System and methods for producing magic states for universal quantum computation using GKP error correction
Applying Gottesman-Kitaev-Preskill (GKP) error correction to Gaussian input states, such as vacuum, produces distillable magic states, achieving universality without additional non-Gaussian elements. Gaussian operations are sufficient for fault-tolerant, universal quantum computing given a supply of GKP-encoded Pauli eigenstates.
1. A method of producing a magic state for a quantum computer, the method comprising steps of:
providing a Gaussian quantum computer including a circuit;
generating a Gaussian input state of the circuit;
applying a bosonic error correction code to the Gaussian input state, wherein the bosonic error correction code is a Gottesman-Kitaev-Preskill (GKP) error correction code consisting of Gaussian operations and a GKP Pauli eigenstate, the GKP error correction code requiring no non-Gaussian resources beyond the GKP Pauli eigenstate and requiring no additional external qubits, and
producing the magic state.
2. The method of claim 1 , wherein the Gaussian input state is a thermal state.
3. The method of claim 1 , wherein the Gaussian input state is a vacuum state.
4. The method of claim 1 , wherein the magic state produced is used with fault tolerant quantum computing.
5. The method of claim 1 , wherein the magic state is a H-type magic state.
6. The method of claim 1 , wherein the magic state is a T-type magic state.
7. A method for producing a magic state for a quantum computer, the method comprising steps of:
providing a Gaussian quantum computer including a circuit;
generating a Gaussian input state of the circuit;
applying a Gottesman-Kitaev-Preskill (GKP) error correction code to the Gaussian input state, wherein the GKP error correction code comprises both a non-Gaussian state and a Gaussian operation, the GKP error correction code requiring no non-Gaussian resources beyond a GKP Pauli eigenstate and requiring no additional external qubits; and
producing the magic state.
8. The method of claim 7 , wherein the non-Gaussian state is a GKP logical-0 state.
9. The method of claim 7 , wherein the Gaussian input state is a thermal state or a vacuum state.
10. The method of claim 7 , wherein the magic state produced is used with fault tolerant quantum computing.
11. The method of claim 7 , wherein the magic state is a H-type magic state or a T-type magic state.
12. The method of claim 1 , wherein the GKP Pauli eigenstate is a logical-0 state.
13. The method of claim 7 , wherein the non-Gaussian state is a GKP Pauli eigenstate.