Quantum gate teleportation is a key technique in fault-tolerant quantum computation that uses resource states to implement logical gates. Here, we develop a theory of quantum gate teleportation protocols that implement non-Clifford gates on arbitrary input states without revealing any information about them; we refer to these protocols as magic gate teleportation (MGT). We uncover a hidden structure within MGT -- after backpropagating the Pauli measurements, MGT protocols can be viewed as encoding the input state into a stabilizer code heralded by the measurement outcomes, followed by a logical non-Clifford gate. Using this structure, we construct MGT protocols for any resource state obtained by applying commuting Pauli rotations to a stabilizer state, and provide an efficient algorithm for synthesizing their circuit implementations. Conversely, we prove that useful resource states for MGT, i.e., states that can be used for non-Clifford gates through MGT protocols, are necessarily Clifford-equivalent to diagonal states; in particular, the output state distilled from the $[\![5, 1, 3]\!]$ protocol is not useful for MGT. Finally, we identify conditions under which the feedforward operators can be implemented by Pauli operators, shedding light on the paradigm of algorithmic fault tolerance and simplifying the feedforward operations needed for quantum computing.
Yunzhe Zheng, A. Zang, Aleksander Kubica· 1 citation
Distributed quantum computing interconnects small, high-quality nodes through optical links, but this architecture carries a pronounced asymmetry: in-node gates and measurements are cheap and high-fidelity, whereas inter-node communication relies on a low-coherence communication qubit and faulty photonics. Previous approaches overcame the noisy link by placing several high-quality data qubits in each node and consuming them for Bell pair and GHZ state distillation. Here we show that distillation can be avoided altogether. The key observation is that we can engineer a communication error bias, where photonic Bell pairs suffer frequent phase errors but only rare bit-flip errors. We design the syndrome-extraction circuits so that this phase noise appears solely as a measurement error that does not propagate to the data qubits, and is therefore suppressed by simply repeating the measurement; letting the error-correcting code itself, rather than a dedicated distillation subroutine, to purify the link. This dramatically reduces the need for ancillary nuclei: Floquet codes require only a single data qubit per node, while general stabilizer codes require just one additional ancilla. We demonstrate high error-correction thresholds throughout this regime, and we identify lattice surgery as inherently robust for this setting, enabling logical operations at a threshold close to that of quantum memory. As a result, the performance of the quantum computer is limited by the high-quality data qubits, while the requirements on photon indistinguishability and coherence of the communication qubit are substantially relaxed.
Yotam Vaknin, Shoham Jacoby, Roi Nevo et al.· 0 citations