Preparation of qunaught states for a surface GKP code using a three (or higher) level ancilla system

A method, comprising:

• preparing a qunaught state in an auxiliary mode for data and ancilla Gottesman Kitaev Preskill (GKP) qubits of a surface GKP code implemented using physical elements of quantum hardware, wherein the qunaught state is prepared using a three-level ancilla system;
• and
• maintaining a cavity displacement of the auxiliary mode associated with the three-level ancilla system when the three-level ancilla system is in a second excited state corresponding to a third level of the three-level ancilla system and when the three-level ancilla system is in a first excited state corresponding to a second level of the three-level ancilla system.

One or more non-transitory computer-readable media storing program instructions, usable to cause a piece of quantum hardware to:

• prepare a qunaught state in an auxiliary mode for data and ancilla Gottesman Kitaev Preskill (GKP) qubits of a surface GKP code, wherein the qunaught state is prepared using a three-level ancilla system, and
• wherein the program instructions cause the piece of quantum hardware to prepare the three-level ancilla system such that:
• cavity displacement of the auxiliary mode associated with the three-level ancilla system maintains a cavity displacement when the three-level ancilla system is in a second excited state corresponding to a third level of the three-level ancilla system and when the three-level ancilla system is in a first excited state corresponding to a second level of the three-level ancilla system.