In statistical models of barren plateaus, any two Pauli observables have non-zero regions whose overlap is exponentially smaller than each region, a phenomenon the paper calls anti-concentration.
Estimating the randomness of quantum circuit ensembles up to 50 qubits
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abstract
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 ans\"atze 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.
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Statistical models of barren plateaus and anti-concentration of Pauli observables
In statistical models of barren plateaus, any two Pauli observables have non-zero regions whose overlap is exponentially smaller than each region, a phenomenon the paper calls anti-concentration.