Noise modelling, simulation and benchmarking for near-term quantum computers

Abstract

The field of quantum computing is rapidly evolving and concentrates increasing attention from both academia and industry. With predictions of commercial quantum computing around the corner, this thesis approaches some of the major challenges of the field: the efficiency of quantum circuits, the study of quantum noise and benchmarking the behaviour of Noisy Intermediate-Scale Quantum (NISQ) devices. The first part of the thesis examines two circuit approaches for quantum walks: one consisting of controlled inversions and the other replacing them with rotations. The rotational approach nullifies the large amount of ancilla qubits required by the inverters implementation. The theoretical results concentrate around the comparison of the two architectures in terms of structure, benefits and detriments, as well as computational resources. It is proven that the inverters approach requires exponentially fewer gates than the rotations but almost half the number of qubits in the system. Experiments on a quantum computer show that small quantum walks evolve closer to the expectations, whereas larger circuits are severely affected by noise. The second major part of the thesis is concentrated around quantum noise, an effect that dominates every aspect of near-term quantum computers. The research is concerned with the modelling of noise in NISQ devices. The focus is on three error groups that represent the main sources of noise during a computation and each source is modelled via a quantum channel. A noise model that combines all three noise channels is engineered and used to simulate the evolution of the quantum computer using a set of calibrated error rates. Various experiments show that the new model provides a better approximation of the quantum computer’s behaviour than when compared to other noise models. Following this, a genetic algorithm optimises the parameters used by the new noise model, bringing its behaviour even closer to the quantum computer. A comparison between the pre- and post-optimisation parameters reveals how certain operations can be more or less erroneous than the hardware-calibrated parameters show. Finally, this thesis presents a framework that utilises quantum algorithms, the above noise model and an ideal simulator to benchmark quantum computers. The benchmark metrics highlight the difference between the quantum computer evolution and the simulated noisy and ideal evolutions. This framework is then used for benchmarking three IBMQ devices. The use of diverse algorithms as benchmarks stresses the computers in different ways, highlighting their behaviour for different circuits. The complexity of each quantum circuit affects the efficiency of a quantum computer, with increasing circuit size resulting to worse performance. The results show that the proposed benchmarks provide sufficient and well-rounded information regarding the performance of each quantum computer