Quantum Computing Advances Partition Function Estimation Using D-Wave Systems

Estimating the partition function, a fundamental quantity in statistical physics that describes the probability of a system being in a particular state, presents a significant computational challenge, especially for complex systems. Thinh Le and Elijah Pelofske, from Information Systems and Modeling at Los Alamos National Laboratory, and their colleagues, now demonstrate a method for approximating this function using analog quantum processors. Their research leverages the unique capabilities of superconducting flux qubits on D-Wave systems, employing innovative sampling techniques to efficiently explore the energy landscape of Ising models. The team achieves results comparable to established classical Monte Carlo methods, and importantly, shows that rapid, quantum-driven sampling can generate remarkably accurate estimates of the partition function, reaching a relative error of less than one percent from samples generated in just seconds, representing a substantial step towards utilising quantum computers for thermodynamic calculations.

D-Wave Systems And Quantum Annealing Foundations

This body of work comprehensively explores quantum annealing, a computational method implemented on D-Wave systems, and its applications in optimization and simulation. Research focuses on the fundamental principles of quantum annealing, the hardware challenges of building and calibrating these machines, and the performance of the algorithm on various problems. Studies by King and colleagues demonstrate potential scaling advantages of quantum annealing over classical Monte Carlo methods, particularly for complex systems like spin glasses. A significant portion of the research details applications of quantum annealing to diverse fields, including materials science, machine learning, and optimization.

Scientists utilize quantum annealing to simulate spin glasses and frustrated magnets, optimize machine learning models, and solve combinatorial optimization problems. Hybrid approaches, combining quantum annealing with classical algorithms like genetic algorithms and multicanonical ensembles, are also explored to tackle complex challenges. Theoretical studies delve into the underpinnings of quantum annealing, investigating fair sampling, the Kibble-Zurek mechanism, and the foundations of adiabatic quantum computation. Researchers are also developing software tools to facilitate quantum annealing experiments and analysis. Key observations highlight the strong emphasis on materials science applications, the importance of reverse annealing as a performance-enhancing technique, and the ongoing debate surrounding scaling and advantage over classical methods. Future research directions include improving reverse annealing techniques, understanding the conditions for reliable ground state finding, and exploring the application of quantum annealing to specific problems in various fields.

Density of States Estimation via Quantum Annealing

Scientists have developed a new method to estimate the partition function of Ising models using D-Wave quantum annealers. This approach utilizes two sampling techniques, chains of Monte Carlo-like reverse quantum anneals and standard linear-ramp quantum annealing, allowing for comparative analysis. Researchers carefully optimized simulation quality by manipulating parameters like the effective energy scale, annealing time, and anneal-pause duration. The core of this work involves sampling the energy spectrum of the Ising model, enabling the creation of a density of states estimate for each energy level and facilitating computation of the partition function with quantifiable error.

Experiments on a 25-spin hardware graph yielded results comparable to established classical Monte Carlo methods, specifically Multiple Histogram Reweighting and Wang-Landau. Remarkably, fast quench-like anneals rapidly generated ensemble distributions closely approximating the true partition function, achieving a logarithmic relative error of 7.6 × 10−6 from 171,000 samples in just 0.2 seconds.

Quantum Annealing Estimates Ising Model Partition Function

Researchers have demonstrated that D-Wave quantum annealers can effectively estimate the partition function of Ising models, achieving performance comparable to established classical methods. The team developed two quantum annealing protocols, a standard linear ramp and a Monte Carlo chain of reverse anneals, to sample the energy spectrum of classical Hamiltonians and estimate the density of states at each energy level. Experiments revealed that fast, quench-like annealing can rapidly generate ensemble distributions closely approximating the true partition function, achieving a logarithmic relative error of 0.089 on a Pegasus graph-structured quantum processing unit. This result was obtained from samples generated in just two seconds of quantum processing unit time, with an individual sample time of 200 nanoseconds. By comparing these quantum methods against classical algorithms like Wang-Landau and Multiple Histogram Reweighting, scientists established a benchmark for future quantum annealing applications.

Ising Partition Function Approximated on D-Wave

Scientists have demonstrated that D-Wave quantum annealers can effectively approximate the partition function of Ising models, a key calculation in statistical mechanics and computational physics. The team developed two sampling methods, a forward quantum annealing approach and an iterated reverse annealing technique, both of which successfully generate a density of states distribution for the underlying Ising model. The results indicate that these methods achieve comparable accuracy to established classical Monte Carlo techniques, such as Multiple Histogram Reweighting and Wang-Landau sampling. Notably, researchers observed that rapid, quench-like annealing processes can quickly produce ensemble distributions closely estimating the true partition function. Future research will focus on scaling these techniques to larger problems and assessing their performance on models exhibiting geometric frustration.