Qubit discretizations of d=3 conformal field theories

Abstract

We propose that scaling dimensions of d=3 conformal field theories can be studied on a system of qubits with near term quantum simulation platforms. Our proposal chooses couplings of quantum many-body problems on a polyhedral lattice at which the conformal state-operator correspondence can be observed most accurately in the spectrum. We validate our protocol on the Ising model where we extract the scaling dimensions of a number of scaling operators with a few percent accuracy from the spectrum of a system of just 20 qubits. The procedure makes only minor assumptions beyond general conformal invariance -- it may hence be applied widely. Requirements and challenges to realize this proposal on quantum computers are discussed. Our results demonstrate that for current or near term qubit platforms, three dimensional conformal field theories present a unique opportunity -- a forefront problem that is difficult on classical computers but may be solved through quantum simulation.