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arXiv:1811.02623 · Physical Review A

Detuning-modulated composite pulses for high-fidelity robust quantum control

Elica S. Kyoseva, Hadar Greener, Haim Suchowski

Published Sep 25, 2019• 31 citations
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Abstract

We introduce a control method for off-resonant robust quantum information processing suited for quantum integrated photonics. We utilize detunings as control parameters to derive a family of composite pulses for high-fidelity complete population transfer. The presented detuning-modulated composite sequences can be implemented within the decay lifetime of the qubit and correct for control inaccuracies in various parameters including pulse strength, duration, detuning, phase jitter, Stark shift, and unwanted frequency chirps. We implement the proposed robust sequences in an integrated photonics platform to achieve complete light transfer insensitive to fabrication errors.

DOI
10.1103/physreva.100.032333

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We introduce a control method for off-resonant robust quantum information processing suited for quantum integrated photonics. We utilize detunings as control parameters to derive a family of composite pulses for high-fidelity complete population transfer. The presented detuning-modulated composite sequences can be implemented within the decay lifetime of the qubit and correct for control inaccuracies in various parameters including pulse strength, duration, detuning, phase jitter, Stark shift, and unwanted frequency chirps. We implement the proposed robust sequences in an integrated photonics platform to achieve complete light transfer insensitive to fabrication errors.
Technologies which harness the laws of quantum mechanics in computational science are pushing toward exponential improvement of information processing tasks. This, as well as innovative functionalities in sensing and imaging, break the fundamental classical limits of computation and measurement. Yet, quantum computation and quantum information processing (QIP) rely on the accuracy of unitary gate operations. In all quantum systems, unitary gates are highly sensitive to deviations from the target control parameters due in part to fabrication errors and environmental changes. Thus, translating quantum information schemes from abstraction to realistic conditions requires robust designs to overcome inherent errors. Moreover, such gates must be universal, meaning that they are independent of the initial state of the qubit system. This adds to the complexity of implementing precise unitary gates that are required for scalable quantum computation. Herein, detuning-modulated composite pulses (DMCPs) are a promising method for achieving accurate and robust state transfer in any qubit hardware platform. We present a DMCP scheme to achieve such universal quantum gates well within the error threshold suitable for QIP. Universal DMCPs are a compelling mechanism for realizing unitary gates in quantum computers under error-prone experimental conditions. These pulses are robust to inaccuracies in pulse strength, duration, resonance offset errors, Stark shifts, etc. within the lifetime of the system.
We present a general method to derive detuning-modualted composite pulses (DMCPs) as N rotations of a canonical two-state quantum system to create accurate and robust pulses that are independent of the initial state of the system. This scheme has minimal pulse overhead, and achieves pulses that are stable against amplitude errors well within the 10−410^{-4}10−4 threshold that may be suitable for quantum information processing (QIP), within the lifetime of the system. This family of pulses enables to overcome inevitable fabrication errors in silicon photonics, and relax the need for a precise initial state of light coupled into the system to achieve accurate light transfer. Furthermore, we extend universal DMCPs to n-level systems with irreducible SU(2) symmetry to create state transfer that is highly robust to errors in the pulse area from any initial state.
Coherent control of two-state systems is traditionally achieved by resonant pulses of specific Rabi frequency and duration, by adiabatic techniques using level crossings or delayed pulses, or by sequences of pulses with precise relative phases (composite pulses). Here we develop a method for high-fidelity coherent control which uses a sequence of detuning pulses. By using the detuning pulse areas as control parameters, and driving on an analogy with composite pulses, we report a great variety of detuning pulse sequences for broadband and narrow-band transition probability profiles.
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.
Composite pulses---sequences of pulses with well-defined relative phases---are an efficient, robust, and flexible technique for coherent control of quantum systems. Composite sequences can compensate for a variety of experimental errors in the driving field (e.g., in the pulse amplitude, duration, detuning, chirp, etc.) or in the quantum system and its environment (e.g., inhomogeneous broadening, stray electric or magnetic fields, unwanted couplings, etc.). The control parameters are the relative phases between the constituent pulses in the composite sequence, an accurate control over which is required in all composite sequences reported hitherto. In this paper, we introduce two types of composite pulse sequences which, in addition to error compensation in the basic experimental parameters, compensate for systematic errors in the composite phases. In the first type of such composite sequences, which compensate for pulse area errors, relative phase errors of over 10% can be tolerated with reasonably short sequences while maintaining the fidelity above the 99.99% quantum computing benchmark. In the second type of composite sequences, which compensate for simultaneous pulse area and detuning errors, relative phase errors of over 5% can be compensated.