Abstract High-fidelity entangled-state generation in driven two-atom systems is often optimized at a nominal transition frequency, which can produce control pulses that are fragile against detuning errors and experimental imperfections. To address this limitation, we develop a sampled-detuning quantum optimal-control approach in which different detuning values are treated as control scenarios driven by a common laser field. Time-domain equality constraints, including zero pulse area and fixed fluence, are incorporated directly into the pulse update. The resulting constraint-projected update provides a common ascent direction for the sampled detuning objectives while preserving the imposed pulse constraints. Numerical simulations show that the optimized robust pulses maintain a high target-state population over a wider detuning interval than resonant Gaussian pulses and conventional single-objective optimal pulses. The results further reveal a fluence-bandwidth trade-off for robust plateau formation. Frequency-domain analysis indicates that the enhanced robustness is associated with optimized off-resonant spectral components, and the robustness window can be tuned by selecting the sampled-detuning training range.
Abstract High-fidelity entangled-state generation in driven two-atom systems is often optimized at a nominal transition frequency, which can produce control pulses that are fragile against detuning errors and experimental imperfections. To address this limitation, we develop a sampled-detuning quantum optimal-control approach in which different detuning values are treated as control scenarios driven by a common laser field. Time-domain equality constraints, including zero pulse area and fixed fluence, are incorporated directly into the pulse update. The resulting constraint-projected update provides a common ascent direction for the sampled detuning objectives while preserving the imposed pulse constraints. Numerical simulations show that the optimized robust pulses maintain a high target-state population over a wider detuning interval than resonant Gaussian pulses and conventional single-objective optimal pulses. The results further reveal a fluence-bandwidth trade-off for robust plateau formation. Frequency-domain analysis indicates that the enhanced robustness is associated with optimized off-resonant spectral components, and the robustness window can be tuned by selecting the sampled-detuning training range.
We present a quantum optimal control theory study combined with theoretical analysis to determine a pulsed laser field, capable of generating a maximally entangled state in two trapped two-level atoms. By expanding the time-dependent unitary operator to the first leading term of Magnus expansion, we reexamine the pulse area theorem for the trapped atoms driven by an arbitrarily temporary field. Due to the dipole-dipole interaction blockade, we find that the two trapped atoms described by a three-level ladder system can be reduced into an equivalent two-level model by using narrow-bandwidth pulses, leading to an analytical solution for generating the maximally entangled state. We also solve a highly constrained optimization problem to search for optimal laser pulses with broad bandwidths. A zero pulse-area constraint is employed to remove the dc offset of the optimized laser pulses, and a fixed fluence limitation combined with a constant pulse-area constraint at the resonant frequency of the equivalent two-level system are utilized to restrict the unitary evolution of quantum systems by the first leading term of Magnus expansion. This work provides a potentially useful approach to find all-optical control schemes for generating the maximally entangled state by using ultrafast laser pulses while satisfying multiple strict limitations.
Rydberg-based two-qubit gate fidelities in neutral atom arrays are limited chiefly by laser intensity inhomogeneity and by detuning errors from frequency miscalibration, background-field drift, intermediate state light shift and Doppler shifts. Quantum optimal control can suppress the former, but no pulse can render a controlled-Z gate first-order insensitive to detuning. Here we show that this obstruction can be circumvented by designing Rydberg gate pulses with every leading-order detuning error relegated to single-qubit Z-rotations, which an echoed sequence removes. The resulting maximally-entangling ZZ gate has no leading-order response to arbitrary detunings on either atom, maintaining an infidelity below 10−3 within a much wider range of single-atom detunings than the time-optimal gates. We further show that a large fraction of residual error is dominated by population outside the computational subspace, which can be converted into heralded erasures. Our results significantly reduce the requirements on laser frequency stability and intensity homogeneity, field calibration and atomic temperature toward practical fault-tolerant quantum computing with neutral atoms.
