Signed quantum weight enumerators characterize qubit magic state distillation
arXiv:1702.06990
Abstract
Many proposals for fault-tolerant quantum computation require injection of 'magic states' to achieve a universal set of operations. Some qubit states are above a threshold fidelity, allowing them to be converted into magic states via 'magic state distillation', a process based on stabilizer codes from quantum error correction. We define quantum weight enumerators that take into account the sign of the stabilizer operators. These enumerators completely describe the magic state distillation behavior when distilling T-type magic states. While it is straightforward to calculate them directly by counting exponentially many operator weights, it is also an NP-hard problem to compute them in general. This suggests that finding a family of distillation schemes with desired threshold properties is at least as hard as finding the weight distributions of a family of classical codes. Additionally, we develop search algorithms fast enough to analyze all useful 5 qubit codes and some 7 qubit codes, finding no codes that surpass the best known threshold.
arXiv comment10 pages, 1 figure
References in corpus (15)
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Contextuality supplies the magic for quantum computation
- The Resource Theory of Stabilizer Computation
- Magic state distillation with low overhead
- Graphical description of the action of local Clifford transformations on graph states
- Improved magic states distillation for quantum universality
- Classicality in discrete Wigner functions
- Contextuality and Wigner function negativity in qubit quantum computation
- Qutrit Magic State Distillation
- Bound States for Magic State Distillation in Fault-Tolerant Quantum Computation
- Equivalence between contextuality and negativity of the Wigner function for qudits
- Qutrit Magic State Distillation Tight in Some Directions
- Quantum MacWilliams Identities
- Determining the full weight distribution of any irreducible cyclic code over any finite field of dimension two
- On the Structure of Protocols for Magic State Distillation