arXiv subjects

Seth Lloyd

Publications and source records attributed to Seth Lloyd.

At least 235 records · Page 13Linked to original sources

arXiv2003

Universal quantum interfaces

To observe or control a quantum system, one must interact with it via an interface. This letter exhibits simple universal quantum interfaces--quantum input/output ports consisting of a single two-state system or quantum bit that interacts with the system to be observed or controlled. It is shown that under very general conditions the ability to observe and control the quantum bit on its own implies the ability to observe and control the system itself. The interface can also be used as a quantum communication channel, and multiple quantum systems can be connected by interfaces to become an efficient universal quantum computer. Experimental realizations are proposed, and implications for controllability, observability, and quantum information processing are explored.

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arXiv2003

The quantum speed limit

How fast can a quantum system evolve? We answer this question focusing on the role of entanglement and interactions among subsystems. In particular, we analyze how the order of the interactions shapes the dynamics.

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arXiv2003

Topological Protection and Quantum Noiseless Subsystems

Encoding and manipulation of quantum information by means of topological degrees of freedom provides a promising way to achieve natural fault-tolerance that is built-in at the physical level. We show that this topological approach to quantum information processing is a particular instance of the notion of computation in a noiseless quantum subsystem. The latter then provide the most general conceptual framework for stabilizing quantum information and for preserving quantum coherence in topological and geometric systems.

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arXiv2003

Fidelity Decay as an Efficient Indicator of Quantum Chaos

Recent work has connected the type of fidelity decay in perturbed quantum models to the presence of chaos in the associated classical models. We demonstrate that a system's rate of fidelity decay under repeated perturbations may be measured efficiently on a quantum information processor, and analyze the conditions under which this indicator is a reliable probe of quantum chaos and related statistical properties of the unperturbed system. The type and rate of the decay are not dependent on the eigenvalue statistics of the unperturbed system, but depend on the system's eigenvector statistics in the eigenbasis of the perturbation operator. For random eigenvector statistics the decay is exponential with a rate fixed precisely by the variance of the perturbation's energy spectrum. Hence, even classically regular models can exhibit an exponential fidelity decay under generic quantum perturbations. These results clarify which perturbations can distinguish classically regular and chaotic quantum systems.

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arXiv2002

Scalable Architecture for Adiabatic Quantum Computing of NP-Hard Problems

We present a comprehensive review of past research into adiabatic quantum computation and then propose a scalable architecture for an adiabatic quantum computer that can treat NP-hard problems without requiring local coherent operations. Instead, computation can be performed entirely by adiabatically varying a magnetic field applied to all the qubits simultaneously. Local (incoherent) operations are needed only for: (1) switching on or off certain pairwise, nearest-neighbor inductive couplings in order to set the problem to be solved and (2) measuring some subset of the qubits in order to obtain the answer to the problem.

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arXiv2002

Quantum limits to dynamical evolution

We establish the minimum time it takes for an initial state of mean energy E and energy spread DE to move from its initial configuration by a predetermined amount. Distances in Hilbert space are estimated by the fidelity between the initial and final state. In this context, we also show that entanglement is necessary to achieve the ultimate evolution speed when the energy resources are distributed among all subsystems.

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arXiv2002

Using unitary operations to preserve quantum states in the presence of relaxation

When a quantum system interacts with an external environment, it undergoes the loss of quantum correlation (decoherence) and the loss of energy (relaxation) and eventually all of the quantum information becomes classical. Here we show a general principle to use unitary operations to establish and preserve particular non-equilibrium states in arbitrary relaxing quantum systems. We elucidate these concepts with examples of state preservation in one-spin and two-spin entangled systems.

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arXiv2002

Fidelity Decay Saturation Level for Initial Eigenstates

We show that the fidelity decay between an initial eigenstate state evolved under a unitary chaotic operator and the same eigenstate evolved under a perturbed operator saturates well before the 1/N limit, where $N$ is the size of the Hilbert space, expected for a generic initial state. We provide a theoretical argument and numerical evidence that, for intermediate perturbation strengths, the saturation level depends quadratically on the perturbation strength.

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arXiv2002

Experimental Implementation of the Quantum Baker's Map

This paper reports on the experimental implementation of the quantum baker's map via a three bit nuclear magnetic resonance (NMR) quantum information processor. The experiments tested the sensitivity of the quantum chaotic map to perturbations. In the first experiment, the map was iterated forward and then backwards to provide benchmarks for intrinsic errors and decoherence. In the second set of experiments, the least significant qubit was perturbed in between the iterations to test the sensitivity of the quantum chaotic map to applied perturbations. These experiments are used to investigate previous predicted properties of quantum chaotic dynamics.

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arXiv2002

Positioning and clock synchronization through entanglement

A method is proposed to employ entangled and squeezed light for determining the position of a party and for synchronizing distant clocks. An accuracy gain over analogous protocols that employ classical resources is demonstrated and a quantum-cryptographic positioning application is given, which allows only trusted parties to learn the position of whatever must be localized. The presence of a lossy channel and imperfect photodetection is considered. The advantages in using partially entangled states is discussed.

