We describe the OpenCL GPGPU solver for Quantum Boltzmann equation to study the dynamics of interacting Bose gas. GPU approach allows to manage large system of equations and the required amount of calculations.
Abstract State vector describing the state of an n-qubit quantum system requires 2ncomplex numbers, which means the memory usage of simulating a quantum computer grows exponentially with respect to the number of qubits. For the memory of a single hardware is limited, distributed computation is necessary for simulating quantum systems with large number of qubits. In our proposal, we developed a multi-GPU solution. State vector is divided into several chunks and allocated to different GPU device. Making it possible to simulate quantum circuits of any size on appropriate GPU cluster. We analyse the theoretical computation resource and come to the conclusion that memory copy bandwidth between GPUs is the bottleneck of time consumption. Total execution time is O(logDN/DN) if peer-to-peer memory copy is supported, otherwise time elapsed is O(logDN) where DN is number of GPU devices. Memory consumption on one GPU is O(1/DN).
We present the efficient and universal numerical method for simulation of interacting quantum gas kinetics on a finite momentum lattice, based on the Boltzmann equation for occupation numbers. Usually, the study of models with two-particle interaction generates the excessive amount of terms in the equations essentially limiting the possible system size. Here we employ the original analytical transformation to decrease the scaling index of the amount of calculations. As a result, lattice sizes as large as 48x48x48 can be simulated, allowing to study realistic problems with complex interaction models. The method was applied to the simulation of weakly interacting Fermi and Bose gases where we calculated the relaxation times depending on the momentum and temperature.
Quantum computing is an emerging technology, promising a paradigm shift in computing, and allowing for speedups in many different problems. However, quantum devices are still in their early stages, most with only a small number qubits. This places a reliance on simulation to develop quantum algorithms and to verify these devices. While there exists many algorithms for the simulation of quantum circuits, there is (at the time of writing) no tools which use OpenCL to parallelize this simulation, thereby taking advantage of devices such as GPUs while still remaining portable. In this paper, such a tool is described, including optimizations in areas such as gate application. This leads to a new approach that outperforms other popular state vector based simulators. An implementation of the proposed simulator is available at https://qcgpu.github.io.
The rapid development of the quantum computing field has created the need for effective study tools.Although the physical implementation of quantum systems is still at an early stage, the simulation of quantum circuits using classical computational resources offers a feasible and practical way for experimentation and evaluation.This work focuses on creating functions that enable the implementation of basic quantum gates and circuits on graphics cards (GPUs).Functions were developed that include fundamental operations for the representation and execution of quantum gates and circuits.Through examples and tests, their performance is evaluated, while a simple command-line interface is also provided so that it can be easily used by individuals without prior experience in the field.
Quantum Boltzmann equation (QBE) is a viable option to study strongly out-of-equilibrium thermalisation dynamics which are becoming increasingly critical for many novel physical applications like Ultrafast thermalisation, Terahertz radiation etc. However its applicability is greatly limited by the impractical scaling of the solution to the collision integral in QBE. In our previous work[1] we had proposed a numerical solver for the solution of the collision integral in QBE and then improved on it[2] to include second degree momentum discretisation and adaptive time stepping, thus making it fully compatible to the standard numerical solvers for the transport part of QBE. The improved solver is numerically efficient and extremely robust against inherent numerical instabilities.Here we showcase the applications of this improved solver to a simple 2D system, doped graphene, and analyse thermalisations of the introduced out-of-equilibrium populations.