Physical layout of the Floquet code with Majorana-based qubits

A method of performing a Floquet code on a quantum processor, the method comprising:

• assigning, using a classical processor, a plurality of Majorana-based qubits to plaquettes, the Majorana-based qubits being arranged in qubit columns, and semiconductor columns of a gateable semiconductor device being arranged between the respective qubit columns to perform check measurements on the plurality of Majorana-based qubits;
• identifying, using the classical processor, a bulk portion of the plurality of Majorana-based qubits and corresponding plaquettes with a bulk code of the Floquet code;
• performing, using the classical processor, a sequence of steps of the bulk code on the bulk portion, each step comprising check measurements on qubits in the bulk portion that are performed by controlling a gateable semiconductor device to form connections between respective qubits in the bulk portion;
• and
• detecting, using the classical processor, errors based on results of the check measurements a quantum processor comprising.

A quantum device, comprising:

• a quantum processor comprising,
• a plurality of Majorana-based qubits arranged in qubit columns and assigned to respective plaquettes in a three-colorable lattice, a first set of the plaquettes identified as a bulk portion and a second set of the plaquettes identified as a boundary portion, and
• a gateable semiconductor device comprising semiconductor columns arranged between the respective qubit columns, each of the semiconductor columns passing through one or more of the plaquettes such that each of the plaquettes has one or more qubits on both sides of a semiconductor column, and the gateable semiconductor device performing two-qubit Pauli measurements on the plurality of Majorana-based qubits;
• and
• a classical processor that applies a Floquet code to the quantum processor, the Floquet code detecting errors based on results of the two-qubit Pauli measurements, wherein
• the classical processor applies the Floquet code to the quantum processor by controlling the gateable semiconductor device to perform a sequence of the two-qubit Pauli measurements.