Available control in dynamical decoupled quantum systems

Yu Pan,Wei Cui,Zairong Xi

doi:10.1007/s11434-012-5138-7

Yu Pan, Wei Cui + Show 1 more

Open Access

https://doi.org/10.1007/s11434-012-5138-7

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Abstract

Dynamical decoupling (DD) eliminates qubit-bath coupling by applying a sequence of instantaneous pulses. While qubit-bath couplings generally lead to qubit relaxation and dephasing, qubit-qubit couplings are often used to manipulate or control quantum states. We investigate the available control operations in two DD schemes, named periodic DD (PDD) and Uhrig DD (UDD), to see whether universal quantum computation can be realized in these decoupled systems. We find that universal control is possible using Heisenberg interaction in both periodically decoupled system and Uhrig decoupled system, and the available control operations under two kinds of DD sequences obey the same commutation relation. In the UDD case, we also derive a rough bound for control errors.

Highlights

A quantum bit, commonly represented by a two-level quantum system, is constantly interacting with its surrounding environment
The first type of dynamical decoupling (DD) sequence is provided by nuclear magnetic resonance spectroscopy, known as “periodic DD” (PDD) [2], which averages out the non-unitary evolution of a qubit by applying a predetermined sequence periodically
Heisenberg interaction is commonly used to swap any pair of qubits [13], and able to perform universal quantum computation on the decoupled system when combined with fast single-qubit operations

Summary

Available control in dynamical decoupled quantum systems

We investigate the available control operations in two DD schemes, named periodic DD (PDD) and Uhrig DD (UDD), to see whether universal quantum computation can be realized in these decoupled systems. Transformations g j of the control group G span the whole space of bounded operators on the qubit subspace and the centralizer Z(G) is trivial, which means Heff = λI ⊗ HB. In this case, whatever “slow” controls we impose on the qubits, they will be quenched completely through dynamical decoupling. Heisenberg interaction is commonly used to swap any pair of qubits [13], and able to perform universal quantum computation on the decoupled system when combined with fast single-qubit operations. The possibility of performing universal control while the qubits are protected by UDD has not been explored yet

We begin by considering a pure dephasing model

Thus the difference δU is given by

Conclusion