[Paper Review] Quantum Teleportation is a Universal Computational Primitive

Daniel Gottesman, Isaac L. Chuang|arXiv (Cornell University)|Aug 2, 1999

Quantum Computing Algorithms and ArchitectureComputer Science770 citations

TL;DR

This paper demonstrates that quantum teleportation, when combined with Bell measurements and Greenberger-Horne-Zeilinger (GHZ) states, can serve as a universal primitive for quantum computation. It shows that any quantum gate can be implemented using only single-qubit operations, entangled resource states, and measurement-based teleportation, enabling fault-tolerant quantum computation with minimal physical resources.

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.

Motivation & Objective

• To establish quantum teleportation as a universal computational primitive capable of implementing any quantum gate.
• To show that universal quantum computation can be achieved using only single-qubit operations, Bell measurements, and entangled resource states such as GHZ states.
• To provide a framework for constructing fault-tolerant quantum gates using teleportation-based techniques.
• To simplify quantum circuit design by reducing reliance on complex two-qubit entangling gates.

Proposed method

• Using teleportation protocols to transfer quantum states via Bell-state measurements and entangled resource states.
• Constructing universal quantum gates by teleporting qubits through specially prepared entangled states, such as GHZ states.
• Employing single-qubit operations on the teleported qubits to implement arbitrary unitary transformations.
• Designing fault-tolerant gate constructions by encoding logical qubits and using teleportation to perform logical operations.
• Utilizing the teleportation framework to replace direct two-qubit entangling gates with measurement-based operations.
• Demonstrating that the combination of single-qubit operations, Bell measurements, and GHZ states is sufficient for universal quantum computation.

Experimental results

Research questions

• RQ1 Can quantum teleportation alone serve as a universal computational primitive for quantum computation?
• RQ2 Is it possible to implement any quantum gate using only single-qubit operations, Bell measurements, and entangled resource states?
• RQ3 How can fault-tolerant quantum gates be constructed using teleportation-based techniques?
• RQ4 Can the need for direct two-qubit entangling gates be eliminated in favor of measurement-based gate implementation?
• RQ5 What role do GHZ states play in enabling universal quantum computation through teleportation?

Key findings

• Quantum teleportation with Bell measurements and GHZ states enables the implementation of any quantum gate, establishing it as a universal computational primitive.
• Universal quantum computation can be achieved using only single-qubit operations, Bell measurements, and entangled resource states such as GHZ states.
• The framework allows for the construction of fault-tolerant quantum gates by encoding logical qubits and using teleportation to perform logical operations.
• The method reduces the need for direct two-qubit entangling gates, simplifying physical implementations.
• The teleportation-based approach provides a scalable and modular framework for quantum computation with inherent fault-tolerance potential.
• The results demonstrate that quantum computation can be realized through measurement-based operations and resource states, without requiring direct entangling gates.