Quantum Chaos and Quantum Algorithms

Abstract

It was recently shown (quant-ph/9909074) that parasitic random interactions between the qubits in a quantum computer can induce quantum chaos and put into question the operability of a quantum computer. In this work I investigate whether already the interactions between the qubits introduced with the intention to operate the quantum computer may lead to quantum chaos. The analysis focuses on two well--known quantum algorithms, namely Grover's search algorithm and the quantum Fourier transform. I show that in both cases the same very unusual combination of signatures from chaotic and from integrable dynamics arises.

7 pages revtex including 8 figures

Cited by in corpus (12)

• Entanglement production in coupled chaotic systems : Case of the Kicked Tops
• Exploring quantum chaos with a single nuclear spin
• The effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators
• Driving superconducting qubits into chaos
• Quantum chaos in the spectrum of operators used in Shor's algorithm
• Quantum chaos algorithms and dissipative decoherence with quantum trajectories
• Distribution of interference in random quantum algorithms
• Phase diagram for the Grover algorithm with static imperfections
• The modular multiplication operator and the quantized bakers maps
• Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry
• Chaotic spin-spin entanglement on a recursive lattice
• Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations