Quantum Teleportation is a Universal Computational Primitive

TL;DR

The paper addresses the challenge of building scalable, fault-tolerant quantum computers by introducing a generalized teleportation framework that uses pre-entangled resources to enact unitary gates. It demonstrates deterministic CNOT implementation through teleportation and extends the approach to a broad class of fault-tolerant gates by preparing specialized ancillas and performing Clifford-group–compatible corrections. By leveraging cat-state–assisted, fault-tolerant measurements and stabilizer codes, the authors outline a recursive scheme to realize higher-level gates (Ck) with offline ancilla preparation, effectively turning entanglement into a reusable computational resource. The work has practical implications for architectures ranging from linear optics to solid-state qubits, suggesting a path toward reduced experimental complexity and modular fault-tolerant gate construction.

Abstract

We present a method to create a variety of interesting gates by teleporting quantum bits through special entangled states. This allows, for instance, the construction of a quantum computer based on just single qubit operations, Bell measurements, and GHZ states. We also present straightforward constructions of a wide variety of fault-tolerant quantum gates.

Figures (6)

• Figure 1: Quantum circuit for teleportation. Time proceeds from left to right. $<$ denotes the EPR state $|\Psi\rangle$, and the box $B$ is a measurement in the Bell basis. The double wires carry classical bits, and the single wires, qubits.
• Figure 2: Quantum circuit for teleporting two qubits through a controlled- not gate, giving $|{\rm out}\rangle = {\sc cnot}\, |\beta\rangle|\alpha\rangle$.
• Figure 3: Quantum circuit to create the $|\chi\rangle$ state from two EPR pairs (left), or from two GHZ states $|\Upsilon\rangle = (|000\rangle+|111\rangle)/\sqrt{2}$ (right). $H$ is the Hadamard gate.
• Figure 4: Quantum circuit to perform $U$ fault tolerantly using quantum teleportation. In general, this works for any $U\in C_k$, since $R'_{xz}\in C_{k-1}$ by definition of $C_k$.
• Figure 5: a) A non-fault-tolerant procedure to measure $M$ with eigenvalues $\pm 1$, b) A coherent version of this procedure.