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We compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers Gurobi and MQLib to solve the MaxCut problem on 3-regular graphs. We identify the minimum noiseless sampling frequency and depthprequired for a quantum device to outperform classical algorithms. There is potential for quantum advantage on hundreds of qubits and moderate depth with a sampling frequency of 10 kHz. We observe, however, that classical heuristic solvers are capable of producing high-quality approximate solutions in linear time complexity. In order to match this quality for large graph sizesN, a quantum device must support depthp > 11. Additionally, multi-shot QAOA is not efficient on large graphs, indicating that QAOAp ≤ 11 does not scale withN. These results limit achieving quantum advantage for QAOA MaxCut on 3-regular graphs. Other problems, such as different graphs, weighted MaxCut, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices. 

Quantum circuit simulations enable researchers to develop quantum algorithms without the need for a physical quantum computer. Quantum computing simulators, however, all suffer from significant memory footprint requirements, which prevents large circuits from being simulated on classical super-computers. In this paper, we explore different lossy compression strategies to substantially shrink quantum circuit tensors in the QTensor package (a state-of-the-art tensor network quantum circuit simulator) while ensuring the reconstructed data satisfy the user-needed fidelity.Our contribution is fourfold. (1) We propose a series of optimized pre- and post-processing steps to boost the compression ratio of tensors with a very limited performance overhead. (2) We characterize the impact of lossy decompressed data on quantum circuit simulation results, and leverage the analysis to ensure the fidelity of reconstructed data. (3) We propose a configurable compression framework for GPU based on cuSZ and cuSZx, two state-of-the-art GPU-accelerated lossy compressors, to address different use-cases: either prioritizing compression ratios or prioritizing compression speed. (4) We perform a comprehensive evaluation by running 9 state-of-the-art compressors on an NVIDIA A100 GPU based on QTensor-generated tensors of varying sizes. When prioritizing compression ratio, our results show that our strategies can increase the compression ratio nearly 10 times compared to using only cuSZ. When prioritizing throughput, we can perform compression at the comparable speed as cuSZx while achieving 3-4× higher compression ratios. Decompressed tensors can be used in QTensor circuit simulation to yield a final energy result within 1-5% of the true energy value. 

One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the simulation running time. This same problem arises in a variety of application areas, such as combinatorial scientific computing, marginalization in probabilistic graphical models, and solving constraint satisfaction problems. In this paper, we reduce the computationally hard portion of this problem to one of graph linear ordering, and demonstrate how existing approaches in this area can be utilized to achieve results up to several orders of magnitude better than existing state of the art methods for the same running time. To do so, we introduce a novel polynomial time algorithm for constructing an optimal contraction tree from a given order. Furthermore, we introduce a fast and high quality linear ordering solver, and demonstrate its applicability as a heuristic for providing orderings for contraction trees. Finally, we compare our solver with competing methods for constructing contraction trees in quantum circuit simulation on a collection of randomly generated Quantum Approximate Optimization Algorithm Max Cut circuits and show that our method achieves superior results on a majority of tested quantum circuits. Reproducibility: Our source code and data are available at https://github.com/cameton/HPEC2022_ContractionTrees.