Good binary quantum codes with transversal CCZ gate

• URL: http://arxiv.org/abs/2408.10140v2
• Date: Mon, 14 Oct 2024 03:39:53 GMT
• Title: Good binary quantum codes with transversal CCZ gate
• Authors: Quynh T. Nguyen,
• Abstract summary: We give anally good family of quantum CSS codes on qubits with a CCZ gate. As a corollary, the constructed code family provides a magic state distillation scheme with constant space overhead.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We give an asymptotically good family of quantum CSS codes on qubits with a transversal CCZ gate, meaning that the parallel logical CCZ on all logical qubits is performed by parallel physical CCZs on (a subset of) physical qubits. The construction is based on the observation that any classical code satisfying a multiplication property can be used to construct a quantum CSS code with transversal (qudit) CCZ. To obtain a constant-rate and linear-distance family, we then instantiate this construction with a classical good family of algebraic-geometry codes on a non-binary, but constant-sized, alphabet. Finally, we use a technique from the arithmetic secret sharing literature to reduce the alphabet to binary. As a corollary, the constructed code family provides a magic state distillation scheme with constant space overhead.

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