For an explicit prefix/tree family of quantum states, adaptive local Pauli tomography achieves polynomial copy complexity while non-adaptive strategies require exponentially many copies.
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Fault-tolerant quantum computation by anyons
Canonical reference. 87% of citing Pith papers cite this work as background.
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abstract
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.
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representative citing papers
Toric code decodability under coherent X/Z errors is dual to Majorana monitored dynamics whose symmetry class (D or DIII) dictates whether the generic transition is a measurement-induced entanglement transition or a topological transition between area-law phases.
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
Convergent renormalization trajectories of Hopf-algebra boundary MPDOs under on-site noise are classified by finite *-quantum hypergroups via a new quantum Goursat lemma.
Block decoder for color codes yields (1+ε)-approx w.h.p. under i.i.d. and smoothed noise plus exact min-weight decoding in sparse low-p regime.
Non-invertible Gauss laws on lattices preserve Haag duality exactly only on cuspless regions; cusped regions require a collar, and group double models satisfy disjoint additivity.
Modified logarithmic Sobolev inequalities hold for Davies semigroups in 2D Abelian quantum double models at positive temperatures via a Dobrushin-Shlosman condition and verified strong martingale property for conditional expectations.
A solvable 3d quantum gravity model is defined by summing Virasoro TQFT copies over all topologies, shown to be dual to a 2d CFT ensemble and to exhibit semiclassical features such as cured negative density of states and Hawking-Page transition in the large-c limit.
Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.
An algorithm converts topological data of 2D bulk stabilizer codes into 1D boundary subsystem codes via operator algebra and normal forms, enabling automatic generation of boundaries and defects demonstrated on toric, color, and other codes.
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
New LTO axioms ensure Haag duality for cones and reflection positivity, verified for all known topologically ordered commuting projector models.
An exact spacetime polymer gas representation is derived for finite-temperature Z_N homological codes, providing low-activity bounds on partition functions and an exact duality exchanging electric/magnetic backgrounds.
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
Multi-entropy exhibits a structural obstruction to replica symmetry breaking in random tensor networks due to incompatible boundary permutations in the replica hypercube, unlike entanglement negativity.
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
BF Lagrangians for non-abelian DW theories (e.g. dihedral groups) are obtained by gauging H^(0) symmetries of abelian DW theories, with twisted cohomologies and condensation-defect operators verified by character-table linking.
Hardware experiment on IBM devices shows reset-free LUCI achieves logical X and Z error suppression ratios of 1.75(10) and 1.93(12), competitive with surface code despite halved syndrome density.
Degenerate perturbation theory on a multiorbital Hubbard model shows isotropic superexchange arises mainly from ground-state Kramers doublet hopping while anisotropy comes from excited multiplets, yielding an orbital design rule for quasi-isotropic exchange in rare-earth insulators.
Sparse Mamba Decoder processes only active defects in surface code syndromes using a 13-feature representation and Mamba backbone for O(k) complexity, reporting speedups and accuracy gains over dense decoders.
Clifford-deformed zero-rate LDPC codes achieve code-capacity thresholds approaching 50% under i.i.d. pure dephasing when the number of biased logical operators scales slower than distance or overlaps satisfy stated conditions, with new examples from tile codes.
Multiple-braiding sequences with multiplicities up to nine in SU(2)_k anyon models enable approximation of a universal gate set {H, T, CNOT} for k>2, k≠4, with numerical evidence from genetic algorithms.
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
Degenerate BP decoders achieve capacity-achieving or near-capacity performance for quantum erasure correction in linear time on bicycle, product, and topological stabilizer codes.
citing papers explorer
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An Exponential Advantage for Adaptive Tomography of Structured States under Pauli Basis Measurements
For an explicit prefix/tree family of quantum states, adaptive local Pauli tomography achieves polynomial copy complexity while non-adaptive strategies require exponentially many copies.
