Codes and protocols for distilling T, controlled-S, and toffoli gates
This application concerns quantum computing and quantum circuits. For example, among the embodiments disclosed herein are codes and protocols to distill T, controlled-S, and Toffoli (or CCZ) gates for use in croantum circuits. Examples of the disclosed codes use lower overhead for a given target accuracy relative to other distillation techniques. In some embodiments, a magic state distillation protocol is generated for creating magic states in the quantum computing device, wherein the magic state distillation protocol includes (a) Reed-Muller codes, or (b) punctured Reed-Muller codes. The quantum computing device can then configured to implement the magic state distillation protocol.
1. A method for distilling magic states in a quantum computing device, comprising:
generating a magic state distillation protocol for creating magic states in the quantum computing device, wherein the magic state distillation protocol includes (a) Reed-Muller codes, or (b) punctured Reed-Muller codes; and
configuring the quantum computing device to implement the magic state distillation protocol,
wherein the magic state distillation protocol is for Toffoli gates or controlled-controlled-Z (CCZ) gates.
2. The method of claim 1 , wherein the magic state distillation protocol includes punctured higher-order Reed-Muller codes.
3. The method of claim 1 , wherein the magic state distillation protocol uses Reed-Muller stabilizers.
4. The method of claim 1 , wherein the magic state distillation protocol includes punctured Reed-Muller codes, wherein the punctured Reed-Muller codes are selected based on Hamming distances.
5. The method of claim 1 wherein the magic state distillation protocol includes punctured Reed-Muller codes, and wherein the punctured Reed-Muller codes are selected by random puncturing and unpuncturing.
6. The method of claim 1 , wherein the method further comprises: measuring a controlled-Z operator using a transversal T gate to measure stabilizers of a CCZ magic state.
7. The method of claim 6 , wherein the stabilizers of the CCZ magic state achieve a second order error reduction or a fourth order error reduction.
8. The method of claim 1 , further comprising simultaneously measuring stabilizers of CCZ magic states using one or more transversal CCZ gates.
9. A quantum computer system comprising:
a classical computer; and
a quantum computing device implementing a plurality of quoits,
wherein the classical computer is programmed to implement a method for controlling the quantum computing device, the method comprising:
generating a magic state distillation protocol for creating magic states in the quantum computing device, wherein the magic state distillation protocol includes (a) Reed-Muller codes, or (b) punctured Reed-Muller codes, and
configuring the quantum computing device to implement the magic state distillation protocol,
wherein the magic state distillation protocol is for Toffoli gates or controlled-controlled-Z (CCZ) gates.
10. The system of claim 9 , wherein the magic state distillation protocol includes punctured higher-order Reed-Muller codes.
11. The system of claim 9 , wherein the magic state distillation protocol uses Reed-Muller stabilizers.
12. The system of claim 9 , wherein the magic state distillation protocol includes punctured Reed-Muller codes, wherein the punctured Reed-Muller codes are selected based on Hamming distances.
13. The system of claim 9 , wherein the magic state distillation protocol includes punctured Reed-Muller codes, and wherein the punctured Reed-Muller codes are selected by random puncturing and unpuncturing.
14. The system of claim 9 , wherein the method further comprises measuring a controlled-Z operator using a transversal T gate to measure stabilizers of a CCZ magic state.
15. The system of claim 14 , wherein the stabilizers of the CCZ magic state achieve a second order error reduction or a fourth order error reduction.
16. The system of claim 9 , wherein the method further comprises simultaneously measuring stabilizers of CCZ magic states using one or more transversal CCZ gates.