[Paper Review] Gap-independent cooling and hybrid quantum-classical annealing

Lukas Theis, Peter Schuhmacher+2 more|arXiv (Cornell University)|Aug 29, 2018

Quantum and electron transport phenomena3 references3 citations

TL;DR

This paper proposes a gap-independent cooling scheme for superconducting flux qubits in quantum annealing by coupling them transversely to a coplanar waveguide (CPW), which enhances relaxation and suppresses diabatic errors. The method achieves up to 50% improvement in adiabatic regimes and up to several hundred percent in non-adiabatic regimes, enabling robust performance without prior knowledge of the energy gap.

ABSTRACT

In this letter we present an efficient gap-independent cooling scheme for a quantum annealer that benefits from finite temperatures. We choose a system based on superconducting flux qubits as a prominent example of current quantum annealing platforms. We propose coupling the qubit system transversely to a coplanar waveguide to counter noise and heating that arise from always-present longitudinal thermal noise. We provide a schematic circuit layout for the system and show how, for feasible coupling strengths, we achieve global performance enhancements. Specifically, we achieve cooling improvements of about $50\%$ in the adiabatic and a few hundred percent in the non-adiabatic regime, respectively.

Motivation & Objective

• To develop a cooling mechanism for quantum annealers that does not rely on knowledge of the energy gap Δ.
• To mitigate diabatic errors caused by finite sweep times in quantum annealing.
• To improve ground state population after avoided level crossings using finite-temperature relaxation.
• To demonstrate that transverse coupling to a CPW enables effective cooling independent of Δ.
• To establish a hybrid quantum-classical annealing (HQCA) framework leveraging thermal relaxation.

Proposed method

• The system uses a superconducting flux qubit coupled to a transverse ohmic bath via a coplanar waveguide (CPW), enabling control over the transverse coupling strength αx.
• The dynamics are modeled using a dissipative Landau-Zener spin-boson Hamiltonian with time-dependent drive ε(t) = vt, where v is the sweep velocity.
• The master equation approach is used to describe the open quantum system, incorporating both longitudinal (σz) and transverse (σx) coupling to thermal baths.
• The relaxation rate γr is enhanced by the transverse coupling, promoting return to the ground state after avoided crossing.
• Numerical simulations solve the quantum master equation to compute final ground state population pG as a function of αx and αz.
• The scheme is validated by comparing results to the Landau-Zener formula and analyzing the transition to semiclassical dynamics at high dissipation.

Experimental results

Research questions

• RQ1 Can a cooling mechanism be designed that is independent of the energy gap Δ in quantum annealing?
• RQ2 How does transverse coupling to a CPW affect relaxation and ground state population in the presence of thermal noise?
• RQ3 What is the performance gain of this scheme in both adiabatic and non-adiabatic regimes?
• RQ4 Does the system exhibit thermally assisted relaxation that improves final state fidelity?
• RQ5 Can the method be generalized to current quantum annealing platforms without requiring gap knowledge?

Key findings

• The proposed scheme improves ground state population by approximately 50% in the adiabatic regime for kBT = 5Δ and v = 0.5Δ².
• In the non-adiabatic regime, the improvement reaches several hundred percent due to enhanced relaxation from transverse coupling.
• For αx ≳ 5×10⁻³, nearly all population relaxes back to the ground state regardless of longitudinal coupling αz.
• The minimum in pG(αz) shifts with temperature, and the non-monotonic behavior is explained by the transition to semiclassical dynamics at high dissipation.
• The cooling effect is attributed solely to enhanced relaxation, not quantum Zeno-like blocking, as confirmed by numerical analysis in Appendix B.
• The method is intrinsically robust against energy gap fluctuations, making it suitable for real-world quantum annealing devices.