[Paper Review] Quantum crosstalk analysis for simultaneous gate operations on superconducting qubits

Peng Zhao, Kehuan Linghu+6 more|arXiv (Cornell University)|Oct 25, 2021

Quantum and electron transport phenomena4 citations

TL;DR

This paper provides a theoretical analysis of quantum crosstalk in superconducting qubit architectures using a tunable bus to implement sub-100-ns controlled-Z (CZ) gates. It identifies that non-negligible cross-driving errors arise during microwave-driven single-qubit gates near frequency collision points, and parasitic next-nearest-neighbor interactions during CZ operations cause leakage and control errors at resonance points, highlighting the need for improved error mitigation and low-crosstalk qubit design in scalable quantum processors.

ABSTRACT

Maintaining or even improving gate performance with growing numbers of parallel controlled qubits is a vital requirement for fault-tolerant quantum computing. For superconducting quantum processors, though isolated one- or two-qubit gates have been demonstrated with high-fidelity, implementing these gates in parallel commonly shows worse performance. Generally, this degradation is attributed to various crosstalks between qubits, such as quantum crosstalk due to residual inter-qubit coupling. An understanding of the exact nature of these crosstalks is critical to figuring out respective mitigation schemes and improved qubit architecture designs with low crosstalk. Here we give a theoretical analysis of quantum crosstalk impact on simultaneous gate operations in a qubit architecture, where fixed-frequency transmon qubits are coupled via a tunable bus, and sub-100-ns controlled-Z (CZ) gates can be realized by applying a baseband flux pulse on the bus. Our analysis shows that for microwave-driven single-qubit gates, the dressing from the qubit-qubit coupling can cause non-negligible cross-driving errors when qubits operate near frequency collision regions. During CZ gate operations, although unwanted near-neighbor interactions are nominally turned off, sub-MHz parasitic next-near-neighbor interactions involving spectator qubits can still exist, causing considerable leakage or control error when one operates qubit systems around these parasitic resonance points. To ensure high-fidelity simultaneous operations, there could raise a request to figure out a better way to balance the gate error from target qubit systems themselves and the error from non-participating spectator qubits. Overall, our analysis suggests that towards useful quantum processors, the qubit architecture should be examined carefully in the context of high-fidelity simultaneous gate operations in a scalable qubit lattice.

Motivation & Objective

• To understand the sources and impacts of quantum crosstalk in superconducting qubit systems during simultaneous gate operations.
• To identify how residual inter-qubit couplings and parasitic interactions degrade gate fidelity in multi-qubit architectures.
• To evaluate the role of spectator qubits and non-participating qubits in introducing errors during parallel gate operations.
• To provide a theoretical framework for assessing crosstalk effects in fixed-frequency transmon qubits coupled via a tunable bus.
• To guide future hardware design and error mitigation strategies by quantifying crosstalk contributions from both target and spectator qubits.

Proposed method

• Uses a theoretical model of a four-qubit square lattice with fixed-frequency transmon qubits coupled via a tunable flux-bus to simulate gate operations.
• Applies baseband flux pulses to the bus to implement sub-100-ns CZ gates, with pulse shape defined by three Fourier coefficients satisfying λ₁ + λ₃ = 1.
• Calculates the actual evolution operator using the time-ordered exponential of the system Hamiltonian, U₂ = P̂T exp(−i∫₀ᵀ H(t)dt).
• Projects the full evolution operator onto computational subspaces using projection operators P₁ and P₂ for single- and two-qubit operations.
• Evaluates gate fidelity using a metric that includes post-gate phase corrections to account for local single-qubit phase errors.
• Analyzes population swap matrices P(o|i) across single-, two-, and three-excitation subspaces to quantify leakage and crosstalk from next-nearest-neighbor qubits.

Experimental results

Research questions

• RQ1 What are the dominant sources of crosstalk during simultaneous single- and two-qubit gate operations in a superconducting qubit lattice?
• RQ2 How do residual inter-qubit couplings and parasitic next-nearest-neighbor interactions affect gate fidelity during parallel CZ gate operations?
• RQ3 To what extent do spectator qubits contribute to gate errors when target qubits are operated near resonance points?
• RQ4 How does the frequency collision region impact cross-driving errors in microwave-driven single-qubit gates?
• RQ5 What is the role of high-order processes in enabling non-negligible population swaps between next-nearest-neighbor qubits?

Key findings

• Non-negligible cross-driving errors occur during microwave-driven single-qubit gates when qubits operate near frequency collision points due to qubit-qubit coupling dressing.
• Parasitic next-nearest-neighbor interactions of sub-MHz strength can cause significant leakage and control errors during CZ gate operations when the system is near resonance with these interactions.
• Population swaps between next-nearest-neighbor qubits are enabled by high-order processes and are suppressed below 10⁻⁴, but still contribute to measurable gate errors.
• The gate fidelity degrades in parallel operations due to a balance between errors from target qubit systems and errors from non-participating spectator qubits.
• The analysis reveals that even with high-fidelity isolated gates, simultaneous operations suffer from crosstalk that must be addressed through improved architecture and control strategies.
• The study underscores the necessity of designing scalable qubit lattices with minimized crosstalk to achieve fault-tolerant quantum computing.