The Resource Theory of Stabilizer Computation

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, for resources for stabilizer codes. 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 behaviour.

References in corpus (17)

• Surface codes: Towards practical large-scale quantum computation
• Instantaneous non-local computation of low T-depth quantum circuits
• Restrictions on Transversal Encoded Quantum Gate Sets
• The resource theory of quantum reference frames: manipulations and monotones
• Evenly distributed unitaries: on the structure of unitary designs
• Magic state distillation with low overhead
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Magic state distillation in all prime dimensions using quantum Reed-Muller codes
• Improved magic states distillation for quantum universality
• Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
• Qudit versions of the qubit "pi-over-eight" gate
• Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation
• Catalysis and activation of magic states in fault tolerant architectures
• Non-negative Wigner functions in prime dimensions
• Distilling one-qubit magic states into Toffoli states
• Nonnegative subtheories and quasiprobability representations of qubits
• Distillation protocols for Fourier states in quantum computing

Cited by in corpus (334)

• Quantum Resource Theories
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Contextuality supplies the magic for quantum computation
• Application of a resource theory for magic states to fault-tolerant quantum computing
• The resource theory of informational nonequilibrium in thermodynamics
• The general structure of quantum resource theories
• The Second Law of Quantum Complexity
• Non-Gaussian Quantum States and Where to Find Them
• Resource theory of quantum non-Gaussianity and Wigner negativity
• The SIC Question: History and State of Play
• Estimating outcome probabilities of quantum circuits using quasiprobabilities
• Kochen-Specker Contextuality
• General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks
• Convex resource theory of non-Gaussianity
• Enhanced fault-tolerant quantum computing in $d$-level systems
• Many-body quantum magic
• A resource theory of superposition
• Resource Destroying Maps
• Genuine quantum coherence
• Wigner function negativity and contextuality in quantum computation on rebits
• Operational Advantage of Quantum Resources in Subchannel Discrimination
• Quantifying the Imaginarity of Quantum Mechanics
• Operational Resource Theory of Quantum Channels
• Quantifying the magic of quantum channels
• Quantifying nonstabilizerness of matrix product states
• Quantifying quantum speedups: improved classical simulation from tighter magic monotones
• Stabilizer entropies and nonstabilizerness monotones
• Quantifying Operations with an Application to Coherence
• Quantifying magic for multi-qubit operations
• Contextuality and Wigner function negativity in qubit quantum computation
• Quantum fluctuation theorems, contextuality and work quasi-probabilities
• Robustness of Magic and Symmetries of the Stabiliser Polytope
• Measuring magic on a quantum processor
• Scalable measures of magic resource for quantum computers
• Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
• Circuit knitting with classical communication
• Practical Bayesian Tomography
• Gaussian quantum resource theories
• One-Shot Operational Quantum Resource Theory
• Conformal field theories are magical
• Efficiently computable bounds for magic state distillation
• No-Go Theorems for Quantum Resource Purification
• Convex geometry of quantum resource quantification
• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Stabilizer entropies are monotones for magic-state resource theory
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Robustness of Measurement, discrimination games and accessible information
• Beyond heat baths: Generalized resource theories for small-scale thermodynamics
• Quantum resource theories in the single-shot regime
• Nonstabilizerness via matrix product states in the Pauli basis
• Application of the Resource Theory of Channels to Communication Scenarios
• Benchmarking one-shot distillation in general quantum resource theories
• Simulating realistic non-Gaussian state preparation
• On the Role of Coherence in Shor's Algorithm
• Scrambling and Complexity in Phase Space
• Quantifying resource in catalytic resource theory
• Measuring nonstabilizerness via multifractal flatness
• Phase transition in magic with random quantum circuits
• Nonstabilizerness determining the hardness of direct fidelity estimation
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• Magic spreading in random quantum circuits
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Efficient quantum algorithms for stabilizer entropies
• A multipartite generalization of quantum discord
• On the statistical complexity of quantum circuits
• Dynamical Entanglement
• Fundamental limitations on distillation of quantum channel resources
• Resource theory of quantum scrambling
• Quantum interference as a resource for quantum speedup
• Skew informations from an operational view via resource theory of asymmetry
• Uniqueness of noncontextual models for stabilizer subtheories
• Quantifying the resource content of quantum channels: An operational approach
• Catalysis of entanglement and other quantum resources
• Axiomatic and operational connections between the $l_1$-norm of coherence and negativity
• Efficient unitary designs with a system-size independent number of non-Clifford gates
• Non-stabilizerness versus entanglement in matrix product states
