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Simulating Noisy Quantum Algorithms and Low Depth Quantum State Preparation using Matrix Product States

Nakhl, Azar Christian ( 2021)

Since the proposal of Quantum Computation in the 1980s, many Quantum Algorithms have been proposed to solve problems in a wide variety of fields. However, due to the limitations of existing quantum devices, analysing the performance of these algorithms in a controlled manner must be performed classically. The leading technique to simulate quantum computers classically is based on the Matrix Product State (MPS) representation of quantum systems. We used this simulation method to benchmark the noise tolerance of a number of quantum algorithms including Grover’s Algorithm, finding that the algorithm’s ability to discern the marked state is exponentially suppressed under noise. We verified the existence of Noise-Induced Barren Plateaus (NIBPs) in the Quantum Approximate Optimisation Algorithm (QAOA) and found that the recursive QAOA (RQAOA) variation is resilient to NIBPs, a novel result. Also integral to the performance of quantum algorithms is the ability to efficiently prepare their initial states. We developed novel techniques to prepare low-depth circuits for slightly entangled quantum states using MPS. We found that we can reproduce Gaussian and W States with circuits of O(log(n)) depth, improving on current best known results which are of O(n).