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.
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.
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), 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.
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 method to construct high-fidelity quantum phase gates, which are insensitive to errors in various experimental parameters. The phase gates consist of a pair of two sequential broadband composite pulses, with a phase difference $\ensuremath{\pi}+\ensuremath{\alpha}/2$ between them, where $\ensuremath{\alpha}$ is the desired gate phase. By using composite pulses which compensate systematic errors in the pulse area, the frequency detuning, or both the area and the detuning, we thereby construct composite phase gates which compensate errors in the same parameters. Particularly interesting are phase gates which use the recently discovered universal composite pulses, which compensate systematic errors in any parameter of the driving field, which keep the evolution Hermitian (e.g., pulse amplitude and duration, pulse shape, frequency detuning, Stark shifts, residual frequency chirps, etc.).
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 π 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.
The Hamiltonian control of n qubits requires precision control of both the strength and timing of interactions. Compensation pulses relax the precision requirements by reducing unknown but systematic errors. Using composite pulse techniques designed for single qubits, we show that systematic errors for n -qubit systems can be corrected to arbitrary accuracy given either two non-commuting control Hamiltonians with identical systematic errors or one error-free control Hamiltonian. We also examine composite pulses in the context of quantum computers controlled by two-qubit interactions. For quantum computers based on the XY interaction, single-qubit composite pulse sequences naturally correct systematic errors. For quantum computers based on the Heisenberg or exchange interaction, the composite pulse sequences reduce the logical single-qubit gate errors but increase the errors for logical two-qubit gates.
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.