We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost function which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences. More broadly, we also use the same theoretical framework to prove the robustness of nonadiabatic geometric quantum gates under specific error models and control constraints.
We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost function which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences. More broadly, we also use the same theoretical framework to prove the robustness of nonadiabatic geometric quantum gates under specific error models and control constraints.
We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering. We use this result to define a cost functional which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density. We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise. We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences. More broadly, we also use the same theoretical framework to prove the robustness of nonadiabatic geometric quantum gates under specific error models and control constraints.
We introduce a quantum control protocol that produces smooth, experimentally implementable control sequences optimized to combat temporally correlated noise for single-qubit systems. The control ansatz is specifically chosen to be a functional expansion of discrete prolate spheroidal sequences, a discrete time basis known to be optimally concentrated in time and frequency, and quite attractive when faced with experimental control hardware constraints. We leverage the filter function formalism to transform the control problem into a filter design problem, and show that the frequency response of a quantum system can be carefully tailored to avoid the most relevant dynamical contributions of noise processes. Using gradient ascent, we obtain optimized filter functions and exploit them to elucidate important details about the relationship between filter function design, control bandwidth, and noise characteristics. In particular, we identify regimes of optimal noise suppression and, in turn, optimal control bandwidth directly proportional to the size of the frequency bands where the noise power is large. In addition to providing guiding principles for filter design, our approach enables the development of controls that simultaneously yield robust noise filtering and high-fidelity single-qubit logic operations in a wide variety of complex noise environments.
We proposed a theoretical protocol to generate robust pulses for executing an arbitrary nonadiabatic holonomic quantum gate operations via reverse engineering. Compared with the traditional scheme that the pulse area needs to satisfy the condition 0 Ω dt = π, the reverse engineering scheme no longer requires this constraint, which greatly improves the flexibility of pulse designing. By optimizing the envelope of the pulses, we show that the gate operations are more robust against the frequency detuning than the traditional scheme. In the meanwhile, we also improve the robustness of the pulse against Rabi frequency fluctuations by utilizing the perturbation theory. The robust pulses can be applied to other ensemble qubit systems to realize quantum error correction, qubit initialization, and quantum gate operations, such as ensemble nitrogen-vacancy center systems, superconducting qubit systems, and other systems where qubits are addressed in frequency.
We study a novel class of open-loop control protocols constructed to perform arbitrary nontrivial single-qubit logic operations robust against time-dependent non-Markovian noise. Amplitude and phase modulation protocols are crafted leveraging insights from functional synthesis and the basis set of Walsh functions. We employ the experimentally validated generalized filter-transfer function formalism in order to find optimized control protocols for target operations in SU(2) by defining a cost function for the filter-transfer function to be minimized through the applied modulation. Our work details the various techniques by which we define and then optimize the filter-synthesis process in the Walsh basis, including the definition of specific analytic design rules which serve to efficiently constrain the available synthesis space. This approach yields modulated-gate constructions consisting of chains of discrete pulse-segments of arbitrary form, whose modulation envelopes possess intrinsic compatibility with digital logic and clocking. We derive novel families of Walsh-modulated noise filters designed to suppress dephasing and coherent amplitude-damping noise, and describe how well-known sequences derived in NMR also fall within the Walsh-synthesis framework. Finally, our work considers the effects of realistic experimental constraints such as limited modulation bandwidth on achievable filter performance.
Quantum control protocols are typically devised in the time domain, leaving their spectral behavior to emerge only a posteriori. Here, we invert this paradigm. Starting from a target frequency-domain filter, we employ the dynamical-invariant framework to derive the continuous driving fields that enact the chosen spectral response on a qubit. This approach, Quantum Invariant Filtering (QIF), maps arbitrary finite-impulse responses, including multi-band and phase-sensitive profiles, into experimentally feasible Hamiltonian modulations. Implemented on a single nitrogen-vacancy center in diamond, the method realizes the prescribed passbands with high fidelity, suppresses noise, and preserves coherence for milliseconds, two orders of magnitude longer than Carr-Purcell-Meiboom-Gill sequences, while remaining robust to 50% drive-amplitude errors. Our results establish QIF as a broadly applicable framework for enhanced quantum control and sensing across diverse physical platforms, including superconducting qubits, trapped ions, and nuclear magnetic resonance systems.
We address the experimentally relevant problem of robust mitigation of dephasing noise acting on a qubit. We first present an extension of the method of Kuopanportti et al. [Phys. Rev. A 77, 032334 (2008)] for representing $1/{\ensuremath{\omega}}^{\ensuremath{\alpha}}$ noise to the efficient representation of arbitrary Markovian noise. We then add qubit control pulses to enable the design of numerically optimized, two-dimensional, bounded amplitude control functions capable of decoupling the qubit from the dephasing effects of a broad variety of Markovian noise spectral densities during one- and two-qubit quantum operations. We illustrate the method with development of numerically optimized control pulse sequences that minimize decoherence due to a combination of $1/\ensuremath{\omega}$ and constant-offset noise sources. Comparison with the performance of standard dynamical decoupling protocols shows that the numerically optimized pulse sequences are considerably more robust with respect to zero-frequency noise. Application to the mitigation of dephasing noise on spin qubits in silicon indicates that high-fidelity quantum gates may, in principle, be implemented for such qubits with the assistance of current pulse-generation technology.