Simulating the Impact of Microwave Control Pulses on Multi-Qubit Superconducting Circuit Quantum Devices Through Maxwell-Schrödinger Modeling Methods

Superconducting quantum computers are poised to revolutionize computation by leveraging quantum mechanics to surpass the capabilities of classical computers. However, despite progress toward achieving quantum advantage, major engineering obstacles remain before these systems can be deployed for real-world applications. A critical challenge lies in developing efficient modeling techniques for improving quantum control through microwave pulse schemes. Traditional methods often prove inadequate, either due to the computational inefficiency of full-wave electromagnetics simulations or the impracticality of manual curve-fitting techniques. To enable the large-scale modeling necessary for advancing quantum hardware, new and scalable approaches must be developed that overcome these limitations. In this work, we extend previous Maxwell-Schrödinger modeling techniques (T. E. Roth and S. T. Elkin, “Maxwell-Schrödinger Modeling of a Superconducting Qubit Coupled to a Transmission Line Network,” IEEE Journal on Multiscale and Multi-physics Computational Techniques, vol. 9, Jan. 2024) to simulate coupled superconducting transmon qubits embedded in transmission line networks which are stimulated through microwave control pulses. These microwave pulses allow these superconducting architectures to perform quantum gate operations that are the basis of the quantum computing revolution. Coupled qubits, in particular, are critical components of quantum devices, enabling multi-qubit gates that generate entanglement, which is a fundamental requirement for practical quantum algorithms. Our method specifically addresses transmon qubits operating in the dispersive regime, where the frequencies of transmission line resonators used to couple qubits together are far detuned from the qubits' transition frequencies. Building upon the self-consistent equations of motion introduced in the original work, we enhance the framework by integrating the multi-qubit exchange coupling rate. This parameter plays a crucial role in capturing quantum effects essential for both the deliberate implementation of multi-qubit gates and the evaluation of unintended quantum crosstalk. Leveraging our previous formulation (G. Khan and T. E. Roth, “Field-Based Formalism for Calculating Multiqubit Exchange Coupling Rates for Transmon Qubits,” Phys. Rev. Applied, vol. 22, 064084, Dec. 2024), we provide an efficient method for calculating this rate, enabling more accurate modeling of quantum interactions in complex qubit systems. This formulation relies on the impedance response of the superconducting quantum circuit, a key advantage since impedance responses can be efficiently computed using classical electromagnetic tools. By leveraging this approach, we showcase fundamental operations such as the cross-resonance gate (C. Rigetti and M. Devoret, “Fully Microwave-Tunable Universal Gates in Superconducting Qubits with Linear Couplings and Fixed Transition Frequencies,” Physical Review B, vol. 81, 134507, Apr. 2010). Further, we demonstrate our method's capability to model complex multi-qubit interactions, while also highlighting the critical role of self-consistent interactions in the Maxwell-Schrödinger framework. When these superconducting devices are stimulated via microwave pulses to perform quantum gates, these interactions between the qubits and the transmission line resonators can significantly alter the state dynamics. By advancing robust simulation tools that can accurately model these interactions, our efforts can help support the design of precise quantum control operations in future devices.