Simulating Collider Physics on Quantum Computers Using Effective Field Theories

Simulating the full dynamics of a quantum field theory over a wide range of energies requires exceptionally large quantum computing resources. Yet for many observables in particle physics, perturbative techniques are sufficient to accurately model all but a constrained range of energies within the validity of the theory. We demonstrate that effective field theories (EFTs) provide an efficient mechanism to separate the high energy dynamics that is easily calculated by traditional perturbation theory from the dynamics at low energy and show how quantum algorithms can be used to simulate the dynamics of the low energy EFT from first principles. As an explicit example we calculate the expectation values of vacuum-to-vacuum and vacuum-to-one-particle transitions in the presence of a time-ordered product of two Wilson lines in scalar field theory, an object closely related to those arising in EFTs of the standard model of particle physics. Calculations are performed using simulations of a quantum computer as well as measurements using the IBMQ Manhattan machine.

Figure 1

Result of transition rates from the vacuum of the Wilson line for three lattice sites and $n_Q=2$ qubits per site to the vacuum and the lowest-lying single excited state. The solid lines show the analytical result with no field digitization while the dashed lines represent the result from a quantum simulator of our circuit. The black data points show the result from the 65-qubit IBMQ Manhattan quantum computer, corrected both for readout errors and CNOT gate errors, and the gray bands show the extrapolation errors from the extrapolation from the CNOT error correction. We only show results from the Manhattan computer for $X=\mathrm{\Omega }$, since the circuit to measure the excited state was too deep to give reliable results.