuators are quantum systems and interact coherently with the system to be controlled: as a result, the entire feedback loop is coherent. Unlike conventional semiclassical feedback control of quantum systems, feedback control by quantum controllers is not stochastic, preserves the initial state of the controlled system, and can control quantum systems in ways that are not possible using conventional, incoherent feedback control. In particular, the target state to which the quantum controller drives the system can be entangled with another quantum system. This paper investigates quantum controllers and states necessary and sufficient conditions for a Hamiltonian quantum system to be observable and controllable by a quantum controller.

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arXiv1996

A quantum-mechanical Maxwell's demon

A Maxwell's demon is a device that gets information and trades it in for thermodynamic advantage, in apparent (but not actual) contradiction to the second law of thermodynamics. Quantum-mechanical versions of Maxwell's demon exhibit features that classical versions do not: in particular, a device that gets information about a quantum system disturbs it in the process. In addition, the information produced by quantum measurement acts as an additional source of thermodynamic inefficiency. This paper investigates the properties of quantum-mechanical Maxwell's demons, and proposes experimentally realizable models of such devices.

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arXiv1996

The capacity of the noisy quantum channel

An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. A class of quantum error-correcting codes is presented that allow the information transmitted to attain this limit. The result is the quantum analog of Shannon's bound and code for the noisy classical channel.

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