IQC Math and CS seminar featuring Amolak Ratan Kalra

Invariant Theory and Magic State Distillation

Amolak Ratan Kalra  |  Institute for Quantum Computing

We show that the performance of a linear self-orthogonal GF(4) code for magic state distillation of Bravyi and Kitaev’s |T⟩-state is characterized by its simple weight enumerator. We compute weight enumerators of all such codes with fewer than 20 qubits and find none whose threshold exceeds that of the 5-qubit code. Using constraints on weight enumerators from invariant theory and linear programming, we establish bounds on the exponent characterizing noise suppression of a |T⟩-state distillation protocol.

We also obtain new non-negativity constraints on such weight enumerators by demanding consistency of the associated magic state distillation routine. These constraints yield new bounds on the distances of classical Hermitian self-dual and maximal self-orthogonal linear GF(4) codes, notably proving the nonexistence of such codes with parameters [12m, 6m, 4m + 2]. This is work done in collaboration with Shiroman Prakash.

Location

• QNC 1201

• Online on Zoom

  • Meeting ID: 964 9999 3499

    Passcode: 150881