Contextual bound states for qudit magic state distillation
arXiv:1905.00392 · doi:10.1103/PhysRevA.101.010303
Abstract
Identifying necessary and sufficient conditions for universal quantum computing is a long-standing open problem for which contextuality is, perhaps, the only promising solution [Howard et al., Nature 510, 351 (2014)]. To justify this conjecture, Howard et al. showed that contextuality is equivalent to Wigner negativity for qudits, and is therefore necessary and possibly sufficient for qudit magic state distillation. Here, we reformulate magic state distillation in the language of discrete phase space, to show that any finite qudit magic state distillation routine contains bound states outside the Wigner polytope -- these states exhibit contextuality but are useless for magic state distillation.
arXiv comment7 pages, 3 figures; final version accepted in Physical Review A
References in corpus (35)
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Improved Simulation of Stabilizer Circuits
- Quantum Computing with Very Noisy Devices
- Hidden Variables and the Two Theorems of John Bell
- A Theory of Fault-Tolerant Quantum Computation
- Stabilizer Codes and Quantum Error Correction
- Contextuality for preparations, transformations, and unsharp measurements
- Contextuality supplies the magic for quantum computation
- The Resource Theory of Stabilizer Computation
- Positive Wigner functions render classical simulation of quantum computation efficient
- The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
- Discrete phase space based on finite fields
- Negative Quasi-Probability as a Resource for Quantum Computation
- Graph-Theoretic Approach to Quantum Correlations
- Hudson's Theorem for finite-dimensional quantum systems
- SIC-POVMs and the Extended Clifford Group
- Estimating outcome probabilities of quantum circuits using quasiprobabilities
- A Combinatorial Approach to Nonlocality and Contextuality
- Magic state distillation in all prime dimensions using quantum Reed-Muller codes
- Fault-Tolerant Quantum Computation with Higher-Dimensional Systems
- Contextuality as a resource for models of quantum computation on qubits
- Improved magic states distillation for quantum universality
- Classicality in discrete Wigner functions
- Quantifying the magic of quantum channels
- Qudit versions of the qubit "pi-over-eight" gate
- 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
- Normal form for single-qutrit Clifford+T operators and synthesis of single-qutrit gates
- Qutrit Magic State Distillation Tight in Some Directions
- Quantum Online Memory Checking
- On the security and degradability of Gaussian channels
- Quantum Contextuality with Stabilizer States
- Spectra of phase point operators in odd prime dimensions and the extended Clifford group
- Contextuality and The Single-Qubit Stabilizer Formalism