Compressing diagonal Clifford gates

1. A computer system comprising:

a quantum processor including a plurality of qubits;

one or more non-quantum processors; and

a non-transitory computer readable medium having stored thereon program code executable by the one or more non-quantum processors, the program code causing the one or more non-quantum processors to:

generate a first matrix M based on a collection of indices that reference a second matrix H, wherein the second matrix H is a submatrix of a matrix G comprising an (k+g 0 )-by-n triorthogonal binary matrix and the collection of indices are references to a portion of the matrix G that corresponds to a set of the qubits for which a result tk was obtained that includes (−1) or that does not include (+1) generated based on errors detected in one or more Pauli measurements;

determine a set of compressed Clifford gates based on the first matrix, the compressed Clifford gates comprising compressed diagonal Clifford gates;

apply the set of compressed Clifford gates to a first set of the wherein the set of compressed Clifford gates are collectively applied in a single instance of classical feedback on the set of the plurality of qubits; and

obtain a set of magic states of the quantum processor as a result of the set of compressed Clifford gates being applied, thereby reducing a number of operations involved in magic state distillation.

2. The computer system of claim 1 , execution of the program code causing the one or more non-quantum processors to:

perform a multiqubit Pauli measurement on the plurality of qubits to obtain first Pauli measurement results; and

update the collection of indices based on the multiqubit Pauli measurement results.

3. The computer system of claim 1 , execution of the program code causing the one or more non-quantum processors to:

perform a set of Pauli measurements on a second set of the qubits to obtain a set of Pauli measurement results;

determine that the set of Pauli measurement results include a defined value; and

update the collection of indices to include an index referencing a portion of the second matrix.

4. The computer system of claim 1 , wherein the first matrix is a symmetric matrix that is generated based on an asymmetric matrix.

5. The computer system of claim 1 , execution of the program code causing the one or more non-quantum processors to:

perform a plurality of Pauli measurements to obtain a plurality of Pauli measurement results; and

consume a set of T states on a set of the qubits, wherein the set of compressed Clifford gates are applied subsequent to consumption of the set of T states.

6. A method performed by one or more non-quantum processors, comprising:

generating a first matrix M based on a collection of indices that reference a second matrix H, wherein the second matrix H is a submatrix of a matrix G comprising an (k+g 0 )-by-n triorthogonal binary matrix and the collection of indices are references to a portion of the matrix G that corresponds to a set of the qubits for which a result tk was obtained that includes (−1) or that does not include (+1) generated based on errors detected in one or more Pauli measurements;

determining a set of compressed Clifford gates based on the first matrix, the compressed Clifford gates comprising compressed diagonal Clifford gates;

applying the set of compressed Clifford gates to a first set of the qubits wherein the set of compressed Clifford gates are collectively applied in a single instance of classical feedback on the set of the plurality of qubits; and

obtaining a set of magic states of the quantum processor as a result of the set of compressed Clifford gates being applied, thereby reducing a number of operations involved in magic state distillation.

7. The method of claim 6 , wherein the set of compressed Clifford gates include a set of compressed diagonal Clifford gates.

8. The method of claim 6 , wherein the first matrix is a symmetric matrix that is generated based on an asymmetric matrix.

9. The method of claim 6 , comprising:

consuming a set of T states on a second set of the qubits during a first time period, wherein the set of compressed Clifford gates are applied during a second time period subsequent to the first time period.

10. The method of claim 6 , comprising:

performing a multiqubit Pauli measurement on the plurality of qubits to obtain first Pauli measurement results; and

updating a collection of indices based on the multiqubit Pauli measurement results.