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arXiv:2505.02679

Data-driven Hamiltonian correction for qubits for design of gates

John GeorgeFrancis, Anil Shaji

Published May 5, 2025• 0 citations
arXivHTMLPDF

Abstract

We obtain correction terms for the standard Hamiltonian of 2 transmons driven by microwaves in cross resonance. Data is obtained from a real transmon system, namely ibm kyiv on the IBM quantum platform. Various data points obtained correspond to different microwave amplitudes and evolution times. We have an ansatz for the correction term and a correction operator whose matrix elements are parameters to be optimized for. We use adjoint sensitivity and gradient descent to obtain these parameters. We see a good fit in the predictions from the corrected Hamiltonian and hardware results demonstrating the effectiveness of scientific machine learning for fine tuning theoretical models to faithfully reproduce observed data on time evolution multiple qubit systems.

DOI
10.48550/arxiv.2505.02679

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We obtain correction terms for the standard Hamiltonian of 2 transmons driven by microwaves in cross resonance. Data is obtained from a real transmon system, namely ibm kyiv on the IBM quantum platform. Various data points obtained correspond to different microwave amplitudes and evolution times. We have an ansatz for the correction term and a correction operator whose matrix elements are parameters to be optimized for. We use adjoint sensitivity and gradient descent to obtain these parameters. We see a good fit in the predictions from the corrected Hamiltonian and hardware results demonstrating the effectiveness of scientific machine learning for fine tuning theoretical models to faithfully reproduce observed data on time evolution multiple qubit systems.
We present a new machine learning technique which calculates a real-valued, time independent, finite dimensional Hamiltonian matrix from only experimental data. A novel cost function is given along with a proof that the cost function has the theoretically correct Hamiltonian as a global minimum. We present results based on data simulated on a classical computer and results based on simulations of quantum systems on IBM's ibmqx2 quantum computer. We conclude with a discussion on the limitations of this data driven framework, as well as several possible extensions of this work. We also note that algorithm presented in this article not only serves as an example of using domain knowledge to design a machine learning framework, but also as an example of using domain knowledge to improve the speed of such algorithm.
We theoretically consider a cross-resonance (CR) gate implemented by pulse sequences proposed by Calderon-Vargas and Kestner [Phys. Rev. Lett. 118, 150502 (2017)]. These sequences mitigate systematic error to first order, but their effectiveness is limited by one-qubit gate imperfections. Using additional microwave control pulses, it is possible to tune the effective CR Hamiltonian into a regime where these sequences operate optimally. This improves the overall feasibility of these sequences by reducing the one-qubit operations required for error correction. We illustrate this by simulating randomized benchmarking for a system of weakly coupled transmons and show that while this pulse sequence does not offer an advantage with the current state of the art in transmons, it does improve the scaling of CR gate infidelity with one-qubit gate infidelity.
High-fidelity quantum control relies on accurate models of driven dynamics. We examine this re- quirement for single-qubit gates in superconducting transmons by comparing control pulses derived from the standard Duffing approximation and from a Hamiltonian constructed by diagonalizing the transmon eigenbasis. Using the same correction-pulse construction for both models, we show that correction fields derived from the Duffing approximation can substantially reduce the gate error pre- dicted by that model while remaining less effective when combined with an independently calibrated baseline pulse in the diagonalized-transmon model. In the fast-gate regime, such transferred correc- tions can even fail to improve over the uncorrected diagonalized-transmon baseline. We show that small model-dependent differences in both the energy spectrum and the representation of the drive operator can compound during driven evolution, resulting in different predicted error generators and correction pulses. A mismatch in the accumulated AC Stark phase provides one illustrative di- agnostic of this dynamical model dependence. We further demonstrate that the model Hamiltonian informs the choice of control framework: Omitting relevant leakage pathways or higher-order error channels can lead to an overly restricted correction strategy. Including these channels motivates an extended correction framework that improves the gate performance using the same physical control resources.
The two-qubit entangler is one of the most important components of quantum computers. The cross-cross resonance (CCR) gate has recently been proposed and shown to operate faster than the cross-resonance (CR) gate as an iSWAP gate. However, unlike the CR gate, the CCR gate requires frequency modifications of the input microwave pulses induced by a Stark shift. We present a theoretical study on the CCR gate in the two-transmon system. Using the Schrieffer-Wolff transformation and the rotating-wave approximation, we obtain both the effective Hamiltonian and the input microwave pulse frequencies of the CCR gate. It is well known that the static ZZZZZZ term degrades the performance of the CR gate in the transmon system. For the CCR gate, an additional dynamic ZZZZZZ term arises from the combined coupling to the qubits by the input microwave pulses, whose strength increases as the product of the two pulse amplitudes ${\mathrm{\ensuremath{\Omega}}}_{0}{\mathrm{\ensuremath{\Omega}}}_{1}$. We perform numerical simulations using the set of parameters for the IBM Hanoi quantum processor. We show that the CCR gate has a phase tunability and that varying the relative phase of the input microwave pulses can significantly improve the gate performance. This demonstrates that the static ZZZZZZ term in the CCR gate can be effectively reduced by optimizing the relative phase of the input microwave pulses.
Implementing high-fidelity multiqubit gates is critical for reducing circuit depth in near-term quantum processors and fault-tolerant architectures. However, realizing multiqubit interactions and entanglement remains a critical challenge that limits the implementation of multiqubit gates. Here we propose an all-microwave scheme to realize single-step multiqubit gates incorporating n control and m target qubits, tailored for frequency-tunable superconducting transmon networks. By leveraging cross-resonance (CR) drives, this approach induces effective two-body ZX interactions that are significantly stronger than those achieved in conventional resonant regimes, circumventing the need for tunable couplers. The system's effective Hamiltonian is analytically derived using both quad frame rotation and rigorous block diagonalization. These combined theoretical methods facilitate the identification of optimal parameter regimes that simultaneously enhance desired target couplings and suppress parasitic higher-order terms, such as ZXX interactions. Through numerical simulations and gradient-based pulse-shape optimization, we demonstrate three-qubit gates achieving fidelities exceeding 99.9% within a 60 ns gate duration. Furthermore, we evaluate the fundamental scalability of this framework by extending the optimization to a five-qubit CXXXX architecture, confirming the physical viability of the multi-target driving scheme. Because these multiqubit operations naturally emulate stabilizer measurements, this architecture provides a hardware-efficient strategy for reducing the circuit depth of stabilizer-type operations by replacing sequential two-qubit gate decompositions with single-step multiqubit gates.
Abstract The utility of a quantum computer is highly dependent on the ability to reliably perform accurate quantum logic operations. For finding optimal control solutions, it is of particular interest to explore model-free approaches, since their quality is not constrained by the limited accuracy of theoretical models for the quantum processor—in contrast to many established gate implementation strategies. In this work, we utilize a continuous control reinforcement learning algorithm to design entangling two-qubit gates for superconducting qubits; specifically, our agent constructs cross-resonance and CNOT gates without any prior information about the physical system. Using a simulated environment of fixed-frequency fixed-coupling transmon qubits, we demonstrate the capability to generate novel pulse sequences that outperform the standard cross-resonance gates in both fidelity and gate duration, while maintaining a comparable susceptibility to stochastic unitary noise. We further showcase an augmentation in training and input information that allows our agent to adapt its pulse design abilities to drifting hardware characteristics, importantly, with little to no additional optimization. Our results exhibit clearly the advantages of unbiased adaptive-feedback learning-based optimization methods for transmon gate design.