The second project phase has been dedicated to increasing the level of complexity of flows amenable to QCFD algorithms and comparing their scaling and resources requirements to standard CFD methods. We made significant progress in developing tensor network methods for QCFD, translating them to quantum algorithms, carrying out gate-level simulations of QCFD algorithms and performing extensive systematic runs on quantum hardware and develop verification and benchmarking methods.
We have been analyzing complex boundary conditions, curvilinear coordinates, compressible flows including shock waves, the evolution of high-dimensional probability distribution functions, shear reactive flows, the Magnus effect for a rotating cylinder, Rayleigh-Benard convection, and flow through an S-bend pipe. We have improved and generalized algorithms for efficiently translating tensor network simulations into quantum circuits to run on quantum hardware. We have derived a quantum Nyquist-Shannon theorem that explicitly shows that the number of qubits required for accurate amplitude encoding of flow fields scales logarithmically with the Reynolds number. We showed that the tripartite mutual information regularizers serve as a powerful tool for detecting and preventing information scrambling and the emergence of barren plateaus in the optimization landscape. For comparing resource requirements between conventional and QCFD approaches we have introduced figures of merit quantifying memory and compute time requirements.
These findings further motivate the development of platform-optimized QCFD algorithms for near-term flagship quantum computers. Quantum algorithms for basic QCFD problems like the 1D Schrödinger equation for superfluid flows and Burgers equation were implemented and extensively tested. We mapped out the cost of evolving the Burgers equation in time to obtain a visible shockwave, in terms of the number of measurement shots, SWAP gates required for the specific quantum topology, entangling gate fidelities, and resilience to noise. A variety of optimizer methods, gradient improvement, variance reduction, noise mitigation, and circuit simplification studies were undertaken. In collaboration with hardware platform developers leading sources of errors have been suppressed and the quality of phase readout has been improved. The simulation of the Burgers equation at finite time has been successfully concluded on the AQT ion-based device with high fidelity. Importantly we have further developed validation and verification techniques for quantum simulations to be able to assess the quality and accuracy of solutions obtained in QCFD simulations.
