Quantum computing modelling on field programmable gate array based on state vector and heisenberg models

Abstract

As current trend of miniaturization in computing technology continues, modern computing devices would start to exhibit the behaviour of nanoscopic quantum objects. Quantum computing, which is based on the principles of quantum mechanics, becomes a promising candidate for future generation computing system. However, modelling quantum computing systems on existing classical computing platforms before the realization of viable large-scale quantum computer remains a major challenge. The exploration on the modelling of quantum computing systems on field programmable gate array (FPGA) platform, which offers the potential of massive parallelism and allows computational optimization at register-transfer level, is crucial. Due to the exponential growth of resource utilization with the increase in the number of quantum bits (qubit), existing works on modelling of quantum systems on FPGA platform are restricted to simple case studies using small qubit sizes. This work explores the modelling of quantum computing for emulation on FPGA platform based on two types of data structure: (a) state vector model and (b) Heisenberg model. For the conventional state vector modelling approach, an efficient datapath design that is based on serial-parallel hardware architecture, which allows resource sharing between unitary transformations, is proposed. Heisenberg model has been proven to be efficient in modelling stabilizer circuits, which are critical in error correction operations. In the effort to include the consideration of vital quantum error correction in practical quantum systems, a novel FPGA emulation framework that is based on the Heisenberg model is proposed. Effective algorithms for accurate global phase maintenance are proposed to facilitate the modelling of quantum systems based on the Heisenberg representation. The feasibility of the proposed state vector and Heisenberg emulation models are demonstrated based on a number of case studies with different characteristics, which include quantum Fourier transform, Grover’s search algorithm, and stabilizer circuits. Based on the state vector approach, this work has demonstrated the advantage of FPGA emulation over software simulation where hardware emulation of 7-qubit Grover’s search is about 3 × 104 times faster than the software simulation performed on Intel Core i7-4790 processor running at 3.6GHz clock rate. In contrast to the 8-qubit implementation based on the state vector model, the proposed FPGA emulation framework based on the Heisenberg model has successfully modelled 120-qubit stabilizer circuits on the Altera Stratix IV FPGA. In summary, the proposed work in this thesis contributes to the formulation of a proof-of-concept of efficient FPGA emulation framework based on the state vector and Heisenberg models.