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Bound states for magic state distillation in fault-tolerant quantum computation
Earl T Campbell1, Dan E Browne
1Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, United Kingdom.
Physical Review Letters
|April 7, 2010
Summary
Magic state distillation is crucial for quantum computation. Researchers found that some mixed states cannot be distilled into magic states, even with limited resources, introducing "bound states for magic state distillation."
Area of Science:
- Quantum Information Science
- Fault-Tolerant Quantum Computation
Background:
- Magic state distillation is a key primitive for enabling fault-tolerant quantum computation.
- Pure nonstabilizer states, known as magic states, can be distilled from specific mixed nonstabilizer states using only Clifford group operations.
- The Gottesman-Knill theorem suggests that mixtures of Pauli eigenstates are not distillable, but the distillability of all other mixed states remained an open question.
Purpose of the Study:
- To investigate the existence of nondistillable mixed states beyond those excluded by the Gottesman-Knill theorem.
- To explore the limits of magic state distillation under finite resource constraints.
- To introduce a new class of states relevant to quantum computation.
Main Methods:
- Analysis of magic state distillability for mixed states outside the set of Pauli eigenstate mixtures.
- Consideration of finite resource limitations in quantum distillation protocols.
- Development of a theoretical framework to identify nondistillable states.
Main Results:
- Demonstrated the existence of nondistillable mixed states that lie outside the stabilizer octahedron.
- Established that not all mixed states, even those not mixtures of Pauli eigenstates, are distillable.
- Introduced the concept of "bound states for magic state distillation" for states that cannot be distilled.
Conclusions:
- Magic state distillation has inherent limitations, with certain mixed states being fundamentally nondistillable.
- The newly identified "bound states for magic state distillation" represent a significant finding in quantum information theory.
- These results refine our understanding of the resources required for fault-tolerant quantum computation.
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