{"total":14,"items":[{"citing_arxiv_id":"2607.08626","ref_index":45,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"A Nonstabilizerness Resource Law for Universal Quantum State Purification","primary_cat":"quant-ph","submitted_at":"2026-07-09T15:57:19+00:00","verdict":"ACCEPT","verdict_confidence":"HIGH","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Universal two-copy quantum state purification under depolarizing noise requires magic resources that scale linearly with the fidelity gain, establishing an exact resource law for odd dimensions and tight bounds for multi-qubit systems.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2607.06683","ref_index":70,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Universal purification dynamics of monitored Clifford circuits","primary_cat":"quant-ph","submitted_at":"2026-07-07T18:02:16+00:00","verdict":"ACCEPT","verdict_confidence":"HIGH","novelty_score":7.5,"formal_verification":"none","one_line_summary":"Purification of weakly monitored Clifford circuits on prime-dimensional qudits reduces exactly to a pure-death Markov process on the density-matrix rank, producing compact universal scaling functions for all Rényi entropies.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2607.02444","ref_index":9,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Optimal Stabilizer Testing and Learning with Limited Quantum Memory","primary_cat":"quant-ph","submitted_at":"2026-07-02T17:11:38+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Stabilizer testing requires Θ(n-k) copies and non-adaptive learning Θ(n²/k) copies with k-qubit memory, removing the testing-learning separation.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.29443","ref_index":43,"ref_count":2,"confidence":0.98,"is_internal_anchor":true,"paper_title":"Stabilizer entropy is trustworthy for mixed states","primary_cat":"quant-ph","submitted_at":"2026-06-28T15:10:16+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Linear stabilizer entropy (purity minus stabilizer purity) is an exponentially reliable non-stabilizerness monotone, a 'resource proxy', over Haar-random, Clifford-orbit and random-MPS ensembles, with a positive averaged gap across the XY-model phase diagram.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2606.09773","ref_index":63,"ref_count":1,"confidence":0.98,"is_internal_anchor":true,"paper_title":"From Pauli Strings to Quantum Dynamics: A Unified Characterization","primary_cat":"quant-ph","submitted_at":"2026-06-08T17:33:15+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Develops an invariant-based framework connecting Pauli Lie algebras to transvection-generated Clifford subgroups for quantum reachability and dynamics analysis.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.11150","ref_index":29,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Lecture Notes on Replica Tensor Networks for Random Quantum Circuits","primary_cat":"quant-ph","submitted_at":"2026-05-11T18:57:53+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":2.0,"formal_verification":"none","one_line_summary":"Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Walter,Multipartite entanglement in stabilizer tensor networks, Phys. Rev. Lett.125, 241602 (2020), doi:10.1103/PhysRevLett.125.241602. [28]B. Magni, A. Christopoulos, A. De Luca and X. Turkeshi,Anticoncentration in clifford circuits and beyond: From random tensor networks to pseudomagic states, Phys. Rev. X15, 031071 (2025), doi:10.1103/p8dn-glcw. [29]L. Bittel, J. Eisert, L. Leone, A. A. Mele and S. F . E. Oliviero,A complete theory of the clifford commutant(2025), 2504.12263. [30]T . Zhou and A. Nahum,Emergent statistical mechanics of entanglement in random unitary circuits, Phys. Rev. B99, 174205 (2019), doi:10.1103/PhysRevB.99.174205. [31]T . Zhou and A. Nahum,Entanglement membrane in chaotic many-body systems, Phys."},{"citing_arxiv_id":"2604.19625","ref_index":37,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Coherent-State Propagation: A Computational Framework for Simulating Bosonic Quantum Systems","primary_cat":"quant-ph","submitted_at":"2026-04-21T16:13:57+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Coherent-state propagation enables quasi-polynomial classical simulation of bosonic circuits with logarithmically many Kerr gates at exponentially small trace-distance error, with polynomial runtime in the weak-nonlinearity regime.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"and denote the two states after layerℓby ψ(ℓ) wk E = SX j=1 D(ℓ) j eα(ℓ) j E ,(37) 7 and ψ(ℓ) gen E = SN FX i=1 C(ℓ) i α(ℓ) i E .(38) Their overlap D ψ(ℓ) gen ψ(ℓ) wk E can be computed an- alytically. This allows us to numerically upper bound (albeit loosely) the error induced at each step, in a manner analogous to that done in MPS [37, 38] and Pauli Propagation [14, 39]. For more details see Appendix C 1. III. Apply the final Gaussian layer.This step is exactly as in the general-Kerr algorithm UG SX k=1 D(L) k eα(L) k E = SX k=1 D(L) k |Gk⟩.