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Applications of Concatenated Composite Pulses to NMR

Masamitsu Bando, Mikio Nakahara, Yasushi Kondo, Nobuaki Nemoto, Tsubasa Ichikawa, Yutaka Shikano

Published Aug 12, 2015• 0 citations
OpenAlex

Abstract

ConCatenated Composite Pulses (CCCPs) are derived from various composite pulses widely employed in NMR and have been developed as high-precision unitary operations in Quantum Information Processing (QIP). CCCPs are robust against two systematic errors, pulse-length and off-resonance errors, in NMR simultaneously. We show experiments that demonstrate CCCPs are powerful and versatile tools not only in QIP but also in NMR measurements.

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ConCatenated Composite Pulses (CCCPs) are derived from various composite pulses widely employed in NMR and have been developed as high-precision unitary operations in Quantum Information Processing (QIP). CCCPs are robust against two systematic errors, pulse-length and off-resonance errors, in NMR simultaneously. We show experiments that demonstrate CCCPs are powerful and versatile tools not only in QIP but also in NMR measurements.
The error-robust and short composite operations named ConCatenated Composite Pulses (CCCPs), developed as high-precision unitary operations in quantum information processing (QIP), are derived from composite pulses widely employed in nuclear magnetic resonance (NMR). CCCPs simultaneously compensate for two types of systematic errors, which was not possible with the known composite pulses in NMR. Our experiments demonstrate that CCCPs are powerful and versatile tools not only in QIP but also in NMR.
In NMR experiments and quantum computation, many pulse (quantum gate) sequences called the composite pulses, were developed to suppress one of two dominant errors; a pulse length error and an off-resonance error. We describe, in this paper, a general prescription to design a single-qubit concatenated composite pulse (CCCP) that is robust against two types of errors simultaneously. To this end, we introduce a new property, which is satisfied by some composite pulses and is sufficient to obtain a CCCP. Then we introduce a general method to design CCCPs with shorter execution time and less number of pulses.
In NMR experiments and quantum computation, many pulse (quantum gate) sequences called the composite pulses, were developed to suppress one of two dominant errors; a pulse length error and an off-resonance error. We describe, in this paper, a general prescription to design a single-qubit concatenated composite pulse (CCCP) that is robust against two types of errors simultaneously. To this end, we introduce a new property, which is satisfied by some composite pulses and is sufficient to obtain a CCCP. Then we introduce a general method to design CCCPs with shorter execution time and less number of pulses.
Composite pulses, originally developed in nuclear magnetic resonance (NMR), have found widespread use in experimental quantum information processing (QIP) to reduce the effects of systematic errors. Most pulses used so far have simply been adapted from existing NMR designs, and while techniques have been developed for designing composite pulses with arbitrary precision, the results have been quite complicated and have found little application. Here, I describe techniques for designing short but effective composite pulses to implement robust not gates, bringing together existing insights from NMR and QIP, and present some composite pulses.
We propose a simple formalism to design unitary gates robust against given systematic errors. This formalism generalizes our previous observation [Y. Kondo and M. Bando, J. Phys. Soc. Jpn. 80, 054002 (2011)] that vanishing dynamical phase in some composite gates is essential to suppress pulse-length errors. By employing our formalism, we derive a composite unitary gate which can be seen as a concatenation of two known composite unitary operations. The obtained unitary gate has high fidelity over a wider range of error strengths compared to existing composite gates.