Emulating XX catalysts for quantum annealing via self-consistent transverse fields

Research Approach

Quantum annealing (QA) often struggles with first-order phase transitions, where the energy gap between the ground state and excited states becomes exponentially small, leading to long computation times. Theoretical research has shown that adding fully-connected transverse interactions (XX catalysts) can convert these first-order transitions into more manageable second-order ones. However, these interactions are difficult to implement on current hardware. The authors propose an emulation strategy that replaces these complex interactions with a time-dependent transverse field, adjusted self-consistently based on the system's average magnetization measured at discrete intervals.

Methodology

To validate this, the authors define a hierarchy of protocols: the 'Self-consistent exact' (SCE) protocol, which uses continuous updates; the 'Self-consistent discrete' (SCD) protocol, which uses updates at fixed intervals; and the 'Self-consistent measurement' (SCM) protocol, which accounts for finite-sample statistical noise. They test these protocols using the p-spin model, a standard benchmark in quantum annealing, by numerically solving the Schrödinger equation. They quantify the error between these emulated dynamics and the 'exact' dynamics (ED) of the original transverse-interaction catalyst.

Key Findings

The study confirms that the self-consistent protocol successfully reproduces the dynamics of the original XX catalyst. The error between the emulated and exact dynamics scales inversely with system size, meaning the approximation becomes more accurate as the problem size increases. While the protocol requires a quadratic runtime overhead due to the need to restart the annealing process for each measurement, the authors demonstrate that the errors introduced by discrete updates and finite-sample measurements are controllable and can be kept sufficiently small for practical applications on near-term quantum hardware.

This work provides a viable, experimentally accessible path to implementing powerful quantum annealing catalysts on existing devices. By shifting the requirement from complex, non-native hardware interactions to a protocol that relies on transverse-basis measurements—a feature already demonstrated on platforms like D-Wave—this research lowers the barrier for testing advanced annealing strategies that could potentially solve hard optimization problems more efficiently.