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Quasiprobability representations of quantum mechanics with minimal negativity
• Complexity of frustration: a new source of non-local non-stabilizerness
• Probabilistic transformations of quantum resources
• Beyond heat baths II: Framework for generalized thermodynamic resource theories
• Resource speed limits: Maximal rate of resource variation
• Quantification and manipulation of magic states
• Cost-Reduced All-Gaussian Universality with the Gottesman-Kitaev-Preskill Code: Resource-Theoretic Approach to Cost Analysis
• Efficient classical simulation of Clifford circuits with nonstabilizer input states
• Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems
• No-go theorems for quantum resource purification II: new approach and channel theory
• Symmetry-protected sign problem and magic in quantum phases of matter
• Contextuality as a resource for measurement-based quantum computation beyond qubits
• Critical behaviors of non-stabilizerness in quantum spin chains
• Entanglement-magic separation in hybrid quantum circuits
• Linking Entanglement Detection and State Tomography via Quantum 2-Designs
• Error Correction of Quantum Reference Frame Information
• Pseudomagic Quantum States
• Real quantum operations and state transformations
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Lower bound for the T count via unitary stabilizer nullity
• Qutrit Magic State Distillation Tight in Some Directions
• Learning efficient decoders for quasi-chaotic quantum scramblers
• Error mitigation and quantum-assisted simulation in the error corrected regime
• Stabilizer Tensor Networks: universal quantum simulator on a basis of stabilizer states
• Characterization of an operational quantum resource in a critical many-body system
• Fundamental limitations on photoisomerization from thermodynamic resource theories
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding
• The first law of general quantum resource theories
• Resource theories of multi-time processes: A window into quantum non-Markovianity
• Gaussian conversion protocols for cubic phase state generation
• Tight constraints on probabilistic convertibility of quantum states
• Quantification of quantum dynamics with input-output games
• Stabilizer entropy in non-integrable quantum evolutions
• Efficient simulatability of continuous-variable circuits with large Wigner negativity
• Classical simulation of fermionic linear optics augmented with noisy ancillas
• Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei
• Generating steady quantum coherence and magic through an autonomous thermodynamic machine by utilizing a spin bath
• Contextuality of general probabilistic theories
• General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
• Magic-induced computational separation in entanglement theory
• Narratives of Quantum Theory in the Age of Quantum Technologies
• Resource theory of quantum uncomplexity
• Optimal Extensions of Resource Measures and their Applications
• Probability representation of quantum dynamics using pseudostochastic maps
• Virtual quantum resource distillation
• Nonstabilizerness of Permutationally Invariant Systems
• Retrieving information from a black hole using quantum machine learning
• Qutrit and Ququint Magic States
• SIC-POVMs and Compatibility among Quantum States
• Magic of quantum hypergraph states
• Maximum nonlocality and minimum uncertainty using magic states
• Discrete Wigner Functions from Informationally Complete Quantum Measurements
• Universal limitations on implementing resourceful unitary evolutions
• Quantum Advantage in Information Retrieval
• Quantifying non-stabilizerness via information scrambling
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Probing quantum complexity via universal saturation of stabilizer entropies
• Constraints on magic state protocols from the statistical mechanics of Wigner negativity
• Coherence of operations and interferometry
• Toward physical realizations of thermodynamic resource theories
• Magic State Distillation from Entangled States
• Quantum gate verification and its application in property testing
• Resource theory of superposition: State transformations
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Order 3 Symmetry in the Clifford Hierarchy
• Efficient mutual magic and magic capacity with matrix product states
• Stabilizer disentangling of conformal field theories
• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
• Pseudorandom unitaries are neither real nor sparse nor noise-robust
• Mana and thermalization: probing the feasibility of near-Clifford Hamiltonian simulation
• Contextuality and The Single-Qubit Stabilizer Formalism
• Quantum Non-Local Nonstabilizerness
• Gravitational back-reaction is magical
• Magic Resource Can Enhance the Quantum Capacity of Channels
• Negativity Bounds for Weyl-Heisenberg Quasiprobability Representations
• Magic State Distillation with the Ternary Golay Code
• Effects of quantum resources on the statistical complexity of quantum circuits
• Experimental quantification of spatial correlations in quantum dynamics
• Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits
• Chaos and magic in the dissipative quantum kicked top
• Coherence makes quantum systems 'magical'
• Stabilizer entropy of quantum tetrahedra
• Quantifying Spatial Correlations of General Quantum Dynamics
• Entanglement and Stabilizer entropies of random bipartite pure quantum states
• Entanglement of random hypergraph states
• Knots, links, and long-range magic
• Resource theory of quantum coherence with probabilistically non-distinguishable pointers and corresponding wave-particle duality
