Adaptive basis selection for encoded fusion measurements

A system, comprising:

• a non-transitory computer-readable memory medium;
• a first encoded qubit comprising a first plurality of physical qubits;
• a second encoded qubit comprising a second plurality of physical qubits;
• a fusion controller;
• and
• a plurality of fusion sites coupled to the fusion controller, wherein the system is configured to:
• perform a first fusion measurement at a first fusion site of the plurality of fusion sites on a first physical qubit of the first plurality of physical qubits and a second physical qubit of the second plurality of physical qubits;
• obtain a first classical measurement result of the first fusion measurement;
• select a basis for performing a second fusion measurement based at least in part on the first classical measurement result, wherein the selected basis determines a failure basis for the second fusion measurement based at least in part on whether the first classical measurement result comprises a success, failure or loss outcome;
• perform the second fusion measurement at a second fusion site of the plurality of fusion sites on a third physical qubit of the first plurality of physical qubits and a fourth physical qubit of the second plurality of physical qubits according to the selected basis;
• obtain a second classical measurement result of the second fusion measurement;
• determine an encoded fusion measurement result of a fusion of the first encoded qubit and the second encoded qubit based at least in part on the first and second classical measurement results;
• and
• store the encoded fusion measurement result in a non-transitory memory medium,
• wherein, in selecting the basis for performing the second fusion measurement based at least in part on the first classical measurement result, the system is further configured to:
• determine that, when the second fusion measurement fails in a first basis, the encoded qubit measurement result may still be determined based at least in part on the first and the second classical measurement results;
• and
• select the first basis as the selected basis for performing the second fusion measurement based at least in part on determining that, when the second fusion measurement fails in the first basis, the encoded qubit measurement result may still be determined based at least in part on the first and second classical measurement results.

A non-transitory computer-readable memory medium storing program instructions which, when executed by a processor, cause a fusion controller to:

• perform a first fusion measurement on a first physical qubit of a first encoded qubit and a second physical qubit of a second encoded qubit;
• obtain a first classical measurement result of the first fusion measurement;
• select a first basis for performing a second fusion measurement based at least in part on the first classical measurement result, wherein the selected basis determines a failure basis for the second fusion measurement based at least in part on whether the first classical measurement result comprises a success, failure or loss outcome;
• perform the second fusion measurement on a third physical qubit of the second encoded qubit and a fourth physical qubit of a third encoded qubit according to the first basis;
• obtain a second classical measurement result of the second fusion measurement;
• select a second basis for performing a third fusion measurement based at least in part on the first and second classical measurement results;
• perform the third fusion measurement on a fifth physical qubit of the third encoded qubit and a sixth physical qubit of the first encoded qubit according to the second basis;
• obtain a third classical measurement result of the third fusion measurement;
• determine an encoded fusion measurement result of a fusion of the first, second and third encoded qubits based at least in part on the first, second and third classical measurement results;
• and
• store the encoded fusion measurement result in the non-transitory computer-readable memory medium,
• wherein, in selecting the first basis for performing the second fusion measurement based at least in part on the first classical measurement result, the program instructions are further executable to cause the fusion controller to:
• determine that, when the second fusion measurement fails in the first basis, the encoded qubit measurement result may still be determined based at least in part on the first and the second classical measurement results.