Qutrit Magic State Distillation Tight in Some Directions

Abstract

Magic state distillation is a crucial component in the leading approaches to implementing universal fault tolerant quantum computation, with existing protocols for both qubit and higher dimensional systems. Early work focused on determining the region of distillable states for qubit protocols, yet comparatively little is known about which states can be distilled and with what distillable region for d>2. Here we focus on d=3 and present new four-qutrit distillation schemes that improve upon the known distillable region, and achieve distillation tight to the boundary of undistillable states for some classes of state. As a consequence of recent results, this implies that there is a family of quantum states that enable universality if and only if they exhibit contextuality with respect to stabilizer measurements. We also identify a new routine whose fixed point is a magic state with maximal sum-negativity i.e., it is maximally non-stabilizer in a specific sense.

removed erroneous paragraph on Clifford corrections

References in corpus (6)

• Fault-tolerant quantum computation with high threshold in two dimensions
• Magic state distillation with low overhead
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Improved magic states distillation for quantum universality
• Multilevel distillation of magic states for quantum computing
• Spectra of phase point operators in odd prime dimensions and the extended Clifford group

Cited by in corpus (25)

• Quantifying the magic of quantum channels
• Measuring magic on a quantum processor
• Efficiently computable bounds for magic state distillation
• A unified framework for magic state distillation and multi-qubit gate-synthesis with reduced resource cost
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• Pseudomagic Quantum States
• Normal form for single-qutrit Clifford+T operators and synthesis of single-qutrit gates
• An efficient magic state approach to small angle rotations
• Characterization of an operational quantum resource in a critical many-body system
• Experimental test of contextuality in quantum and classical systems
• Qutrit and Ququint Magic States
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Graph-theoretic strengths of contextuality
• Magic State Distillation with the Ternary Golay Code
• Local Dimension Invariant Qudit Stabilizer Codes
• Contextual bound states for qudit magic state distillation
• Small Codes for Magic State Distillation
• Scaling W state circuits in the qudit Clifford hierarchy
• Signed quantum weight enumerators characterize qubit magic state distillation
• A Complete and Natural Rule Set for Multi-Qutrit Clifford Circuits
• Hierarchy and robustness of multilevel two-time temporal quantum correlations
• Low Overhead Qutrit Magic State Distillation
• Quantifying magic via quantum $(\alpha ,\beta )$ Jensen-Shannon divergence
• Simulating Quantum Circuits by Shuffling Paulis
• Transversal AND in Quantum Codes