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Journal of Physics B Atomic Molecular and Optical Physics

Composite π / 2 pulses robust to systematic phase miscalibration and pulse-area errors

Petar Chernev, Andon A. Rangelov

Published Aug 14, 2026• 0 citations
Publisher

Abstract

Abstract We construct composite half- π pulses that are simultaneously robust to systematic mistracking of the control phases and to small pulse-area deviations. We extend the errant-phase composite-pulse approach from population-inversion ( π ) gates to π / 2 rotations, which are intrinsically more sensitive to phase miscalibration because they rely on controlled interference to create a specific superposition. The phases of the constituent pulses are chosen to cancel, order by order, the leading error terms associated with a correlated phase-scaling parameter while preserving broadband tolerance to pulse-area errors. We provide explicit non-anagram phase solutions for odd-length sequences and verify their performance by numerical simulations of the full composite propagator.

DOI
10.1088/1361-6455/ae9a1e

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Abstract We construct composite half- π pulses that are simultaneously robust to systematic mistracking of the control phases and to small pulse-area deviations. We extend the errant-phase composite-pulse approach from population-inversion ( π ) gates to π / 2 rotations, which are intrinsically more sensitive to phase miscalibration because they rely on controlled interference to create a specific superposition. The phases of the constituent pulses are chosen to cancel, order by order, the leading error terms associated with a correlated phase-scaling parameter while preserving broadband tolerance to pulse-area errors. We provide explicit non-anagram phase solutions for odd-length sequences and verify their performance by numerical simulations of the full composite propagator.
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.
We present a systematic method for constructing universal composite phase gates with a continuously tunable target phase. Using a general Cayley--Klein parametrization of the single-pulse propagator, we design gates from an even number of nominal πππ pulses and derive analytic phase families by canceling, order by order in a small deviation parameter, the leading contributions to the undesired off-diagonal element of the composite propagator, independently of the dynamical phase. The resulting sequences provide intrinsic robustness against generic control imperfections and parameter fluctuations and remain valid for arbitrary pulse shapes. Numerical simulations in a standard two-level model confirm high-order error suppression and demonstrate broad, flat high-fidelity plateaus over wide ranges of simultaneous pulse-area and detuning errors, highlighting the efficiency of the proposed universal composite phase gates for resilient phase control in quantum information processing.
Systematic control errors remain a primary obstacle to realizing high-fidelity single-qubit gates. We introduce composite pulse sequences that implement X and Hadamard gates while simultaneously compensating amplitude (Rabi-frequency), detuning (frequency), and duration errors. Our construction uses two complementary strategies: (i) derivative-based cancellation of error terms in the full unitary (not just the transition probability), formulated via the Cayley-Klein parametrization, and (ii) direct minimization of the average gate infidelity over prescribed error ranges. We derive symmetric five-pulse solutions with closed-form phases that cancel all first-order terms (including the mixed derivative), and numerically optimize longer sequences -- up to 15 pulses -- to achieve higher-order suppression. We also show that standard ``universal'' five-pulse sequences (U5a/U5b) emerge as simple phase-shifted instances of our symmetric solutions, yielding broad robustness to both detuning and amplitude errors. Finally, we construct variable-area sequences for Rx(π/2)R_x(π/2)Rx​(π/2), which, up to virtual Z rotations, benchmark the Hadamard gate. Across all families we observe the expected trade-off between sequence length and robustness window, with substantial boosts in fidelity over large error domains.
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.
We present three classes of symmetric broadband composite pulse sequences. The composite phases are given by analytic formulas (rational fractions of $\ensuremath{\pi}$) valid for any number of constituent pulses. The transition probability is expressed by simple analytic formulas and the order of pulse area error compensation grows linearly with the number of pulses. Therefore, any desired compensation order can be produced by an appropriate composite sequence; in this sense, they are arbitrarily accurate. These composite pulses perform equally well as or better than previously published ones. Moreover, the current sequences are more flexible as they allow total pulse areas of arbitrary integer multiples of $\ensuremath{\pi}$.
We design composite controlled-phase gates, which compensate errors in the phase of a single gate. The errors can be of various natures, such as relative, absolute, or both. We present composite sequences which are robust to relative errors up to the sixth order with the number of the constituent gates growing just linearly with the desired accuracy, and we describe a method to achieve even higher accuracy. We show that the absolute error can be canceled entirely with only two gates. We describe an ion-trap implementation of our composite gates in which simultaneous cancellation of the error in both the pulse area and the detuning is achieved.