• Virtual quantum resource distillation: General framework and applications
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Un-Weyl-ing the Clifford Hierarchy
• The operational advantages provided by non-classical teleportation
• Magic informationally complete POVMs with permutations
• Simulation of quantum optics by coherent state decomposition
• Spectral Properties Versus Magic Generation in $T$-doped Random Clifford Circuits
• Testing quantum mechanics: a statistical approach
• Independent stabilizer Rényi entropy and entanglement fluctuations in random unitary circuits
• A solution of the generalised quantum Stein's lemma
• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Spekkens' toy model in all dimensions and its relationship with stabilizer quantum mechanics
• On the distribution of the mean energy in the unitary orbit of quantum states
• Magic of Random Matrix Product States
• Bridging magic and non-Gaussian resources via Gottesman-Kitaev-Preskill encoding
• Quantum Advantage for Shared Randomness Generation
• The axiomatic and the operational approaches to resource theories of magic do not coincide
• Certifiable Lower Bounds of Wigner Negativity Volume and Non-Gaussian Entanglement with Conditional Displacement Gates
• Stabilizer Testing and Magic Entropy via Quantum Fourier Analysis
• The magic of universal quantum computing with permutations
• Magic phase transition and non-local complexity in generalized $W$ State
• Long-range nonstabilizerness and phases of matter
• A review and reformulation of macroscopic realism: resolving its deficiencies using the framework of generalized probabilistic theories
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Nonstabilizerness dynamics in many-body localized systems
• Magic transition in measurement-only circuits
• Entanglement Dynamics of the Non-Unitary Holographic Channel
• Variational Quantum Algorithms for Trace Distance and Fidelity Estimation
• States that are far from being stabilizer states
• Coherence manipulation in asymmetry and thermodynamics
• Stabilizer Rényi Entropy and Conformal Field Theory
• States that "look the same" with respect to every basis in a mutually unbiased set
• Minimal informationally complete measurements for probability representation of quantum dynamics
• Contextual bound states for qudit magic state distillation
• Nonstabilizerness in open XXZ spin chains: Universal scaling and dynamics
• $\psi$-epistemic interpretations of quantum theory have a measurement problem
• Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond
• Hierarchies of resources for measurement-based quantum computation
• Sufficient condition for universal quantum computation using bosonic circuits
• Interplay of entanglement structures and stabilizer entropy in spin models
• Extracting randomness from magic quantum states
• Simple Bounds for One-shot Pure-State Distillation in General Resource Theories
• Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
• Local Operator Entanglement in Spin Chains
• A nonstabilizerness monotone from stabilizerness asymmetry
• Geometric Rényi Divergence and its Applications in Quantum Channel Capacities
• Simulating macroscopic quantum correlations in linear networks
• Universal resources for quantum computing
• The non-stabilizerness of fermionic Gaussian states
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination
• Harnessing quantumness of states using discrete Wigner functions under (non)-Markovian quantum channels
• Quantum catalysis in cavity quantum electrodynamics
• Group geometrical axioms for magic states of quantum computing
• Fermionic Magic Resources of Quantum Many-Body Systems
• Geometric-Like imaginarity: quantification and state conversion
• Quantum Preparation Games
• Disentangling magic states with classically simulable quantum circuits
• Unlocking early fault-tolerant quantum computing with mitigated magic dilution
• Quantum computing, Seifert surfaces and singular fibers
• Efficient witnessing and testing of magic in mixed quantum states
• Quantum Ruzsa Divergence to Quantify Magic
• Accessible bounds for general quantum resources
• Genuine Multipartite Entanglement in Quantum Optimization
• Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation
• Clifford operations and homological codes for rotors and oscillators
• Entanglement theory with limited computational resources
• Quantum Causal Structure and Quantum Thermodynamics
• Resource engines
• Computing quantum magic of state vectors
• Maximal Magic for Two-qubit States
• Hybrid magic state distillation for universal fault-tolerant quantum computation
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• An Exact Link between Nonlocal Nonstabilizerness and Operator Entanglement
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Prepare-and-Magic: Semi-Device Independent Magic Certification in the Prepare-and-Measure Scenario
• Counting stabiliser codes for arbitrary dimension
• Black Box Work Extraction and Composite Hypothesis Testing
• Classical codes in quantum state space
• Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
• Multipartite Nonlocality in Clifford Networks
• Non-stabilizerness in quantum-enhanced metrological protocols
• Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity
• Qubit from the classical collision entropy
• Resource Theory of Non-absolute Separability
• Unconditional quantum magic advantage in shallow circuit computation
• Normalizer Circuits and Quantum Computation
• Quantifying the imaginarity via different distance measures
• Local spreading of stabilizer Rényi entropy in a brickwork random Clifford circuit
