Scalable Quantum Simulations of Scattering in Scalar Field Theory on 120
  Qubits
Simulations of collisions of fundamental particles on a quantum computer are
expected to have an exponential advantage over classical methods and promise to
enhance searches for new physics. Furthermore, scattering in scalar field
theory has been shown to be BQP-complete, making it a representative problem
for which quantum computation is efficient. As a step toward large-scale
quantum simulations of collision processes, scattering of wavepackets in
one-dimensional scalar field theory is simulated using 120 qubits of IBM's
Heron superconducting quantum computer ibm_fez. Variational circuits
compressing vacuum preparation, wavepacket initialization, and time evolution
are determined using classical resources. By leveraging physical properties of
states in the theory, such as symmetries and locality, the variational quantum
algorithm constructs scalable circuits that can be used to simulate
arbitrarily-large system sizes. A new strategy is introduced to mitigate errors
in quantum simulations, which enables the extraction of meaningful results from
circuits with up to 4924 two-qubit gates and two-qubit gate depths of 103. The
effect of interactions is clearly seen, and is found to be in agreement with
classical Matrix Product State simulations. The developments that will be
necessary to simulate high-energy inelastic collisions on a quantum computer
are discussed.
Nikita A. Zemlevskiy