We present a comprehensive theoretical analysis of ultrafast entanglement generation between two Rydberg-blockaded atoms, explicitly accounting for realistic laser noise. Using femtosecond Gaussian pulses as a baseline, we systematically evaluate Bell-state fidelity sensitivity to amplitude and phase noise across white, pink (1/f), and Ornstein-Uhlenbeck spectra using Monte Carlo ensemble simulations. Our results show that amplitude noise is well tolerated, with fidelities above 90% even at 30% noise levels, while phase noise is the primary limiting factor, causing fidelity to drop rapidly beyond about 1% noise amplitude. The spectral structure of the noise is also important: pink noise consistently causes less fidelity loss than white noise of the same amplitude. By applying quantum optimal control theory (QOCT) with the D-MORPH algorithm under multiple equality constraints, we obtain a double-pulse structure with a spectral notch that achieves approximately 99% fidelity in the noise-free case and maintains high fidelity under moderate amplitude noise. A breakdown threshold near 1% amplitude noise is identified, beyond which even optimized pulses cannot sustain coherent control. These results offer practical benchmarks for the development of ultrafast neutral-atom quantum processors operating in the femtosecond regime.
Abstract We propose a high-fidelity and robust scheme for generating two-excitation Bell entangled states in a driven system of two dipole-dipole coupled two-level atoms. By exploiting the cascade structure of the collective states and applying a Morris-Shore transformation, the dynamics is reduced to an effective two-level system, enabling an analytical derivation of pulse area conditions for deterministic entanglement generation. The protocol is implemented in two sequential stages, allowing complete population transfer from the ground state to the maximally coherent superposition of the zero- and double-excitation states. To enhance robustness against pulse area and detuning errors, we replace single pulse pairs with composite pulse sequences featuring tailored phase patterns. Numerical simulations demonstrate substantial enlargement of high-fidelity regions, with different phase sequences providing different robustness profiles against pulse area and detuning errors. Our results provide a simple and analytically tractable route toward robust entanglement generation in driven atomic platforms.
Control pulses that nominally optimize fidelity are sensitive to routine hardware drift and modeling errors. Robust quantum optimal control seeks error-insensitive control pulses that maintain fidelity thresholds and obey hardware constraints. Distinct numerical approximations to the first-order error susceptibility include adjoint end-point and toggling-frame approaches. Although theoretically equivalent, we provide a novel, systematic study demonstrating important numerical differences between these two approaches. We also introduce a critical discretization correction to the widely-used toggling-frame robustness estimator, measurably improving its estimate of first-order error susceptibility. We accomplish our study by positioning robustness as a first-class objective within direct, constrained optimal control. Our approach uniquely handles control and fidelity constraints while cleanly isolating robustness for dedicated optimization. In both single- and two-qubit examples under realistic constraints, our approach provides an analytic edge for obtaining precise, physics-informed robustness.
Abstract Precise control of quantum systems is one of the most important milestones for achieving practical quantum technologies, such as computation, sensing, and communication. Several factors deteriorate the control precision and thus their suppression is strongly demanded. One of the dominant factors is systematic errors, which are caused by discord between an expected parameter in control and its actual value. Error-robust control sequences, known as composite pulses, have been invented in the field of nuclear magnetic resonance (NMR). These sequences mainly focus on the suppression of errors in one-qubit control. The one-qubit control, which is the most fundamental in a wide range of quantum technologies, often suffers from detuning error. As there are many possible control sequences robust against the detuning error, it will practically be important to find ‘optimal’ robust controls with respect to several cost functions such as time required for operation, and pulse-area during the operation, which corresponds to the energy necessary for control. In this paper, we utilize the Pontryagin’s maximum principle (PMP), a tool for solving optimization problems under inequality constraints, to solve the time and pulse-area optimization problems. We analytically obtain pulse-area optimal controls robust against the detuning error. Moreover, we found that short-CORPSE, which is the shortest known composite pulse so far, is a probable candidate of the time optimal solution according to the PMP. We evaluate the performance of the pulse-area optimal robust control and the short-CORPSE, comparing with that of the direct operation.