The resource theory of stabilizer quantum computation

2013/07/26 by Victor Veitch, Seyed Ali Hamed Mousavian, S A Hamed Mousavian +2 · 1 voice · 511 citations
Computer Science · Physics and Astronomy · #Algorithm #Computation #Computer science #MAGIC (telescope) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum computer #Quantum entanglement #Quantum mechanics #Resource dependence theory #Scalability #Statistical physics #Theoretical computer science #Theoretical physics #quant-ph

paper · pdf · doi:10.1088/1367-2630/16/1/013009

published in New Journal of Physics 16(1), 013009 (IOP Publishing)

arxiv created 2013/07/26 · arxiv published 2013/07/26 · arxiv updated 2013/07/26 · openalex publication_date 2014/01/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/08

Abstract

Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the theory of entanglement, that is relevant for fault-tolerant stabilizer computation. We introduce two quantitative measures—monotones—for the amount of non-stabilizer resource. As an application we give absolute bounds on the efficiency of magic state distillation. One of these monotones is the sum of the negative entries of the discrete Wigner representation of a quantum state, thereby resolving a long-standing open question of whether the degree of negativity in a quasi-probability representation is an operationally meaningful indicator of quantum behavior.

Citations

• Qudit versions of the qubitπ/8gate
• Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
• Logarithmic Negativity: A Full Entanglement Monotone That is not Convex
• Reversible transformations from pure to mixed states and the unique measure of information
• Non-negative subtheories and quasiprobability representations of qubits
• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• Qutrit magic state distillation
• Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and the butterfly network
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• The resource theory of quantum reference frames: manipulations and monotones
• Evenly distributed unitaries: On the structure of unitary designs
• Distillation protocols for Fourier states in quantum computing
• Quantum entanglement
• On the Quantum Correction For Thermodynamic Equilibrium

Cited by

• Schmidt-Gauge Non-Local Magic: Representation, Optimality, and Mathematical Properties
• Fibonacci many-body scars in a decorated Rule-54 quantum cellular automaton
• Quantum magic of strongly correlated fermions - the Hubbard dimer
• Non-stabilizerness generation in a multi-particle quantum walk
• Efficient witnessing and testing of magic in mixed quantum states
• Quantum pseudoresources imply cryptography
• A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
• Non-Local Magic from the Entanglement Spectrum
• Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics
• No-Go Theorems for Universal Quantum State Purification via Classically Simulable Operations
• Are Molecules Magical? Non-Stabilizerness in Molecular Bonding

Discussions

• And of course, then someone went and defined something called "mana". As the name suggests, it quantifies how much 'magic' is in a quantum state. No word on how much a potion of the stuff costs, thoug [bsky, 1 points, 0 comments]

Related

• Application of a resource theory for magic states to fault-tolerant quantum computing
• Negative Quasi-Probability as a Resource for Quantum Computation
• Quantifying magic for multi-qubit operations
• Identifying quantum resources in encoded computations
• Operational interpretation of the Stabilizer Entropy