Exponential speedup with a single bit of quantum information: measuring the average fidelity decay.

  title={Exponential speedup with a single bit of quantum information: measuring the average fidelity decay.},
  author={David Poulin and Robin Blume-Kohout and Raymond Laflamme and Harold Ollivier},
  journal={Physical review letters},
  volume={92 17},
We present an efficient quantum algorithm to measure the average fidelity decay of a quantum map under perturbation using a single bit of quantum information. Our algorithm scales only as the complexity of the map under investigation. Thus for those maps admitting an efficient gate decomposition, it provides an exponential speedup over known classical procedures. Fidelity decay is important in the study of complex dynamical systems, where it is conjectured to be a signature of eigenvector… 

Figures from this paper

Characterization of complex quantum dynamics with a scalable NMR information processor.

Experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor show measurable differences between regular and complex behavior and for complex dynamics are faithful to the expected theoretical decay rate.

Unitary quantum gates, perfect entanglers, and unistochastic maps

Non-local properties of ensembles of quantum gates induced by the Haar measure on the unitary group are investigated. We analyze the entropy of entanglement of a unitary matrix U equal to the Shannon

Experimental approximation of the Jones polynomial with one quantum bit.

Experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time.

Stabilization of quantum information by combined dynamical decoupling and detected-jump error correction

It is demonstrated that random decoupling is also a convenient tool for stabilizing quantum algorithms and a decoupled scheme is presented which involves a randomDecoupling method compatible with detected-jump error correcting quantum codes.

Impact of dynamics, entanglement, and Markovian noise on the fidelity of few-qubit digital quantum simulation

For quantum computations without error correction, the dynamics of a simulation can strongly influence the overall fidelity decay rate as well as the relative impact of different noise processes on

Measurement-Based Quantum Correlations for Quantum Information Processing

It is shown that MbQCs exist more generally than entanglement and discord in optimal assisted quantum state discrimination and in a deterministic quantum computation with a single qubit.

Some Theory and Applications of Probability in Quantum Mechanics

It is proved that quantum states are more difficult to estimate than their classical counterparts by finding optimal estimation strategies, requiring the solution to a difficult optimization problem, are difficult to implement in practise.

A cold-atoms based processor for deterministic quantum computation with one qubit in intractably large Hilbert spaces

We propose the use of Rydberg interactions and ensembles of cold atoms in mixed state for the implementation of a protocol for deterministic quantum computation with one quantum bit that can be

Quantum dissonance and deterministic quantum computation with a single qubit

This work provides conclusive evidence that there are instances where quantum entanglement is not present in any part of this model, nevertheless it establishes the fact that quantum dissonance present in fully separable (FS) states provide power to DQC1 model.



Fidelity decay as an efficient indicator of quantum chaos.

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

Efficient quantum computing of complex dynamics.

We propose a quantum algorithm which uses the number of qubits in an optimal way and efficiently simulates a physical model with rich and complex dynamics described by the quantum sawtooth map. The

Testing integrability with a single bit of quantum information

We show that deterministic quantum computing with a single bit can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where N is the

Exponential gain in quantum computing of quantum chaos and localization.

We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos,

Classicality of quantum information processing

The ultimate goal of the classicality program is to quantify the amount of quantumness of certain processes. Here, classicality is studied for a restricted type of process: quantum information

Power of One Bit of Quantum Information

In standard quantum computation, the initial state is pure and the answer is determined by making a measurement of some of the bits in the computational basis. What can be accomplished if the initial

Simulating quantum systems on a quantum computer

  • Christof Zalka
  • Physics, Computer Science
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1998
It is shown that the time evolution of the wave function of a quantum–mechanical many–particle system can be simulated precisely and efficiently on a quantum computer, and that ultimately the simulation of quantum field theory might be possible on large quantum computers.

Quantum and classical correlations in quantum Brownian motion.

It is shown that there exists a large class of initial states for which no entanglement will be created at all times between the system of salient interest and the environment.

Using a quantum computer to investigate quantum chaos

We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has an efficient realization in terms of quantum gates. Chaos in the quantum baker's map

Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer

To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer.