Crosstalk and leakage in superconducting qubits: noise models

Short answer: On superconducting transmon chips, crosstalk and leakage are two error sources that simple noise models can miss. A 2023 arXiv paper characterizes crosstalk across an entire quantum chip and proposes a crosstalk-aware noise model for simulating noisy hardware. A 2021 Physical Review Letters paper suggests that software control optimization can largely mitigate crosstalk in simulation. These are characterization and simulation results.

The setting

The 2023 arXiv paper says currently available superconducting transmon hardware realizes networks of hundreds of qubits with the possibility of controlled nearest-neighbour interactions, but that inherent noise and decoherence considerably limit what such chips can do. It focuses on characterizing crosstalk, meaning, in its words, errors that occur during gate operations on specific subsets of qubits and influence the performance of other qubits in the vicinity.

Where crosstalk comes from

The paper lists several origins, including radiation from high-energy phonons produced when particles ionize the substrate, and crosstalk caused by frequency collisions among neighbouring qubits. A frequency collision is a degeneracy of the transition frequencies of neighbouring transmon qubits, which can cause undesired resonances when microwave pulses implement gates. The paper says these can cause undesired excitations of neighbouring qubits and so-called leakage, meaning population of higher energy levels outside the computational subspace. It says leakage is particularly problematic because that population permanently damages the respective qubits and so influences the result of the computation.

A crosstalk-aware noise model

The authors measure the magnitude of crosstalk on an entire quantum chip and use that information to devise a crosstalk-aware noise model, to simulate noisy quantum hardware more accurately. The value of such a model is that simulations of what a device will do match its behaviour better than models that treat each qubit as independent. The paper summary we reviewed does not report the accuracy gain, so we do not state one.

Handling crosstalk in software

The 2021 Physical Review Letters paper describes an efficient and scalable framework for modelling crosstalk on quantum information processors. By applying optimal control techniques, the authors show how to tune up arbitrary high-fidelity parallel operations on systems with substantial local and nonlocal crosstalk. As an example they simulate a 2D square array of 100 superconducting transmon qubits, including 50 simultaneous maximally entangling cross-resonance gates, and report large improvements in process infidelity with optimized control compared with unoptimized control under the same crosstalk. They suggest that rather than engineering away undesirable interactions during fabrication, such effects can largely be mitigated with software through careful characterization and control optimization. This is a simulation result.

Why it matters for error correction

A PhD thesis from TU Delft on mitigating leakage and noise in superconducting quantum computing notes that quantum error correction has mostly been studied with idealized error models, even as it starts to be tested in experiments. It says error correction carries substantial overhead, especially when error rates are barely below threshold, and that the physical error rates of the fundamental operations are still high. The thesis focuses on achieving lower error rates for fundamental operations on superconducting qubits.

What this does not tell you

These sources do not give crosstalk or leakage rates for any commercial processor, and the 100-qubit array result is simulated, not measured on hardware.

FAQ

What is crosstalk?

Errors during gate operations on some qubits that affect nearby qubits, per the 2023 paper.

What causes it?

The paper names frequency collisions between neighbouring transmons and phonons from ionizing events in the substrate, among others.

What is leakage?

Population of energy levels outside the computational subspace, which the paper calls particularly problematic.

Can software fix crosstalk?

A 2021 paper reports in simulation that optimized control largely mitigates it for a 100-qubit array.

Do idealized noise models suffice for error correction?

The TU Delft thesis says error correction performance has mostly been studied with idealized error models.