The Triangle Criterion detects mixed-state magic, proves multi-qubit distillation is strictly stronger than single-qubit schemes, and identifies a purity bound plus undetectable unfaithful magic states.
On the Geometry of Stabilizer States
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that preserve them. Such states are obtained by stabilizer circuits (consisting of CNOT, Hadamard and Phase gates) and can be represented compactly on conventional computers using $O(n^2)$ bits, where $n$ is the number of qubits. As an additional application, the work by Aaronson and Gottesman suggests the use of superpositions of stabilizer states to represent arbitrary quantum states. To aid in such applications and improve our understanding of stabilizer states, we characterize and count nearest-neighbor stabilizer states, quantify the distribution of angles between pairs of stabilizer states, study succinct stabilizer superpositions and stabilizer bivectors, explore the approximation of non-stabilizer states by single stabilizer states and short linear combinations of stabilizer states, develop an improved inner-product computation for stabilizer states via synthesis of compact canonical stabilizer circuits, propose an orthogonalization procedure for stabilizer states, and evaluate several of these algorithms empirically.
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Nonlocal magic in fermionic Gaussian states is bounded by the entanglement spectrum of the covariance matrix, is extensive in the Haar ensemble, peaks at criticality in the Kitaev chain, and grows diffusively under random circuits.
Quotienting the Cayley graph of the Clifford group by a quantum state's stabilizer subgroup produces a graph of the state's Clifford orbit.
No-go theorems prove hierarchy level and state-independent sequences cannot maximize operational magic in early FTQC, requiring state-aware differentiable optimization and nonlinear phases for scalable magic generation.
Non-stabilizerness in the Hubbard dimer is quantified via robustness of magic and stabilizer Renyi entropy, revealing the latter's failure on mixed states and distinguishing it from non-Gaussianity and superselected entanglement.
Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.
citing papers explorer
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Triangle Criterion: a mixed-state magic criterion with applications in distillation and detection
The Triangle Criterion detects mixed-state magic, proves multi-qubit distillation is strictly stronger than single-qubit schemes, and identifies a purity bound plus undetectable unfaithful magic states.
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Nonlocal nonstabilizerness in free fermion models
Nonlocal magic in fermionic Gaussian states is bounded by the entanglement spectrum of the covariance matrix, is extensive in the Haar ensemble, peaks at criticality in the Kitaev chain, and grows diffusively under random circuits.
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Clifford Orbits from Cayley Graph Quotients
Quotienting the Cayley graph of the Clifford group by a quantum state's stabilizer subgroup produces a graph of the state's Clifford orbit.
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Quantum Magic in early FTQC: From Diagonal Clifford Hierarchy No-Go Theorems to Architecture Design Blueprints
No-go theorems prove hierarchy level and state-independent sequences cannot maximize operational magic in early FTQC, requiring state-aware differentiable optimization and nonlinear phases for scalable magic generation.
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Quantum magic of strongly correlated fermions $-$ the Hubbard dimer
Non-stabilizerness in the Hubbard dimer is quantified via robustness of magic and stabilizer Renyi entropy, revealing the latter's failure on mixed states and distinguishing it from non-Gaussianity and superselected entanglement.
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Magic and Non-Clifford Gates in Topological Quantum Field Theory
Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.