Computing Partition Functions on Limited Quantum Devices

Barry Simon A

David Poulin, Paweł Wocjan

Akhil Francis, Daiwei Zhu, C. Huerta Alderete +6 more

Partition functions are ubiquitous in physics: They are important in determining the thermodynamic properties of many-body systems and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtain its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here, we show how to find partition function zeros on noisy intermediate-scale trapped-ion quantum computers in a scalable manner, using the XXZ spin chain model as a prototype, and observe their transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the future calculation of critical phenomena for systems beyond classical computing limits.

L.R. Evangelista, Luís Carlos Malacarne, R.S. Mendes

Akhil Francis, Daiwei Zhu, C. Huerta Alderete +6 more

Partition functions are ubiquitous in physics: They are important in determining the thermodynamic properties of many-body systems and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtain its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here, we show how to find partition function zeros on noisy intermediate-scale trapped-ion quantum computers in a scalable manner, using the XXZ spin chain model as a prototype, and observe their transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the future calculation of critical phenomena for systems beyond classical computing limits.

S.J. Sweeney, Krishnendu Guha

Quantum algorithms offer an exponential speedup over classical algorithms for a range of computational problems. The fundamental mechanisms underlying quantum computation required the development and construction of quantum computers. These devices are referred to as NISQ (Noisy Intermediate-Scale Quantum) devices. Not only are NISQ devices extremely limited in their qubit count but they also suffer from noise during computation and this problem only gets worse as the size of the circuit increases which limits the practical use of quantum computers for modern day applications. This paper will focus on utilizing quantum circuit partitioning to overcome the inherent issues of NISQ devices. Partitioning a quantum circuit into smaller subcircuits has allowed for the execution of quantum circuits that are too large to fit on one quantum device. There have been many previous approaches to quantum circuit partitioning and each of these approaches differ in how they work with some focusing on hardware-aware partitioning, optimal graph-based partitioning, multi-processor architectures and many more. These approaches achieve success in their objective but they often fail to scale well which impacts cost and noise. The ultimate goal of this paper is to mitigate these issues by minimizing 3 important metrics; noise, time and cost. To achieve this we use dynamic partitioning for practical circuit cutting and we take advantage of the benefits of hybrid execution where classical computation will be used alongside quantum hardware. This approach has proved to be beneficial with respect to noise with classical execution enabling a 42.30% reduction in noise and a 40% reduction in the number of qubits required in cases where a mixture of classical and quantum computation were required.