Jumping Along Geodesics Fast-forwards Adiabatic Quantum Computation, Circumventing Energy Gap Constraints Without Extra Hamiltonians

Adiabatic quantum computation offers a powerful approach to problem-solving, but its reliance on slow evolution times presents a significant challenge, potentially compromising accuracy. Thi Ha Kyaw from LG Electronics Toronto AI Lab, Guillermo Romero from Universidad de Santiago de Chile, and Gaurav Saxena from LG Electronics Toronto AI Lab, investigate a novel pathway to accelerate this process without introducing complex experimental requirements. Their work demonstrates that carefully navigating the system’s energy landscape along geodesics, the shortest paths between states, effectively suppresses the creation of unwanted excitations in many-body systems. Notably, the team analytically proves and numerically confirms a rate-independent defect plateau in the spin-XY model, a result that challenges established theories like the Kibble-Zurek and anti-Kibble-Zurek mechanisms and opens new avenues for faster, more reliable quantum computation.

Geodesic Quantum Annealing Circumvents Scaling Limits

Adiabatic quantum computing faces a fundamental challenge: the need for evolution times that scale inversely with a power of the system size. This limitation hinders the potential speedup offered by quantum algorithms compared to their classical counterparts. Researchers have investigated a new approach, termed ‘geodesic quantum annealing’, which drives the system along geodesic paths in the parameter space of the Hamiltonian. This method circumvents the stringent energy gap requirements of traditional adiabatic computation, allowing for faster annealing schedules and potentially significant computational advantages.

Their analysis demonstrates that geodesic quantum annealing can break the established Kibble-Zurek scaling, achieving a quadratic speedup in annealing time compared to standard adiabatic protocols. The team established a theoretical framework to predict the number of defects created during this non-adiabatic process. This framework reveals that defect creation depends on the curvature of the geodesic path and the speed at which the system traverses it. Furthermore, the researchers demonstrated the robustness of this scheme against realistic noise and imperfections, suggesting its potential for implementation on near-term quantum devices. These results indicate that geodesic quantum annealing offers a promising pathway towards realizing the full potential of quantum annealing for solving complex optimization problems.

Defect Creation and Rate-Independent Quenches

This research investigates the creation of defects, or excitations, in quantum spin systems when rapidly driven from one state to another, a process known as a quantum quench. The central goal is to understand how these defects are created and to identify conditions where the number of defects remains constant, regardless of the speed of the quench. This challenges the traditional Kibble-Zurek mechanism, which predicts that the number of defects increases with decreasing quench speed. The researchers focused on the XY model and the quantum Ising model, employing numerical simulations to explore the dynamics of defect creation.

A key finding is the discovery of a ‘rate-independent defect plateau’, where the number of defects becomes independent of the quench rate. This is achieved through a specific driving strategy, termed the ‘geo-jump strategy’, which involves dividing the evolution path into a series of small jumps along geodesic paths in parameter space. The simulations demonstrate that this strategy leads to a surprising and robust result, challenging conventional understanding of quantum quenches. The results show that the geo-jump strategy consistently leads to a rate-independent defect plateau in both the XY model and the quantum Ising model.

This behavior persists over a wide range of quench rates, confirming its robustness. The findings have significant implications for understanding the dynamics of quantum quenches and could have potential applications in areas such as quantum computing and materials science. Controlling defect creation is crucial for building stable and reliable quantum devices.

Geo-Jump Protocol Defeats Kibble-Zurek Mechanism

This research demonstrates a novel approach to accelerating adiabatic quantum computation by utilizing geodesic pathways. The team discovered that by discretizing the evolution along these paths, effectively taking a series of optimal rotations, they could significantly suppress the creation of unwanted excitations. This contrasts with traditional adiabatic methods and the Kibble-Zurek mechanism, which predict a decrease in excitations proportional to the inverse square root of the quench time. The key finding is that the ‘geo-jump’ protocol achieves a rate-independent defect plateau, meaning the number of defects remains constant regardless of how quickly the system is evolved.

Numerical simulations across multiple models confirmed this behavior, demonstrating a breakdown from standard predictions for defect scaling. The researchers acknowledge that the defect density, while constant, is not zero and is determined by the geometric distance between the initial and final Hamiltonians. Future work could explore methods to further minimize this residual defect density or investigate the applicability of this geo-jump protocol to more complex quantum systems and optimization problems. The research provides a new pathway for designing faster and more accurate adiabatic quantum algorithms by leveraging geometric principles and precise control over system evolution.