[Paper Review] Suppression of static ZZ interaction in an all-transmon quantum processor

Peng Zhao, Dong Lan+6 more|arXiv (Cornell University)|Nov 8, 2020

Quantum and electron transport phenomena27 references4 citations

TL;DR

This paper proposes a method to suppress static $ZZ$ interactions in all-transmon superconducting quantum processors by engineering quantum interference through a three-qubit architecture with a tunable coupler. By tuning the coupler frequency and coupling strengths, the authors achieve a parameter regime where $ZZ$ coupling is heavily suppressed while preserving strong $XY$ interaction, enabling high-fidelity iSWAP gates with gate fidelities exceeding 99.98% and conditional phase errors below 0.003 rad.

ABSTRACT

The superconducting transmon qubit is currently a leading qubit modality for quantum computing, but gate performance in quantum processor with transmons is often insufficient to support running complex algorithms for practical applications. It is thus highly desirable to further improve gate performance. Due to the weak anharmonicity of transmon, a static ZZ interaction between coupled transmons commonly exists, undermining the gate performance, and in long term, it can become performance limiting. Here we theoretically explore a previously unexplored parameter region in an all-transmon system to address this issue. We show that an feasible parameter region, where the ZZ interaction is heavily suppressed while leaving XY interaction with an adequate strength to implement two-qubit gates, can be found for all-transmon systems. Thus, two-qubit gates, such as cross-resonance gate or iSWAP gate, can be realized without the detrimental effect from static ZZ interaction. To illustrate this, we demonstrate that an iSWAP gate with fast gate speed and dramatically lower conditional phase error can be achieved. Scaling up to large-scale transmon quantum processor, especially the cases with fixed coupling, addressing error, idling error, and crosstalk that arises from static ZZ interaction could also be strongly suppressed.

Motivation & Objective

• Address the performance-limiting issue of static $ZZ$ interactions in all-transmon superconducting quantum processors.
• Overcome the challenge of suppressing $ZZ$ coupling without sacrificing $XY$ interaction strength needed for two-qubit gates.
• Enable high-fidelity two-qubit gates—such as iSWAP and cross-resonance gates—by identifying a feasible parameter region where $ZZ$ coupling is minimized.
• Demonstrate that fixed-coupling transmon architectures can achieve reduced crosstalk, idling error, and addressing error by suppressing $ZZ$ interactions.

Proposed method

• Design a three-qubit system with two transmons coupled via a coupler circuit combining a capacitor and an ancilla transmon.
• Model the system as three coupled weakly anharmonic oscillators, using a Hamiltonian that includes transmon energies, anharmonicities, and coupling terms.
• Apply perturbation theory to derive expressions for $XY$ coupling $J$ and static $ZZ$ coupling $\zeta$ in terms of coupling strengths $g_{1c}, g_{2c}$ and frequency detunings.
• Identify parameter regions in the $(\omega_c, g_{12})$ space where $\zeta \approx 0$ while $J$ remains significant, using symmetry and quantum interference between virtual transitions.
• Implement a diabatic iSWAP gate using Gaussian flat-top pulses that modulate the coupler and target transmon frequencies, maintaining synchronization between swap and leakage channels.
• Operate the system in both dispersive and quasi-dispersive regimes to validate robustness and performance across different coupling conditions.

Experimental results

Research questions

• RQ1 Can static $ZZ$ interactions be suppressed in an all-transmon system without turning off inter-qubit coupling?
• RQ2 Is there a parameter regime where $ZZ$ coupling is minimized while $XY$ coupling remains strong enough to implement high-fidelity two-qubit gates?
• RQ3 Can quantum interference between different virtual transition paths be engineered to selectively suppress $ZZ$ coupling while preserving $XY$ interaction?
• RQ4 What are the gate fidelities and error rates achievable in such a parameter regime, particularly for iSWAP gates?
• RQ5 Can the suppression of $ZZ$ coupling reduce crosstalk, idling error, and addressing error in fixed-coupling transmon architectures?

Key findings

• A feasible parameter region exists in the $(\omega_c, g_{12})$ space where static $ZZ$ coupling is heavily suppressed while $XY$ coupling remains strong enough to implement two-qubit gates.
• In the dispersive regime ($\omega_c/2\pi \approx 7.79$ GHz), an iSWAP gate with a fidelity of 99.994% and leakage below 0.006% is achieved with a hold time of 57 ns.
• In the quasi-dispersive regime ($\omega_c/2\pi \approx 7.04$ GHz), an iSWAP gate with fidelity above 99.988% and leakage below 0.012% is achieved with a hold time of 14.3 ns.
• The conditional phase error $\delta_\theta$ is suppressed below 0.001 rad in the dispersive regime and below 0.003 rad in the quasi-dispersive regime, confirming strong suppression of $ZZ$ interaction.
• The suppression of $ZZ$ coupling is attributed to quantum interference between different virtual transition paths involving distinct intermediate states, enabling selective cancellation.
• The proposed method enables significant reduction in crosstalk, idling error, and addressing error in fixed-coupling transmon processors by eliminating the dominant $ZZ$-induced decoherence channel.