Quantum computing system and method for time evolution of bipartite Hamiltonians on a lattice

A hybrid quantum-classical computing system for evolving a lattice of qubits in a quantum computer, wherein the lattice of qubits is an a×2 lattice comprising a first row and a second row, the lattice of qubits comprising a first plurality of qubits forming the first row in the quantum computer and a second plurality of qubits forming the second row in the quantum computer, wherein each qubit in the first plurality of qubits is adjacent to at least one qubit in the second plurality of qubits located in a same column, the hybrid quantum-classical computing system comprising:

• the quantum computer, the quantum computer including a plurality of qubits and a qubit controller that manipulates the plurality of qubits, the plurality of qubits including the first plurality of qubits and the second plurality of qubits;
• and
• a classical computer storing machine-readable instructions that, when executed by the classical computer, control the classical computer to cooperate with the quantum computer to perform a method, the method comprising:
• (A) applying, in parallel, a first set of quantum gates between the first plurality of qubits and the second plurality of qubits to create a first set of entangled pairs of qubits in respective columns of the lattice;
• (B) after (A), swapping, in parallel, pairs of qubits, the swapping comprising:
• (B)(1) swapping pairs of adjacent qubits in the first plurality of qubits within the first row according to a first swap criterion, and
• (B)(2) swapping pairs of adjacent qubits in the second plurality of qubits within the second row according to a second swap criterion, wherein the second swap criterion differs from the first swap criterion;
• (C) after (B), applying, in parallel, a second set of quantum gates between the first plurality of qubits and the second plurality of qubits to create a second set of entangled pairs of qubits;
• and
• (D) after (C), swapping, in parallel, pairs of qubits, the swapping comprising:
• (D)(1) swapping pairs of adjacent qubits in the first plurality of qubits according to the second swap criterion;
• and
• (D)(2) swapping pairs of adjacent qubits in the second plurality of qubits according to the first swap criterion.