• Role of quantum state texture in probing resource theories and quantum phase transition
• A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
• One-shot manipulation of coherence in dynamic quantum resource theory
• Unified Framework for Calculating Convex Roof Resource Measures
• Certifying nonstabilizerness in quantum processors
• Covariant influences for finite discrete dynamical systems
• Hidden variable model for quantum computation with magic states on qudits of any dimension
• Superdense Coding in Resource Theory of Asymmetry
• Misreading EPR: Variations on an Incorrect Theme
• Nonclassical correlations in subsystems of globally entangled quantum states
• Nonstabilizerness and Error Resilience in Noisy Quantum Circuits
• Signed quantum weight enumerators characterize qubit magic state distillation
• Quantum coherence with incomplete set of pointers and corresponding wave-particle duality
• Wigner's Theorem for stabilizer states and quantum designs
• Projective robustness for quantum channels and measurements and their operational significance
• MUBs and SIC-POVMs of a spin-1 system from the Majorana approach
• Resource distillation in convex Gaussian resource theories
• On the role of coherence for quantum computational advantage
• Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version)
• Breaking global symmetries with locality-preserving operations
• Fundamental limits on concentrating and preserving tensorized quantum resources
• Polytopes of Absolutely Wigner Bounded Spin States
• Momentum space magic for the transverse field quantum Ising model
• Choi-Defined Resource Theories
• Rise and fall of nonstabilizerness via random measurements
• Minimizing the negativity of quantum circuits in overcomplete quasiprobability representations
• Low Overhead Qutrit Magic State Distillation
• Magic of discrete lattice gauge theories
• Analyzing the free states of one quantum resource theory as resource states of another
• Robustness of Magic in the quantum Ising chain via Quantum Monte Carlo tomography
• Stellar representation of extremal Wigner-negative spin states
• Harvesting Contextuality from the Vacuum
• A Bayesian quasi-probability approach to inferring the past of quantum observables
• The Magic Barrier before Thermalization
• Applications of differential geometry and representation theory to description of quantum correlations
• Path superposition activating perfect quantum teleportation ability for separable states
• Quantum Coherence and Distinguishability as Complementary Resources: A Resource-Theoretic Perspective from Wave-Particle Duality
• Invariant Off-Diagonality: SICs as Equicoherent Quantum States
• Invested and Potential Magic Resources in Measurement-Based Quantum Computation
• Optimisation of time-ordered processes in the finite and asymptotic regime
• Contextuality Can be Verified with Noncontextual Experiments
• Improving quantum channel discrimination with resourceful states
• Contextuality of Quantum Error-Correcting Codes
• Complexity of Quantum Trajectories
• Completely positive completely positive maps (and a resource theory for non-negativity of quantum amplitudes)
• Entropic and operational characterizations of dynamic quantum resources
• Twenty years of quantum contextuality at USTC
• General entropic constraints on CSS codes within magic distillation protocols
• Simulation of quantum computation with magic states via Jordan-Wigner transformations
• Enhancement of non-Stabilizerness within Indefinite Causal Order
• Detecting quantum resources in a semi-device independent framework
• On the Hardness of Measuring Magic
• How contextuality and antidistinguishability are related
• Harvesting stabilizer entropy and non-locality from a quantum field
• Symmetric channel verification for purifying noisy quantum channels
• Quantum Magic in Discrete-Time Quantum Walk
• Entanglement and magic on the light-front
• Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States
• On the stabilizer complexity of Hawking radiation
• The Kraus representation for the dynamics of open quantum systems
• Quantifying magic via quantum $(\alpha ,\beta )$ Jensen-Shannon divergence
• Clifford operators in SU(N)1; N not odd prime
• Operator Entanglement from Non-Commutative Symmetries
• An Algorithm for Estimating $\alpha$-Stabilizer Rényi Entropies via Purity
• Limits of Clifford Disentangling in Tensor Network States
• Non-Gaussianity from superselection rules
• Almost no experiments have classical Kirkwood-Dirac representations
• Negative probability
• Gottesman-Knill Limit on One-way Communication Complexity: Tracing the Quantum Advantage down to Magic Resources
• Convexity of noncontextual wirings and how they order the set of correlations
• High-expressibility Quantum Neural Networks using only classical resources
• On the extremal points of the $\Lambda$-polytopes and classical simulation of quantum computation with magic states
• A Quantum Interpretation of Bunched Logic for Quantum Separation Logic
• Hypergraph States in SU(N)1, N odd prime, Chern-Simons Theory
• On the classification of two-qubit group orbits and the use of coarse-grained 'shape' as a superselection property
• Functoriality of Quantum Resource Theory and Variable-Domain Modal Logic
• Maximal Sets of Equiangular Lines
• Mathematical methods for resource-based type theories
• Van Hove singularities in stabilizer entropy densities
• Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains
• Ideal stochastic process modeling with post-quantum quasiprobabilistic theories
• Resource complexity of Symmetry Protected Topological phases