# Decoherence-Free Subspaces for Quantum Computation

@article{Lidar1998DecoherenceFreeSF, title={Decoherence-Free Subspaces for Quantum Computation}, author={Daniel A. Lidar and Isaac L. Chuang and K. Birgitta Whaley}, journal={Physical Review Letters}, year={1998}, volume={81}, pages={2594-2597} }

Decoherence in quantum computers is formulated within the semigroup approach. The error generators are identified with the generators of a Lie algebra. This allows for a comprehensive description which includes as a special case the frequently assumed spin-boson model. A generic condition is presented for errorless quantum computation: decoherence-free subspaces are spanned by those states which are annihilated by all the generators. It is shown that these subspaces are stable to perturbations…

## 1,172 Citations

Quantum computation in triangular decoherence-free subdynamic space

- Physics
- 2015

A formalism of quantum computing with 2000 qubits or more in decoherence-free subspaces is presented. The subspace is triangular with respect to the index related to the environment. The quantum…

Quantum Computing in Decoherence-Free Subspace Constructed by Triangulation

- Physics
- 2010

A formalism for quantum computing in decoherence-free subspaces is presented. The constructed subspaces are partial triangulated to an index related to environment. The quantum states in the…

Algebraic Method in the Analysis of Decoherence-Free Subspaces in Open Quantum Systems

- Physics, Computer Science
- 2018

This paper will study a general framework of decoherence-free subspaces and provide a criterion for the existence of a deco coherent subspace in open quantum systems.

Method to find quantum noiseless subsystems.

- Computer SciencePhysical review letters
- 2006

A structure theory for decoherence-free subspaces and noiseless subsystems that applies to arbitrary quantum operations and suggests that this work brings the fundamental passive technique for error correction in quantum computing an important step closer to practical realization.

A quantum code in decoherence-free and interaction-free subspaces

- Physics
- 2003

A quantum code based on decoherence-free subspace is considered. We investigate a special interaction—exchange interaction in the quantum system—and show that quantum states encoded by the quantum…

Universal quantum computation with electronic qubits in decoherence-free subspace

- PhysicsQuantum Inf. Comput.
- 2008

This work designs building blocks for two noncommutable single-logic-qubit gates and a logic controlled phase gate, based on which a universal and scalable quantum information processing robust to dephasing is available in a deterministic way.

Generalized Noiseless Quantum Codes utilizing Quantum Enveloping Algebras

- Physics
- 1998

A generalization of the results of Rasetti and Zanardi concerning avoiding errors in quantum computers by using states preserved by evolution is presented. The concept of dynamical symmetry is…

Algorithm-based analysis of collective decoherence in quantum computation

- Physics
- 2004

In a quantum computer, qubits are often stored in identical two-level systems separated by a distance shorter than the characteristic wavelength of the reservoirs that are responsible for…

Realization of universal ion-trap quantum computation with decoherence-free qubits.

- PhysicsPhysical review letters
- 2009

This work demonstrates the realization of a universal set of quantum gates acting on decoherence-free ion qubits, and combines these gates to realize the first controlled-NOT gate towards a decoherent-free, scalable quantum computer.

Decoherence of encoded quantum registers

- Physics
- 2008

In order to eliminate disturbing effects of decoherence, encoding of quantum information in decoherence-free subspaces has been suggested. We analyze the benefits of this concept for a quantum…

## References

SHOWING 1-10 OF 25 REFERENCES

Quantum Dynamical Semigroups and Applications

- Physics
- 1987

In this text the authors develop quantum dynamics of open systems for a wide class of irreversible processes starting from the concept of completely positive semigroups. This unified approach makes…

Group theory in physics

- Mathematics
- 1984

OF VOLUME 2: The Role of Lie Algebras. Relationships between Lie Groups and Lie Algebras. The Three-Dimensional Rotation Groups. The Structure of Semi-Simple Lie Algebras. Semi-Simple Real Lie…

Phys

- Rev. Lett. 79, 3306
- 1997

Quantum Dynamical Semigroups and Applications, in Lecture Notes in Physics

- Quantum Dynamical Semigroups and Applications, in Lecture Notes in Physics
- 1987

Phys. Rev. A

- Phys. Rev. A
- 1995

Proc. R. Soc. London Sect. A

- Proc. R. Soc. London Sect. A
- 1998

Group Theory in Physics, Techniques of Physics

- Group Theory in Physics, Techniques of Physics
- 1984

A related result was derived independently by

- Phys. Rev. A
- 1998

Phys. Rev. A Phys. Rev. Lett. Phys. Rev. A

- Phys. Rev. A Phys. Rev. Lett. Phys. Rev. A
- 1997

Proceedings of the 35th Annual Symposium on the Foundations of Computer Science

- Proceedings of the 35th Annual Symposium on the Foundations of Computer Science
- 1994