Quantum Control Overcomes Major Hurdle in Complex System Calculations

Arezzo of the International Centre for Theoretical Physics and colleagues have developed a new method for optimising annealing schedules in a frustrated Ising ring model. The method reveals that carefully crafted, continuous-time dynamics can bypass bottlenecks via a nonadiabatic mechanism, achieving a linear scaling of annealing time with system size. This represents a sharp improvement over the exponential scaling of standard approaches. The findings offer a pathway towards more efficient ground-state preparation for nontrivial many-body systems and challenges the necessity of counter-diabatic corrections when schedule optimisation prioritises them.

Linear scaling of annealing times via optimised nonadiabatic schedules

Annealing times to reach a fixed residual-energy threshold have improved from exponential growth with system size to linear growth, a key advancement in quantum annealing performance. Previously, the exponentially small bottleneck gap in frustrated Ising ring models posed an insurmountable barrier to efficient ground-state preparation, requiring impractically long computation times for adiabaticity. By optimising continuous-time annealing schedules using a dressed-CRAB approach, they bypassed a nonadiabatic mechanism, enabling efficient state preparation despite the challenging energy landscape.

This linear scaling signifies a breakthrough, offering a streamlined path towards practical quantum annealing. A lowest-order variational counter-diabatic correction provides no additional benefit once schedule optimisation implements it, further streamlining the process. Annealing time, the duration needed to reach a specific residual energy level, now scales linearly with system size, a sharp improvement over the previously observed exponential growth. The ‘dressed-CRAB’ approach, a method of controlling how the quantum system evolves over time, achieved this linear scaling by bypassing an exponentially small energy gap that typically hinders performance in frustrated Ising ring models. Analysis revealed this improvement stems from a nonadiabatic mechanism, where the system briefly moves away from its lowest energy state before returning near the end of the process, effectively navigating the challenging energy landscape.

Dressed-CRAB optimisation of quantum annealing schedules via Fourier basis functions

Central to achieving efficient ground-state preparation is optimising the annealing schedule, the precise timing of a quantum computation. The team employed a technique called dressed-CRAB, building upon the idea of adding carefully chosen ‘wiggles’ to a standard linear schedule; this is akin to subtly adjusting the path of a ball rolling down a bumpy hill to help it navigate narrow passages more easily. This method uses Fourier basis functions, mathematical building blocks representing different frequencies, to construct increasingly refined schedules, with each iteration adding more complex variations and progressively improving the system’s ability to find its lowest energy state.

They used up to 20 Fourier components to optimise the annealing schedule, iteratively refining it with Fourier basis functions to improve ground-state preparation. Simulations discretised the quantum dynamics into P time steps of 0.1 units, a value justified by minimising Trotter error; they scaled P with the total annealing time τ. This approach was favoured as it allowed efficient gradient evaluation for optimising the continuous-time schedule, bypassing limitations of fixed schedules. The ability to efficiently evaluate gradients proved crucial for refining the annealing process and achieving optimal performance, demonstrating the power of continuous-time optimisation techniques.

Linear scaling in quantum annealing schedules overcomes exponential limitations

Optimising the annealing schedule offers a compelling route to faster quantum computation, but the current work relies heavily on a specific, simplified model: the frustrated Ising ring. This raises an important question regarding generalisability; will these carefully crafted schedules translate effectively to the more complex, higher-dimensional many-body problems where quantum annealing truly needs to excel. The authors acknowledge this limitation, noting that the symmetries and parameters of the ring may not generalise, and future work must address whether this optimisation technique is a universal solution or a tailored fix.

Despite relying on a simplified model, this delivers a significant advance in optimising quantum annealing schedules. Demonstrating linear scaling of annealing time with system size, rather than the expected exponential growth, is a key step forward in quantum computation. This bypasses a major bottleneck, spectral gaps, which previously limited processing speed. Carefully crafted, continuous changes to the system’s parameters can bypass these bottlenecks through a nonadiabatic process, avoiding the need for excessively long computation times and enabling efficient ground-state preparation even when faced with exponentially small energy gaps, a longstanding challenge in the field. Achieving a linear relationship between annealing time and system size represents a substantial improvement over previous exponential scaling, suggesting a pathway towards solving more complex problems.

The research demonstrated that optimising the continuous-time annealing schedule in a frustrated Ising ring resulted in a linear scaling of annealing time with system size. This is significant because it bypasses the previously expected exponential growth in computation time caused by spectral gaps, a major limitation in quantum annealing. By carefully controlling the system’s parameters during the annealing process, researchers achieved efficient ground-state preparation despite the presence of exponentially small energy gaps. The authors plan to investigate whether this optimisation technique can be applied more broadly to more complex many-body problems.