(39) IV. THEORETICAL GUARANTEES We are now ready to state the theoretical guaran- tees for coherent-state propagation. The simulation cost"},{"citing_arxiv_id":"2604.15269","ref_index":4,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Cloning is as Hard as Learning for Stabilizer States","primary_cat":"quant-ph","submitted_at":"2026-04-16T17:41:16+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"For n-qubit stabilizer states the optimal sample complexity of approximate cloning is Θ(n), matching the complexity of learning.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"ory with the foundational question of cloning by proposing a structured version of approximate cloning: Definition 2:(Cloning of structured states - Informal) A classof quantum states admits a(𝑡, 𝑡+𝑚, 𝜖)- quantum cloning scheme if there exists a linear CPTP mapΛ ,𝑡,𝑚,𝜖 :((C 2𝑛 ) ⊗𝑡 ) →((C 2𝑛 ) ⊗𝑡+𝑚 )s.t. sup 𝜌∈ dTD Λ,𝑡,𝑚,𝜖 (𝜌 ⊗𝑡 ), 𝜌 ⊗𝑡+𝑚\u0001 ≤𝜖 .(4) We call𝜖the error incurred by the cloning scheme. We will study structured cloning of stabilizer states. While adapting the reasoning of [Wer98] to stabilizer state cloning may be achievable via the recently developed representation theory of the Clifford group and the Clifford commutant [GNW21; Bit+25], we take an alternative path that relies on more elementary"},{"citing_arxiv_id":"2604.13486","ref_index":73,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Taming Trotter Errors with Quantum Resources","primary_cat":"quant-ph","submitted_at":"2026-04-15T05:19:11+00:00","verdict":"CONDITIONAL","verdict_confidence":"MODERATE","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Entanglement entropy bounds the variance of Trotter error downward, and magic drives the error kurtosis downward (Kur = α + βM, β<0 for large systems).","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Invested and potential magic resources in measurement- based quantum computation, Physical Review Letters 135, 160203 (2025). [71] Z. Webb, The clifford group forms a unitary 3-design (2016), arXiv:1510.02769 [quant-ph]. [72] H. Zhu, R. Kueng, M. Grassl, and D. Gross, The clifford group fails gracefully to be a unitary 4-design (2016), arXiv:1609.08172 [quant-ph]. [73] L. Bittel, J. Eisert, L. Leone, A. A. Mele, and S. F. E. Oliviero, A complete theory of the clifford commutant (2025), arXiv:2504.12263 [quant-ph]. [74] P. H. Westfall, Kurtosis as peakedness, 1905-2014. rip, The American Statistician68, 191 (2014). [75] Y. Zhou and Q. Liu, Performance analysis of multi-shot shadow estimation, Quantum7, 1044 (2023)."},{"citing_arxiv_id":"2604.05031","ref_index":29,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Geometry of Free Fermion Commutants","primary_cat":"quant-ph","submitted_at":"2026-04-06T18:00:03+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The k-commutant of free fermions is the Grassmannian manifold of fermionic Gaussian states on 2k sites, exposing a real-replica space duality.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2509.07255","ref_index":70,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Demonstrating an unconditional separation between quantum and classical information resources","primary_cat":"quant-ph","submitted_at":"2025-09-08T22:18:27+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Demonstrates a task solvable with 12 qubits but requiring 62-382 classical bits of memory, yielding unconditional quantum information supremacy on a trapped-ion processor.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2507.22883","ref_index":53,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Operational interpretation of the Stabilizer Entropy","primary_cat":"quant-ph","submitted_at":"2025-07-30T17:58:40+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"The stabilizer Rényi entropy governs the exponential rate at which Clifford orbits become indistinguishable from Haar-random states and sets the optimal distinguishability from stabilizer states in property testing.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2506.18976","ref_index":44,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Nonstabilizerness and Error Resilience in Noisy Quantum Circuits","primary_cat":"quant-ph","submitted_at":"2025-06-23T18:00:01+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Amplitude damping generates nonstabilizerness in qubit systems unlike depolarizing noise, with local injection washed out collectively after encoding, decoding, and postselection.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2505.10110","ref_index":75,"ref_count":1,"confidence":0.9,"is_internal_anchor":true,"paper_title":"Non-Clifford Cost of Random Unitaries","primary_cat":"quant-ph","submitted_at":"2025-05-15T09:28:10+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Rigorous bounds establish that t = Theta(k^2) non-Clifford gates are necessary and sufficient for frame-potential approximation to unitary k-designs while t = Theta(nk) suffices for relative-error k-designs.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}