[Paper Review] Decoherence of a tunable capacitively shunted flux qubit

R. Trappen, Xi Dai+20 more|arXiv (Cornell University)|Jul 26, 2023

Quantum and electron transport phenomenaPhysics and Astronomy3 citations

TL;DR

This study investigates decoherence mechanisms in a tunable capacitively shunted flux qubit designed for quantum annealing, identifying intrinsic flux noise as the dominant relaxation source below 3 GHz and thermal noise in bias lines at higher frequencies. Key findings reveal that low-frequency flux noise in both qubit loops drives dephasing, with possible noise correlation between loops, informing design improvements for scalable quantum annealers with enhanced coherence.

ABSTRACT

Quantum annealing is a method to solve optimization problems that leverages quantum tunneling in a coupled qubit system. We present a detailed study of the coherence of a tunable capacitively-shunted flux qubit, designed for coherent quantum annealing applications. We find that for high qubit frequencies, thermal noise in the bias line makes a significant contribution to the relaxation, arising from the design choice to experimentally explore both fast annealing and high-frequency control. The measured dephasing rate is primarily due to intrinsic low-frequency flux noise in the two qubit loops, with additional contribution from the low-frequency noise of control electronics used for fast annealing. Our results characterize decoherence in a realistic setup for quantum annealing and are relevant for ongoing efforts toward building superconducting quantum annealers with increased coherence.

Motivation & Objective

• To characterize relaxation and dephasing mechanisms in a tunable capacitively shunted flux qubit for quantum annealing applications.
• To identify the dominant noise sources affecting T₁ and Tϕ across varying qubit frequencies and flux biases.
• To investigate potential noise correlations between the X- and Z-flux loops that may impact qubit coherence.
• To evaluate contributions from critical-current noise, photon-shot noise, and quasi-particle effects on dephasing.
• To guide future design of high-coherence superconducting quantum annealers by isolating key decoherence channels.

Proposed method

• Measured relaxation time T₁ and Ramsey dephasing time Tϕ across a range of flux biases and qubit frequencies.
• Used Bloch-Redfield theory to relate decoherence rates to noise power spectral density (PSD) and matrix elements of the noise coupling operator.
• Employed numerical circuit modeling to compute qubit frequency sensitivity to critical current and flux bias, enabling estimation of noise-induced dephasing.
• Applied low-pass filters (100 MHz and 32 kHz) to control electronic noise from arbitrary waveform generators (AWGs) and isolate their contribution to dephasing.
• Evaluated second-order flux noise coupling and photon-shot noise contributions using analytical expressions derived from quasistatic and Markovian approximations.
• Assessed charge noise and quasi-particle effects by measuring frequency shifts under charge offset variations.

Experimental results

Research questions

• RQ1 What are the dominant noise sources responsible for relaxation (T₁) in the capacitively shunted flux qubit across different frequency regimes?
• RQ2 How does dephasing (Tϕ) depend on flux bias in the X- and Z-flux loops, and what does this imply about noise correlations?
• RQ3 To what extent do critical-current noise, photon-shot noise, and quasi-particle effects contribute to dephasing compared to intrinsic flux noise?
• RQ4 How do thermal noise in bias lines and control electronics affect coherence at high qubit frequencies?
• RQ5 Can the observed dephasing behavior be explained by first-order flux noise coupling, or are higher-order effects significant?

Key findings

• Below ~3 GHz, relaxation at the symmetry point is primarily due to intrinsic low-frequency flux noise in the main qubit loop.
• At higher frequencies (>3 GHz), thermal noise in the bias line becomes a significant contributor to relaxation, due to the design enabling fast annealing and high-frequency control.
• Dephasing is dominated by intrinsic low-frequency flux noise in both the X- and Z-flux loops, with additional contribution from low-frequency noise in fast-annealing control electronics.
• The flux-bias dependence of dephasing time reveals apparent noise correlation between the two qubit loops, suggesting non-local flux noise or junction critical-current noise as possible causes.
• Critical-current noise, estimated with a normalized amplitude of 4.0×10⁻⁶ per junction, contributes significantly to dephasing and may explain the observed correlation between X- and Z-loop noise.
• Photon-shot noise and second-order flux noise coupling are negligible, with estimated dephasing rates of ~1 kHz and ~1 MHz respectively, far below measured values.