Effect of non-unital noise on random circuit sampling | Qiskit Quantum Seminar with Soumik Ghosh

Episode 175
In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the presence of unital sources like the depolarizing channel, the distribution, under the combined noisechannel, never resembles a maximally entropic distribution at any depth.
To show this, we prove that the output distribution of such circuits never anticoncentrates - meaning it is never too ”flat” - regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths.
As consequences, our results have interesting algorithmic implications on both the hardness and easiness of noisy random circuit sampling, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results.
Based on: journals.aps.o...
I am a fourth year Ph.D. student in Computer Science at the University of Chicago, supervised by William Fefferman. Previously, from 2018 to 2020, I was a Master’s student at the University of Waterloo, under the supervision of John Watrous. I was also a part of the Institute for Quantum Computing (IQC). In another life, I was an undergraduate at Jadavpur University, India in the Department of Electronics and Telecommunication Engineering, from 2014 to 2018.