5 papers
Apparent Universal Behavior in Second Moments of Random Quantum Circuits
Daniel Belkin, James Allen, Bryan K. Clark
Just how fast does the brickwork circuit form an approximate 2-design? Is there any difference between anticoncentration and being a 2-design? Does geometry matter? How deep a circ…
Absence of censoring inequalities in random quantum circuits
Daniel Belkin, James Allen, Bryan K. Clark
Ref. 1 asked whether deleting gates from a random quantum circuit architecture can ever make the architecture a better approximate -design. We show that it can. In particular, w…
Conditional t-independent spectral gap for random quantum circuits and implications for t-design depths
James Allen, Daniel Belkin, Bryan K. Clark
A fundamental question is understanding the rate at which random quantum circuits converge to the Haar measure. One quantity which is important in establishing this rate is the spe…
Approximate t-designs in generic circuit architectures
Daniel Belkin, James Allen, Soumik Ghosh +6
Unitary t-designs are distributions on the unitary group whose first t moments appear maximally random. Previous work has established several upper bounds on the depths at which ce…
Simulating Neutral Atom Quantum Systems with Tensor Network States
James Allen, Matthew Otten, Stephen Gray +1
In this paper, we describe a tensor network simulation of a neutral atom quantum system under the presence of noise, while introducing a new purity-preserving truncation technique…