Geometric Aspects of Composite Pulses
arXiv:1204.2437 · doi:10.1098/rsta.2011.0358
Abstract
Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance (NMR) realises such a robust operation by employing a sequence of possibly poor quality pulses. In this article, we demonstrate that two kinds of composite pulses, one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a twoqubit system, have vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.
20 pages, 4 figures. Accepted for publication in Philosophical Transactions of the Royal Society A
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Cited by in corpus (22)
- Experimental implementation of universal nonadiabatic geometric quantum gates in a superconducting circuit
- Robustness of dynamical decoupling sequences
- Concatenated composite pulses compensating simultaneous systematic errors
- Designing short robust NOT gates for quantum computation
- Optimal arbitrarily accurate composite pulse sequences
- Superrobust Geometric Control of a Superconducting Circuit
- Further analysis of some symmetric and antisymmetric composite pulses for tackling pulse strength errors
- Precise pulse shaping for quantum control of strong optical transitions
- Realization of Geometric Landau-Zener-Stückelberg Interferometry
- Minimal and Robust Composite Two-Qubit Gates with Ising-Type Interaction
- Controlling NMR spin systems for quantum computation
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- Atomic spin-wave control and spin-dependent kicks with shaped subnanosecond pulses
- Conditions for Equivalent Noise Sensitivity of Geometric and Dynamical Quantum Gates
- Concatenated Composite Pulses Applied to Liquid-State Nuclear Magnetic Resonance Spectroscopy
- Short composite rotation robust against two common systematic errors
- Reverse engineering of one-qubit filter functions with dynamical invariants
- Quantum Error Correction with Uniformly Mixed State Ancillae
- Genuinely noncyclic geometric gates in two-pulse schemes
- Fault-tolerant composite Householder reflection
- Study of Open Systems with Molecules in Isotropic Liquids
- Construction of Arbitrary Robust One-Qubit Operations Using Planar Geometry