Miles Stoudenmire, What Limits the Simulation of Quantum Computers? скачать в хорошем качестве

Miles Stoudenmire, What Limits the Simulation of Quantum Computers?

Recent experimental demonstrations of quantum computing hardware and claims of quantum supremacy have motivated debates over the true resources needed to perform classical simulations of quantum circuits. While exactly simulating certain circuits would certainly require exponential classical resources, there have been fewer investigations into approximate simulations. We use matrix product states (MPS) to simulate quantum circuits at a cost linear in the number of qubits N and circuit depth D. The tradeoff is a loss of fidelity (finite error rate) incurred at every step, such that the fidelity decreases exponentially. When studying 1D circuits, we observe that the error rate can be decreased with polynomial effort down to a certain value comparable to very high quality qubits. But going beyond this error rate requires exponential resources, an effect which may be explainable by random matrix theory arguments. By pursuing strategies for simulating 2D random circuits we reach fidelities comparable to recent experiments, though only when using a lower-rank type of two-qubit gate. Future directions include both conceptual questions about classical simulability and pushing two-dimensional simulations further.