Achieving high-fidelity control of quantum systems is essential for realization of a practical quantum computer. Composite pulse sequences which suppress different types of errors can be nested to suppress a wide variety of errors but the result is often not optimal, especially in the presence of constraints such as bandwidth limitations. Robust smooth pulse shaping provides flexibility but obtaining such analytical pulse shapes is a nontrivial problem and choosing the appropriate parameters typically requires a numerical search in a high-dimensional space. In this work, we extend a previous analytical treatment of robust smooth pulses to allow the determination of pulse parameters without numerical search. We also show that the problem can be reduced to a set of coupled ordinary differential equations which allows for a more streamlined numerical treatment.
Achieving high-fidelity control of quantum systems is essential for realization of a practical quantum computer. Composite pulse sequences which suppress different types of errors can be nested to suppress a wide variety of errors but the result is often not optimal, especially in the presence of constraints such as bandwidth limitations. Robust smooth pulse shaping provides flexibility but obtaining such analytical pulse shapes is a nontrivial problem and choosing the appropriate parameters typically requires a numerical search in a high-dimensional space. In this work, we extend a previous analytical treatment of robust smooth pulses to allow the determination of pulse parameters without numerical search. We also show that the problem can be reduced to a set of coupled ordinary differential equations which allows for a more streamlined numerical treatment.
The presence of decoherence in quantum computers necessitates the suppression of noise. Dynamically corrected gates via specially designed control pulses offer a path forward, but hardware-specific experimental constraints can cause complications. Existing methods to obtain smooth pulses are either restricted to two-level systems, require an optimization over noise realizations, or limited to piecewise-continuous pulse sequences. In this paper, we present the first general method for obtaining truly smooth pulses that minimizes sensitivity to noise, eliminating the need for sampling over noise realizations and making assumptions regarding the underlying statistics of the experimental noise. We parametrize the Hamiltonian using a neural network, which allows the use of a large number of optimization parameters to adequately explore the functional control space. We demonstrate the capability of our approach by finding smooth shapes, which suppress the effects of noise within the logical subspace as well as leakage out of that subspace.
Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error, can be reliably computed. This measure of robustness is inversely proportional to the upper bound on the differential sensitivity of the fidelity error evaluated under nominal operating conditions. Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties.
Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper, a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error can be reliably computed. This measure of robustness is inversely proportional to the upper bound on the differential sensitivity of the fidelity error evaluated under nominal operating conditions. Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties.
In multi-qubit system, correlated errors subject to unwanted interactions with other qubits is one of the major obstacles for scaling up quantum computers to be applicable. We present two approaches to correct such noise and demonstrate with high fidelity and robustness. We use spectator and intruder to discriminate the environment interacting with target qubit in different parameter regime. Our proposed approaches combines analytical theory and numerical optimization, and are general to obtain smooth control pulses for various qubit systems. Both theory and numerical simulations demonstrate to correct these errors efficiently. Gate fidelities are generally above 0.9999 over a large range of parameter variation for a set of single-qubit gates and two-qubit entangling gates. Comparison with well-known control waveform demonstrates the great advantage of our solutions.
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.