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Decoding coherent errors in toric codes on honeycomb and square lattices: duality to Majorana monitored dynamics and symmetry classes
Toric code decodability under coherent X/Z errors is dual to Majorana monitored dynamics whose symmetry class (D or DIII) dictates whether the generic transition is a measurement-induced entanglement transition or a topological transition between area-law phases.
-
Gauss law codes and vacuum codes from lattice gauge theories
Gauss law codes identify the full gauge-invariant sector as the code space while vacuum codes restrict to the matter vacuum, with the two shown to be unitarily equivalent for finite gauge groups.
-
Renormalization flows for 1D mixed states and a quantum Goursat lemma
Convergent renormalization trajectories of Hopf-algebra boundary MPDOs under on-site noise are classified by finite *-quantum hypergroups via a new quantum Goursat lemma.
-
Average-Case and Smoothed Near-Optimality for Color-Code Decoding
Block decoder for color codes yields (1+ε)-approx w.h.p. under i.i.d. and smoothed noise plus exact min-weight decoding in sparse low-p regime.
-
Algebraic locality and non-invertible Gauss laws
Non-invertible Gauss laws on lattices preserve Haag duality exactly only on cuspless regions; cusped regions require a collar, and group double models satisfy disjoint additivity.
-
Modified logarithmic Sobolev inequalities for Abelian quantum double models
Modified logarithmic Sobolev inequalities hold for Davies semigroups in 2D Abelian quantum double models at positive temperatures via a Dobrushin-Shlosman condition and verified strong martingale property for conditional expectations.
-
A solvable model of 3d quantum gravity
A solvable 3d quantum gravity model is defined by summing Virasoro TQFT copies over all topologies, shown to be dual to a 2d CFT ensemble and to exhibit semiclassical features such as cured negative density of states and Hawking-Page transition in the large-c limit.
-
The Structure of Circle Graph States
Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.
-
Operator algebra and algorithmic construction of boundaries and defects in (2+1)D topological Pauli stabilizer codes
An algorithm converts topological data of 2D bulk stabilizer codes into 1D boundary subsystem codes via operator algebra and normal forms, enabling automatic generation of boundaries and defects demonstrated on toric, color, and other codes.
-
Higher Gauging and Non-invertible Condensation Defects
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
-
Local topological order, Haag duality, and reflection positivity
New LTO axioms ensure Haag duality for cones and reflection positivity, verified for all known topologically ordered commuting projector models.
-
An exact spacetime polymer gas for finite-temperature $\mathbb Z_N$ homological quantum code
An exact spacetime polymer gas representation is derived for finite-temperature Z_N homological codes, providing low-activity bounds on partition functions and an exact duality exchanging electric/magnetic backgrounds.
-
Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
-
Structural Obstruction to Replica Symmetry Breaking for Multi-Entropy in Random Tensor Networks
Multi-entropy exhibits a structural obstruction to replica symmetry breaking in random tensor networks due to incompatible boundary permutations in the replica hypercube, unlike entanglement negativity.
-
Lattice chiral symmetry from bosons in 3+1d
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
-
On Lagrangians of Non-abelian Dijkgraaf-Witten Theories
BF Lagrangians for non-abelian DW theories (e.g. dihedral groups) are obtained by gauging H^(0) symmetries of abelian DW theories, with twisted cohomologies and condensation-defect operators verified by character-table linking.
-
LUCI on IBM Hardware: Error Suppression with Almost Half Syndrome Density
Hardware experiment on IBM devices shows reset-free LUCI achieves logical X and Z error suppression ratios of 1.75(10) and 1.93(12), competitive with surface code despite halved syndrome density.
-
Design Principles for Quasi-Isotropic Exchange in Rare-Earth Quantum Magnets
Degenerate perturbation theory on a multiorbital Hubbard model shows isotropic superexchange arises mainly from ground-state Kramers doublet hopping while anisotropy comes from excited multiplets, yielding an orbital design rule for quasi-isotropic exchange in rare-earth insulators.
