Classical versus quantum errors in quantum computation of dynamical systems

Abstract

We analyze the stability of a quantum algorithm simulating the quantum dynamics of a system with different regimes, ranging from global chaos to integrability. We compare, in these different regimes, the behavior of the fidelity of quantum motion when the system's parameters are perturbed or when there are unitary errors in the quantum gates implementing the quantum algorithm. While the first kind of errors has a classical limit, the second one has no classical analogue. It is shown that, whereas in the first case (``classical errors'') the decay of fidelity is very sensitive to the dynamical regime, in the second case (``quantum errors'') it is almost independent of the dynamical behavior of the simulated system. Therefore, the rich variety of behaviors found in the study of the stability of quantum motion under ``classical'' perturbations has no correspondence in the fidelity of quantum computation under its natural perturbations. In particular, in this latter case it is not possible to recover the semiclassical regime in which the fidelity decays with a rate given by the classical Lyapunov exponent.

8 pages, 7 figures

References in corpus (37)

• Environment-independent decoherence rate in classically chaotic systems
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• Decoherence and the Loschmidt echo
• On general relation between quantum ergodicity and fidelity of quantum dynamics
• Sensitivity of Wave Field Evolution and Manifold Stability in Chaotic Systems
• Quantum chaos in an ion trap: the delta-kicked harmonic oscillator
• Stability of quantum motion and correlation decay
• Fidelity Decay as an Efficient Indicator of Quantum Chaos
• Sensitivity of Quantum Motion for Classically Chaotic Systems
• Diffusion and localization in chaotic billiards
• Using a quantum computer to investigate quantum chaos
• The Edge of Quantum Chaos
• Efficient Quantum Computing of Complex Dynamics
• Semiclassical evaluation of quantum fidelity
• Experimental Implementation of the Quantum Baker's Map
• Exponential speed-up with a single bit of quantum information: Testing the quantum butterfly effect
• Exponential Gain in Quantum Computing of Quantum Chaos and Localization
• Decoherence as Decay of the Loschmidt Echo in a Lorentz Gas
• Quantum computation with phase drift errors
• Can quantum chaos enhance stability of quantum computation?
• Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems
• Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states
• The effect of unitary noise on Grover's quantum search algorithm
• Localization in discontinuous quantum systems
• Stability of Quantum Motion: Beyond Fermi-golden-rule and Lyapunov decay
• Quantum computing of quantum chaos and imperfection effects
• Dynamical localization simulated on a few qubits quantum computer
• Classical decays in decoherent quantum maps
• Faster than Lyapunov decays of classical Loshcmidt echo
• Crossover of quantum Loschmidt echo from golden rule decay to perturbation-independent decay
• Quantum localization and cantori in chaotic billiards
• Loschmidt Echo and Lyapunov Exponent in a Quantum Disordered System
• Quantum algorithms for phase space tomography
• Decay of the classical Loschmidt echo in integrable systems
• Quantum computation of the Anderson transition in presence of imperfections
• Quantum Reversibility: Is there an Echo?
• A quantitative model for the effective decoherence of a quantum computer with imperfect unitary operations

Cited by in corpus (4)

• Dynamics of Loschmidt echoes and fidelity decay
• Decay of the Loschmidt echo in a time-dependent environment
• Robust and efficient generator of almost maximal multipartite entanglement
• The Effects of Symmetries on Quantum Fidelity Decay