Fig. 1: Translationally Invariant Circuit Matrix Product States for groundstate optimisation.
From: Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer
a iMPS circuits to calculate the three terms in the Ising Hamiltonian. The blue boxes indicate realisations of the state unitary U with its factorisation to the Rainbow gate set. The red boxes highlight the environment tensor V. Ry gates refer to the Pauli-Y rotation gates, \(Ry(\theta )=\exp (-i{\sigma }_{y}\theta )\) where σy is the Pauli-Y matrix. The W gate is an arbitrary single qubit unitary with three free parameters. Parameters are shared across the blue tensors to enforce translational invariance. There are eight free parameters in total, four from the environment (red) and four from the state tensor (blue). b Example of the Ising circuits laid out on the Rainbow device. The best performing qubits were chosen on each day of experiment. c iMPS Circuits to determine V ≡ V(U). The three elements shown comprise the three elements required to compute the trace distance between the left- and right-hand sides of the fixed-point equations shown in Fig. 6. The gates needed to perform the required swap test are highlighted in green. d Example of the trace distance circuits laid out on the rainbow device.
