Superconducting Qubits Achieve Programmable Heisenberg Simulation with Five-Qubit Chains

Superconducting qubits, the building blocks of many promising quantum computers, often face a fundamental limitation, a trade-off between the strength of their interactions and the stability of their quantum states. Yi-Han Yu, Xin-Yi Li, and Kai Xu, at institutions including Heng Fan’s research group, now demonstrate a technique called Mathieu control that overcomes this challenge, offering a new level of precision in manipulating qubit interactions. This method employs a carefully tuned energy source to subtly alter how qubits connect without disturbing their core quantum information, allowing researchers to continuously adjust and even completely switch off the coupling between qubits. The team successfully implemented this control on a five-qubit system, enabling the simulation of complex magnetic phenomena and paving the way for more powerful and versatile quantum processors with improved accuracy and programmability.

China, Hefei National Laboratory, Hefei 230088, China, Beijing Key Laboratory for Advanced Quantum Technology, Beijing 100190, China. A fundamental challenge in superconducting quantum circuits involves balancing strong qubit coupling with the integrity of quantum states. Researchers present Mathieu control, a technique employing a non-resonant two-photon drive to create a selective nonlinear frequency shift, modifying interactions while preserving qubit states. This enables continuous tuning of the ZZ coupling, including full suppression, and integrating single- and two-qubit gates with low leakage, facilitating a programmable Heisenberg (XXZ) interaction.

Mathieu Control Enables Tunable Qubit Interactions

The research team pioneered Mathieu control to address a key challenge in superconducting circuits, balancing strong qubit coupling with the preservation of quantum state integrity. This method employs a non-resonant, two-photon drive applied to a quadratic potential to generate a selective nonlinear frequency shift, renormalizing interactions between qubits while shielding computational levels from disturbances. The approach enables continuous tuning of the ZZ coupling, even achieving complete suppression, and facilitates the integration of single- and two-qubit gates with remarkably low leakage. The team leveraged the connection between the Hamiltonian of a frequency-tunable quantum harmonic oscillator and the Mathieu equation, a mathematical description of parametric resonance, to develop their control mechanism.

Applying a high-frequency flux drive, deliberately detuned from a two-photon transition frequency, created a dispersive interaction that selectively modifies the qubit’s energy landscape. Experiments focused on a qubit-coupler-qubit device, where the two-photon drive was applied to the SQUID loop of the central qubit, inducing level repulsion without population transfer. The effective ZZ coupling strength between the qubits could be precisely controlled by varying the amplitude of the Mathieu drive, achieving full suppression at a specific operating point. This precise control was validated through simulations of single-qubit and two-qubit gates, with process matrices confirming high-fidelity performance. Extending this methodology to a five-qubit chain, the researchers demonstrated the system’s ability to simulate the dynamics of magnetic phases, highlighting its potential for programmable quantum simulation.

Mathieu Control Enables Qubit Reconfiguration and Simulation

The team successfully demonstrated Mathieu control for manipulating superconducting circuits, addressing the challenge of balancing strong qubit interactions with the preservation of their quantum states. This method utilizes a non-resonant two-photon signal to selectively alter the frequency of interactions without disturbing the qubits themselves. Consequently, researchers achieved continuous and precise tuning of the coupling between qubits, even suppressing it entirely, and integrated both single- and two-qubit operations with minimal errors. Extending this control to a five-qubit system, the researchers demonstrated the ability to reconfigure the circuit to simulate the dynamics of complex magnetic phases, highlighting the system’s programmability and potential for broader quantum simulations. The principle of selective spectral engineering, achieved through these off-resonant drives, is broadly applicable and could be adapted for use in other quantum computing platforms, such as those based on trapped ions or nanomechanical systems. The results convincingly demonstrate high-fidelity logic and a pathway towards programmable simulation of complex quantum phenomena.