# Estimating the randomness of quantum circuit ensembles up to 50 qubits

arXiv: https://arxiv.org/abs/2205.09900 · HTML: https://mlsanity.com/paper/2205.09900/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 88 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 17 of 17)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs](https://mlsanity.com/paper/1612.05231/) (2016)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Quantum Deep Learning](https://mlsanity.com/paper/1412.3489/) (2014)
- [Analytic theory for the dynamics of wide quantum neural networks](https://mlsanity.com/paper/2203.16711/) (2022)
- [Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers](https://mlsanity.com/paper/2102.05566/) (2021)
- [Cryptography from Pseudorandom Quantum States](https://mlsanity.com/paper/2112.10020/) (2021)
- [Quantum Physical Unclonable Functions: Possibilities and Impossibilities](https://mlsanity.com/paper/1910.02126/) (2019)
- [Pseudorandom States, Non-Cloning Theorems and Quantum Money](https://mlsanity.com/paper/1711.00385/) (2017)
- [Importance of Diagonal Gates in Tensor Network Simulations](https://mlsanity.com/paper/2106.15740/) (2021)
- [On the Connection Between Quantum Pseudorandomness and Quantum Hardware Assumptions](https://mlsanity.com/paper/2110.11724/) (2021)

## Abstract (arXiv)

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.