Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay

2003/10/06 by David Poulin, Robin Blume-Kohout, Raymond Laflamme +2 · 8 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physrevlett.92.177906

published as Phys. Rev. Lett. 92, 177906 (2004) · 4 pages, 2 eps figures

arxiv created 2003/10/06 · openalex publication_date 2004/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 statistics. Our result also illustrates the role of chaos in the process of decoherence.

Citations

• Stabilization of Quantum Computations by Symmetrization
• Elementary gates for quantum computation
• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo

Cited by

• A cold-atoms based processor for deterministic quantum computation with one qubit in intractably large Hilbert spaces
• Effects of symmetries on quantum fidelity decay
• Experimental Approximation of the Jones Polynomial with One Quantum Bit
• Quantum dissonance and deterministic quantum computation with a single qubit
• Hardness of classically sampling the one-clean-qubit model with constant total variation distance error
• Experimental Quantum Computing without Entanglement
• Compressed sensing quantum process tomography for superconducting quantum gates
• Butterfly effect [wikipedia]