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Universal fault-tolerant quantum computation on decoherence-free subspaces

Bacon¹, Kempe, Lidar

¹Department of Chemistry, University of California, Berkeley, California 94720 and Physics Department, University of California, Berkeley, California 94720, USA.

Physical Review Letters

|September 6, 2000

Summary

This study presents a method for universal, fault-tolerant quantum computation using decoherence-free subspaces (DFSs). It enables quantum gates within DFSs, crucial for quantum computing advancements.

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Area of Science:

Quantum Information Science
Quantum Computing

Background:

Decoherence poses a significant challenge to building stable quantum computers.
Decoherence-free subspaces (DFSs) offer a promising avenue for protecting quantum information.

Purpose of the Study:

To present a general scheme for universal, fault-tolerant quantum computation within DFSs.
To demonstrate the implementation of quantum gates while remaining within the DFS.

Main Methods:

Utilizing at most two-qubit interactions for quantum gate implementation.
Performing universal computation on clusters of four-qubit DFSs encoding one logical qubit.
Addressing spatially symmetric (collective) decoherence.

Main Results:

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A scheme for fault-tolerant quantum computation within DFSs is established.

Quantum gates are implemented entirely within the DFS, preserving quantum information.

Universal computation is demonstrated on specific DFS cluster architectures.

Conclusions:

The proposed scheme facilitates robust quantum computation by leveraging DFSs.
This approach is directly applicable to physical implementations using exchange interactions.
The findings are relevant for quantum dot and donor-atom array quantum computer designs.