Geometrically enhanced clifford quantum computer

A system having a memory, computer readable instructions for reducing a qubit count employed by a quantum circuit of a geometrically enhanced Clifford quantum computer, and one or more processors for executing the computer readable instructions, the computer readable instructions controlling the one or more processors to perform operations comprising:

• performing a geometric transformation to boundaries of a three-dimensional (3D) toric code, wherein a Hermite normal form is utilized to parameterize the geometric transformation;
• transforming the 3D toric code to a two-dimensional (2D) toric code for the quantum circuit, wherein the 2D toric code comprises plaquettes;
• and
• causing the quantum circuit to execute the 2D toric code for providing logical qubits.

A method of reducing error in a quantum circuit of a geometrically enhanced Clifford quantum computer, the method comprising:

• performing an entangling operation for a positive x-axis of a three-dimensional (3D) cubic lattice on which a 3D toric code is defined, wherein an ancilla qubit is in a center of a first plaquette in the 3D cubic lattice, wherein another ancilla qubit is in a center of a second plaquette in the 3D cubit lattice, wherein yet another ancilla qubit is in a center of a third plaquette in the 3D cubit lattice, wherein data qubits are respectively positioned on edges of the 3D cubic lattice, wherein the entangling operation in the positive x-axis of the first plaquette is between the ancilla qubit and a first one of the data qubits on a first one of the edges;
• performing the entangling operation for a negative x-axis of the first plaquette between the ancilla qubit and a second one of the data qubits on a second one of the edges in the negative x-axis;
• performing the entangling operation for a positive y-axis of the second plaquette between the another ancilla qubit and another first one of the data qubits on another first one of the edges in the positive y-axis;
• performing the entangling operation for a negative y-axis of the second plaquette between the another ancilla qubit and another second one of the data qubits on another second one of the edges in the negative y-axis;
• performing the entangling operation for a positive z-axis of the third plaquette between the yet another ancilla qubit and yet another first one of the data qubits on yet another first one of the edges in the positive z-axis;
• and
• performing the entangling operation for a negative z-axis of the third plaquette between the yet another ancilla qubit and yet another second one of the data qubits on yet another second one of the edges in the negative z-axis, wherein an ordering of the entangling operation for the positive and negative x-axes, y-axes, and z-axes has an effect that reduces a propagation of errors on the quantum circuit.