[Paper Review] Coherent quantum annealing in a programmable 2000-qubit Ising chain

Andrew King, Sei Suzuki+22 more|arXiv (Cornell University)|Feb 11, 2022

Quantum many-body systems15 citations

TL;DR

This paper demonstrates coherent quantum annealing in a programmable 2000-qubit superconducting Ising chain, achieving quantitative agreement with closed-system quantum dynamics. It observes Kibble-Zurek scaling and positive kink-kink correlations at the quantum critical point, confirming coherent evolution despite environmental coupling.

ABSTRACT

Quantum simulation has emerged as a valuable arena for demonstrating and understanding the capabilities of near-term quantum computers. Quantum annealing has been used successfully in simulating a range of open quantum systems, both at equilibrium and out of equilibrium. However, in all previous experiments, annealing has been too slow to simulate a closed quantum system coherently, due to the onset of thermal effects from the environment. Here we demonstrate coherent evolution through a quantum phase transition in the paradigmatic setting of the 1D transverse-field Ising chain, using up to 2000 superconducting flux qubits in a programmable quantum annealer. In large systems we observe the quantum Kibble-Zurek mechanism with theoretically predicted kink statistics, as well as characteristic positive kink-kink correlations, independent of system temperature. In small chains, excitation statistics validate the picture of a Landau-Zener transition at a minimum gap. In both cases, results are in quantitative agreement with analytical solutions to the closed-system quantum model. For slower anneals we observe anti-Kibble-Zurek scaling in a crossover to the open quantum regime. These experiments demonstrate that large-scale quantum annealers can be operated coherently, paving the way to exploiting coherent dynamics in quantum optimization, machine learning, and simulation tasks.

Motivation & Objective

• To demonstrate coherent quantum annealing in a large-scale superconducting quantum processor despite environmental decoherence.
• To validate the quantum Kibble-Zurek mechanism in a 1D transverse-field Ising chain using a programmable quantum annealer.
• To distinguish coherent dynamics from open-system effects by probing kink statistics and correlations across varying anneal times and temperatures.
• To assess the role of disorder and decoherence in suppressing quantum correlations during finite-time quenches.
• To establish a benchmark for coherent dynamics in near-term quantum annealers using analytically solvable models.

Proposed method

• Implementation of the 1D transverse-field Ising Hamiltonian on a programmable superconducting quantum annealer with up to 2000 qubits.
• Use of a time-dependent annealing schedule controlled by dimensionless parameter $ s = t/t_a $, tuning between transverse field $ ̺(s) $ and Ising coupling $ \mathcal{J}(s) $.
• Employment of periodic boundary conditions and uniform coupling $ J $, programmable to ferromagnetic (negative) or antiferromagnetic (positive) values.
• Measurement of kink density and kink-kink correlation functions to probe topological defects and correlation length near the quantum critical point.
• Comparison of experimental results with analytical solutions of the closed-system model and with tensor network simulations (TEBD) including disorder.
• Use of bootstrap resampling for $ 95\% $ confidence intervals and bond dimension analysis to estimate entanglement in the experimental state.

Experimental results

Research questions

• RQ1 Can coherent quantum annealing be achieved in a large-scale superconducting quantum processor despite environmental coupling?
• RQ2 Do the observed kink statistics and correlations match the predictions of the quantum Kibble-Zurek mechanism in a closed-system model?
• RQ3 What is the role of temperature, disorder, and anneal time in suppressing or preserving quantum correlations during a finite-time quench?
• RQ4 To what extent does the experimental data reflect coherent dynamics versus open-system decoherence effects?
• RQ5 Can tensor network simulations with controlled disorder reproduce the experimental kink-kink correlation functions?

Key findings

• The experiment observes Kibble-Zurek scaling of kink density with anneal time, matching theoretical predictions for a closed quantum system.
• Positive kink-kink correlations are measured at the quantum critical point, confirming coherent dynamics independent of temperature (10–30 mK).
• For slow anneals, anti-Kibble-Zurek scaling emerges, indicating a crossover to the open quantum regime due to decoherence and disorder.
• Kink-kink correlation peaks are suppressed at longer anneal times, with temperature having minimal impact, suggesting disorder and diffusion as dominant mechanisms.
• Bond dimension analysis in TEBD simulations indicates that the experimental state has entanglement consistent with $ D \geq 20 $, suggesting significant many-body entanglement.
• Theoretical and experimental kink distributions, cumulants, and correlation functions show quantitative agreement, validating the coherence of the annealing process.