Estimating the randomness of quantum circuit ensembles up to 50 qubits
This work addresses the need for efficient tools to assess randomness in quantum circuits, which is crucial for applications in quantum supremacy, variational algorithms, and blackhole information, though it is incremental as it builds on existing tensor network methods.
The researchers tackled the problem of estimating how close quantum circuit ensembles are to true randomness, developing a tensor-network-based algorithm with polynomial complexity for shallow circuits and achieving high performance using CPU and GPU parallelism. They applied this method to verify the linear growth in complexity for random circuits as predicted by the Brown-Susskind conjecture and to analyze expressibility and barren plateaus in variational quantum algorithms, demonstrating scalability up to 50 qubits.
Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any random unitaries has consequences on their complexity, expressibility, and trainability. To study this property of random circuits, we develop numerical protocols for estimating the frame potential, the distance between a given ensemble and the exact randomness. Our tensor-network-based algorithm has polynomial complexity for shallow circuits and is high-performing using CPU and GPU parallelism. We study 1. local and parallel random circuits to verify the linear growth in complexity as stated by the Brown-Susskind conjecture, and; 2. hardware-efficient ansätze to shed light on its expressibility and the barren plateau problem in the context of variational algorithms. Our work shows that large-scale tensor network simulations could provide important hints toward open problems in quantum information science.