Lattice Quantum Chromodynamics and Electrodynamics on a Universal Quantum Computer

Abstract

The power of tools, for our understanding of nature and use of it to our benefits, cannot be overstated. One of our newest tools, i.e., a quantum computer, is a computational tool that works according to the quantum principles of nature. It is widely anticipated that a large-scale quantum computer will offer an evermore accurate simulation of nature, opening the floodgates for exciting scientific breakthroughs and technological innovations. Here, we show a complete, instruction-byinstruction rubric to simulate lattice gauge theories (LGTs) of U(1), SU(2), and SU(3) on a quantum computer -these LGTs describe electroweak and strong forces, key ingredients that form the fabric of our universe. Further provided is a concrete estimate of the quantum computational resources required for an accurate simulation of LGTs of arbitrary dimension and size. The simulations include every element of the Kogut-Susskind Hamiltonian, the standard Hamiltonian formulation of LGTs.

3+1D $θ$-Term on the Lattice from the Hamiltonian Perspective

“…Our results also qualitatively match with prior numerical studies in 1+1D [6][7][8]18]. In light of the recent algorithmic developments of TNs [12] and quantum simulations [15,16], our work provides a concrete starting point for a detailed non-perturbative mapping of the 𝜃-dependent phase diagram in 3+1D.…”

“…In the light of the recently developed quantum algorithms for LGTs [15,16], we envision future fault-tolerant quantum simulations of 3+1D LGTs including our 𝜃-term. To build towards this vision, one can create efficient quantum circuits to simulate our 𝜃-term following Ref.…”

“…To build towards this vision, one can create efficient quantum circuits to simulate our 𝜃-term following Ref. [15]. One begins by expanding the electric field and link operators in the group representation basis [31,32], as we have done in this work for the U(1) case.…”

“…LGTs in any dimensions on universal quantum computers have been developed [15,16]. Given the rapid developments of sign-problem free algorithms for LGTs in higher dimensions, it is therefore of timely importance to explore lattice 𝜃-terms beyond 1+1D.…”

The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory

“…With these reductions, the universality class of the lattice model may differ from the original theory [16][17][18][19][20][21][22][23] making the continuum space limit problematic. Recently, studies quantified the truncation errors for quantum simulations of lattice theories from a computational complexity perspective [12,[24][25][26].…”