2020/03/02 by Lucas Kocia, Mohan Sarovar
Computer Science · Mathematics · Physics and Astronomy · #Discrete mathematics #Gaussian #MAGIC (telescope) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quadratic equation #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum mechanics #Quantum-Dot Cellular Automata #Qubit #Qutrit #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1103/physreva.103.022603
published as Phys. Rev. A 103, 022603 (2021)
arxiv created 2020/03/02 · openalex created_date 2020/03/13 · openalex publication_date 2021/02/08 · arxiv updated 2021/02/17 · openalex updated_date 2026/08/05
A compelling way to quantify the separation between classical and quantum computing is to determine how many T-gate magic states, t, a classical computer must simulate to calculate the probability of a universal quantum circuit's output. Unfortunately, efforts to determine the minimum number of stabilizer state inner products necessary to decompose T-gate magic states (\ensuremathχt) have proven intractable past t=7. By using a phase space formalism based on Wootters' discrete Weyl operator basis over a finite field, we develop an algebraic approach to determining \ensuremathχt for single-Pauli measurements. This allows us to extend the bounds on \ensuremathχt to t=14 for qutrits, effectively increasing the space searched by >10^104. Our results show that by using such phase space methods it is possible to validate noisy intermediate-scale quantum circuits of larger size than previously thought possible.