-
Sparse Mamba Decoder for Quantum Error Correction: Efficient Defect-Centric Processing of Surface Code Syndromes
Sparse Mamba Decoder processes only active defects in surface code syndromes using a 13-feature representation and Mamba backbone for O(k) complexity, reporting speedups and accuracy gains over dense decoders.
-
Clifford-deformed zero-rate LDPC codes with 50% biased noise thresholds
Clifford-deformed zero-rate LDPC codes achieve code-capacity thresholds approaching 50% under i.i.d. pure dephasing when the number of biased logical operators scales slower than distance or overlaps satisfy stated conditions, with new examples from tile codes.
-
Universal Quantum Gate Set from Multiple-Braiding Sequences in $SU(2)_k$ ($k>2$, $k\neq 4$) Anyon Models
Multiple-braiding sequences with multiplicities up to nine in SU(2)_k anyon models enable approximation of a universal gate set {H, T, CNOT} for k>2, k≠4, with numerical evidence from genetic algorithms.
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The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
-
Degenerate quantum erasure decoding
Degenerate BP decoders achieve capacity-achieving or near-capacity performance for quantum erasure correction in linear time on bicycle, product, and topological stabilizer codes.
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Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models
Coupling frustration-free or commuting-projector Hamiltonians to bosons produces high-temperature Gibbs states that reproduce low-temperature order.
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Topological Device-Independent Quantum Key Distribution Using Majorana-Based Qubits
A hardware-native error model and loss-disciplined protocol for DI-QKD on Majorana processors is proposed with an EAT security proof, but secure distances are strictly bounded by poisoning-induced visibility collapse during photonic round-trips.
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Engineering of Anyons on M5-Probes via Flux Quantization
Flux quantization of the M5-brane tensor field in twisted Cohomotopy yields Pontrjagin homology observables that reproduce abelian Chern-Simons theory and braid actions on defect anyons.
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The magic of the gravitational vacuum
The vecro hypothesis introduces a lattice model of the gravitational vacuum whose extended correlations nucleate fuzzballs that destroy semiclassical spacetime near trapped surfaces.
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ASEP/DSSYK duality and strange correlator
Moments of the DSSYK transfer matrix equal an ASEP stationary-product state overlap, presented as analogous to the strange correlator in topological state-sum models.
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Symmetry-Protected Topological Phases in the Triangular Majorana-Hubbard Ladder
The study uncovers symmetry-protected topological phases with coexisting spontaneous symmetry breaking in the triangular Majorana-Hubbard ladder model of interacting Majorana fermions.
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Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
Establishes correspondence between equilibrium Majorana zero modes and non-equilibrium kinetic zero modes in dissipative topological superconductors, derives algebraic relation for their numbers, and proposes dissipation engineering recipes demonstrated on Kitaev chain.
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Shuttling of $\mathbb{Z}_4$ parafermions in an electronic ladder model
Numerical study demonstrates controlled transport of Z4 parafermion edge states in a ladder model and quantifies the adiabatic speed limit under realistic conditions.
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Maximum Likelihood Decoding of Quantum Error Correction Codes
A topical review unifying statistical mechanics, tensor network, and AI approaches to approximate maximum likelihood decoding for quantum error correction codes.
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What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
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Quantum Optimization Algorithms for Strongly Correlated Many-Body Systems
Perspective review comparing variational and feedback quantum algorithms for simulating phase transitions in quantum many-body systems, highlighting barren plateaus and advocating physics-informed hybridization.
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Lectures on insulating and conducting quantum spin liquids
The notes argue that the FL* state — small pockets plus a quantized spin-liquid anomaly — resolves the ADMR pocket and v_F >> v_Delta problems that defeated holon-metal and plain fermionic-parton theories of the cuprates.
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Quantum Complexity and New Directions in Nuclear Physics and High-Energy Physics Phenomenology
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.
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Introduction to matrix-product states and tensor networks
Introductory lecture notes on tensor networks with emphasis on matrix-product states, their algorithms, higher-dimensional generalizations, and applications to mixed states and open quantum systems, accompanied by Julia code.
- Closed form logical error rate approximations for surface codes