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arXiv:2203.05754 · Physical Review A

General off-resonance-error-robust symmetric composite pulses with three elementary operations

Shingo Kukita, Haruki Kiya, Yasushi Kondo

Published Oct 25, 2022• 6 citations
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Abstract

Accurate quantum control is a key technology for realizing quantum information processing, such as quantum communication and quantum computation. In reality, a quantum state under control suffers from undesirable effects caused by systematic errors. A composite pulse (CP) is used to eliminate the effects of systematic errors during control. One-qubit control, which is the most fundamental in quantum control, is typically affected by two errors: pulse length error and off-resonance error (ORE). In this paper, we focus on ORE-robust CPs and systematically construct symmetric ones comprising three elementary operations in order to understand their properties. We find an infinitely large number of ORE-robust CPs, including the well-known CORPSE family, and evaluate their performance according to gate infidelity and operation time, both of which are important for the realization of accurate quantum control.

DOI
10.1103/physreva.106.042613

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Accurate quantum control is a key technology for realizing quantum information processing, such as quantum communication and quantum computation. In reality, a quantum state under control suffers from undesirable effects caused by systematic errors. A composite pulse (CP) is used to eliminate the effects of systematic errors during control. One-qubit control, which is the most fundamental in quantum control, is typically affected by two errors: pulse length error and off-resonance error (ORE). In this paper, we focus on ORE-robust CPs and systematically construct symmetric ones comprising three elementary operations in order to understand their properties. We find an infinitely large number of ORE-robust CPs, including the well-known CORPSE family, and evaluate their performance according to gate infidelity and operation time, both of which are important for the realization of accurate quantum control.
Systematic errors hinder precise quantum control. Pulse length errors (PLEs) and off-resonance errors (OREs) are typical systematic errors that are encountered during one-qubit control. A composite pulse (CP) can help compensate for the effects of systematic errors during quantum operation. Several CPs that are robust against either PLE or ORE have been identified. However, few attempts have been made to construct CPs that are robust against both errors (bi-robust). We develop a novel bi-robust CP for one-qubit operations by modifying a PLE robust CP, which exhibits a shorter operation time than that of previously developed bi-robust CPs.
The precision of quantum operations is affected by unavoidable systematic errors. A composite pulse (CP), which has been well investigated in nuclear magnetic resonance (NMR), is a technique that suppresses the influence of systematic errors by replacing a single operation with a sequence of operations. In one-qubit operations, there are two typical systematic errors, Pulse Length Error (PLE) and Off Resonance Error (ORE). Recently, it was found that PLE robust CPs have a clear geometric property. In this study, we show that ORE robust CPs also have a simple geometric property, which is associated with trajectories on the Bloch sphere of the corresponding operations. We discuss the geometric property of ORE robust CPs using two examples.
We propose various composite πππ-pulse sequences for implementing robust z-axis rotation gates widely used in quantum information processing (QIP) scenarios, and discuss their error tolerance of the pulse strength error (PSE) and off-resonance error (ORE), i.e., two typical systematic errors in NMR systems. Compared to existing composite gates, our designed composite pulses exhibit higher gate fidelity and shorter sequence time cost. Furthermore, such short pulse sequences are generalized by simple analytic formulas which can suppress these errors to any desired order simultaneously with linear length scaling, indicating an efficient construction of them with arbitrary accuracy.
Composite pulses are an efficient tool for robust quantum control. In this work, we derive the form of the composite pulse sequence to implement robust single-qubit gates in a three-level system, where two low-energy levels act as a qubit. The composite pulses can efficiently cancel the systematic errors up to a certain order. We find that the three-pulse sequence cannot completely eliminate the first order of systematic errors, but still availably makes the fidelity resistant to variations in a specific direction. When employing more pulses in the sequence (N>3N>3N>3), the fidelity can be insensitive to the variations in all directions and the robustness region becomes much wider. Finally we demonstrate the applications of composite pulses in quantum information processing, e.g., robust quantum information transfer between two qubits.
Abstract Precise control of quantum systems is a cornerstone for realizing high-quality quantum technology such as quantum computing and quantum communication. The performance of control of systems often deteriorates due to systematic errors. In one-qubit control, the pulse length error (PLE) is a typical systematic error, which is often caused by deviation of the strength of the control field. A composite quantum gate (CQG) is a method for suppressing effects of such systematic errors at the cost of a long operation time. A longer operation time implies stronger decoherence, and thus a shorter CQG is preferable from the viewpoint of noise immunity. However, it has not been clear how short CQG can be implemented. This problem can be regarded as an optimization problem under constraints: optimizing the operation time while requiring the error robustness. In this paper, we find a lower bound on operation time of all CQGs with first-order robustness against the PLE, in which effects of the error are eliminated up to its first order. The derivation of this bound is based on a geometric property of robustness against the PLE. This can be used for search after high-performance CQGs.
Composite pulse sequences designed for nuclear magnetic resonance experiments are currently being applied in many quantum information processing technologies. We present an analysis of a family of composite pulse sequences used to address systematic pulse-length errors in the execution of quantum gates. It has been demonstrated by Cummins et al. [Phys. Rev. A 67, 042308 (2003)] that for this family of composite pulse sequences, the fidelity of the resulting unitary operation compared with the ideal unitary operation is $1\ensuremath{-}C{ϵ}^{6}$, where ϵϵϵ is the fractional error in the length of the pulse. We derive an exact expression for the sixth-order coefficient CCC and from this deduce conditions under which this sixth-order dependence is observed. We also present pulse sequences which achieve the same fidelity.