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arXiv2001

Quantum cryptographic ranging

We present a system to measure the distance between two parties that allows only trusted people to access the result. The security of the protocol is guaranteed by the complementarity principle in quantum mechanics. The protocol can be realized with available technology, at least as a proof of principle experiment.

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arXiv2001

The power of entangled quantum channels

All communication channels are at bottom quantum mechanical. Quantum mechanics contributes both obstacles to communication in the form of noise, and opportunities in the use of intrinsically quantum representations for information. This paper investigates the trade-off between power and communication rate for coupled quantum channels. By exploiting quantum correlations such as entanglement, coupled quantum channels can communicate at a potentially higher rate than unentangled quantum channels given the same power. In particular, given the same overall power, M coupled, entangled quantum channels can send M bits in the same time it takes a single channel to send a single bit, and in the same time it takes M unentangled channels to send $\sqrt M$ bits.

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arXiv2001

Computational capacity of the universe

Merely by existing, all physical systems register information. And by evolving dynamically in time, they transform and process that information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The universe is a physical system. This paper quantifies the amount of information that the universe can register and the number of elementary operations that it can have performed over its history. The universe can have performed no more than $10^{120}$ ops on $10^{90}$ bits.

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arXiv2000

Quantum Magic Bullets via Entanglement

Two particles that are entangled with respect to continuous variables such as position and momentum exhibit a variety of nonclassical features. First, measurement of one particle projects the other particle into the state that is the complex conjugate of the state of the first particle, i.e., measurement of one particle projects the other particle into the time-reversed state. Second, continuous-variable entanglement can be used to implement a quantum "magic bullet": when one particle manages to pass through a scattering potential, then no matter how low the probability of this event, the second particle will also pass through a related scattering potential with probability one. This phenomenon is investigated in terms of the original EPR state, and experimental realizations are suggested in terms of entangled photon states.

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arXiv2000

Control of open quantum systems dynamics

We investigate the control resources needed to effect arbitrary quantum dynamics. We show that the ability to perform measurements on a quantum system, combined with the ability to feed back the measurement results via coherent control, allows one to control the system to follow any desired open-system evolution. Such universal control can be achieved, in principle, through the repeated application of only two coherent control operations and a simple ``Yes-No'' measurement.

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arXiv2000

Hybrid quantum computing

Necessary and sufficient conditions are given for the construction of a hybrid quantum computer that operates on both continuous and discrete quantum variables. Such hybrid computers are shown to be more efficient than conventional quantum computers for performing a variety of quantum algorithms, such as computing eigenvectors and eigenvalues.

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arXiv2000

Generalization of the Peres criterion for local realism through nonextensive entropy

A bipartite spin-1/2 system having the probabilities $\frac{1+3x}{4}$ of being in the Einstein-Podolsky-Rosen entangled state $|Ψ^-$$> \equiv \frac{1}{\sqrt 2}(|$$\uparrow>_A|$$\downarrow>_B$$-|$$\downarrow>_A|$$\uparrow>_B)$ and $\frac{3(1-x)}{4}$ of being orthogonal, is known to admit a local realistic description if and only if $x<1/3$ (Peres criterion). We consider here a more general case where the probabilities of being in the entangled states $|Φ^{\pm}$$> \equiv \frac{1}{\sqrt 2}(|$$\uparrow>_A|$$\uparrow>_B \pm |$$\downarrow>_A|$$\downarrow>_B)$ and $|Ψ^{\pm}$$> \equiv \frac{1}{\sqrt 2}(|$$\uparrow>_A|$$\downarrow>_B \pm |$$\downarrow>_A|$$\uparrow>_B)$ (Bell basis) are given respectively by $\frac{1-x}{4}$, $\frac{1-y}{4}$, $\frac{1-z}{4}$ and $\frac{1+x+y+z}{4}$. Following Abe and Rajagopal, we use the nonextensive entropic form $S_q \equiv \frac{1- Tr ρ^q}{q-1} (q \in \cal{R}; $$S_1$$= -$ $Tr$ $ ρ\ln ρ)$ which has enabled a current generalization of Boltzmann-Gibbs statistical mechanics, and determine the entire region in the $(x,y,z)$ space where local realism is admissible. For instance, in the vicinity of the EPR state, classical realism is possible if and only if $x+y+z<1$, which recovers Peres' criterion when $x=y=z$. In the vicinity of the other three states of the Bell basis, the situation is identical. A critical-phenomenon-like scenario emerges. These results illustrate the computational power of this new nonextensive-quantum-information procedure.

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arXiv2000

Quantum searching with continuous variables

A fast quantum search algorithm for continuous variables is presented. The result is the quantum continuous variable analog of Grover's algorithm originally proposed for qubits. A continuous variable analog of the Hadamard (i.e., Fourier transform) operation is used in conjunction with inversion about the average of quantum states to allow the approximate identification of an unknown quantum state in a way that gives a square-root speed-up over search algorithms using classical continuous variables. Also, we show that this quantum search algorithm is robust for a generalised Fourier transformation on continuous variables.

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