Finding decoherence-free subspaces in Markovian quantum systems is computationally intractable, even for quantum computers. New QMA-hardness results suggest fundamental limits to verifying quantum error correction structures.
#QuantumComplexity #ErrorCorrection #QuantumInformation
#QuantumComplexity #ErrorCorrection #QuantumInformation
Computational Complexity of Identifying Decoherence-Free Subspaces
arxiv.org
September 23, 2026 at 4:59 AM
Finding decoherence-free subspaces in Markovian quantum systems is computationally intractable, even for quantum computers. New QMA-hardness results suggest fundamental limits to verifying quantum error correction structures.
#QuantumComplexity #ErrorCorrection #QuantumInformation
#QuantumComplexity #ErrorCorrection #QuantumInformation
Extends the proven Brown-Susskind conjecture on quantum circuit complexity by showing that complexity strictly increases when adding new 2-qubit gate pairs to quantum circuits, advancing theoretical understanding of quantum computational scaling.
#QuantumCircuits #QuantumComplexity #Research
#QuantumCircuits #QuantumComplexity #Research
A Remark on the Brown-Susskind Conjecture
arxiv.org
September 22, 2026 at 2:49 AM
Extends the proven Brown-Susskind conjecture on quantum circuit complexity by showing that complexity strictly increases when adding new 2-qubit gate pairs to quantum circuits, advancing theoretical understanding of quantum computational scaling.
#QuantumCircuits #QuantumComplexity #Research
#QuantumCircuits #QuantumComplexity #Research
Generic local Hamiltonians sustain exponential quantum circuit complexity growth over exponentially long timescales, far beyond thermalization. Rigorous unconditional proof without assumptions resolves key dynamics conjecture.
#QuantumComplexity #QuantumDynamics #Research
#QuantumComplexity #QuantumDynamics #Research
Sustained Growth of Quantum Circuit Complexity in Hamiltonian Dynamics
arxiv.org
September 24, 2026 at 6:01 AM
Generic local Hamiltonians sustain exponential quantum circuit complexity growth over exponentially long timescales, far beyond thermalization. Rigorous unconditional proof without assumptions resolves key dynamics conjecture.
#QuantumComplexity #QuantumDynamics #Research
#QuantumComplexity #QuantumDynamics #Research
Resolves a key open problem by proving the conjectured lower bound Ω(κ√s log(1/ε)) for quantum linear system solvers in sparse-access models, establishing tight complexity dependence on condition number, sparsity, and target precision.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Near-Optimal Joint Lower Bound for Sparse Quantum Linear System Solvers
arxiv.org
September 22, 2026 at 6:15 AM
Resolves a key open problem by proving the conjectured lower bound Ω(κ√s log(1/ε)) for quantum linear system solvers in sparse-access models, establishing tight complexity dependence on condition number, sparsity, and target precision.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Complete characterization of isometry groups for right invariant Riemannian metrics on SU(2N), enabling rigorous geometric approaches to quantum complexity analysis with applications to holographic duality and circuit complexity bounds.
#QuantumComplexity #QuantumAlgorithms #Research
#QuantumComplexity #QuantumAlgorithms #Research
Isometry Groups of Right Invariant Metrics in Geometric Quantum Complexity
arxiv.org
September 21, 2026 at 5:10 AM
Complete characterization of isometry groups for right invariant Riemannian metrics on SU(2N), enabling rigorous geometric approaches to quantum complexity analysis with applications to holographic duality and circuit complexity bounds.
#QuantumComplexity #QuantumAlgorithms #Research
#QuantumComplexity #QuantumAlgorithms #Research
New computational framework quantifies fermionic non-Gaussianity through covariance matrix analysis. Enables practical assessment of quantum state complexity and classical simulability, with applications to quantum advantage and many-body systems.
#QuantumComplexity #QuantumComputing #Research
#QuantumComplexity #QuantumComputing #Research
Computable Measures of Fermionic Non-Gaussianity
arxiv.org
July 3, 2026 at 4:55 AM
New computational framework quantifies fermionic non-Gaussianity through covariance matrix analysis. Enables practical assessment of quantum state complexity and classical simulability, with applications to quantum advantage and many-body systems.
#QuantumComplexity #QuantumComputing #Research
#QuantumComplexity #QuantumComputing #Research
Continuous-variable quantum computing gets rigorous complexity theory. New work establishes bounds for Gaussian dynamics and ground-state problems, revealing how bosonic systems differ fundamentally from discrete-variable quantum computing.
#QuantumComplexity #BosonicQuantum #News
#QuantumComplexity #BosonicQuantum #News
Complexity Theory for Continuous-Variable Quantum Computing
iq.fp2.dev
May 20, 2026 at 11:10 AM
Continuous-variable quantum computing gets rigorous complexity theory. New work establishes bounds for Gaussian dynamics and ground-state problems, revealing how bosonic systems differ fundamentally from discrete-variable quantum computing.
#QuantumComplexity #BosonicQuantum #News
#QuantumComplexity #BosonicQuantum #News
Proves quantum algorithms require exponential Ω(2^(n/24)) queries to find entrance-to-exit paths in welded trees, settling an open question about quantum speedup extent using compressed oracle analysis.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Exponential Query Lower Bound for Path Finding in Welded Trees
iq.fp2.dev
September 18, 2026 at 5:44 AM
Proves quantum algorithms require exponential Ω(2^(n/24)) queries to find entrance-to-exit paths in welded trees, settling an open question about quantum speedup extent using compressed oracle analysis.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Researchers improved the classical simulation bound for bosonic quantum computers from exponential space (EXPSPACE) to polynomial space (PSPACE), advancing understanding of when bosonic systems can provide computational advantage.
#BosonicQuantum #QuantumComplexity #QuantumTheory
#BosonicQuantum #QuantumComplexity #QuantumTheory
Polynomial-Space Classical Simulation of Universal Bosonic Quantum Computation
www.nature.com
May 16, 2026 at 6:02 PM
Researchers improved the classical simulation bound for bosonic quantum computers from exponential space (EXPSPACE) to polynomial space (PSPACE), advancing understanding of when bosonic systems can provide computational advantage.
#BosonicQuantum #QuantumComplexity #QuantumTheory
#BosonicQuantum #QuantumComplexity #QuantumTheory
Canonical encoding framework proves pure-state BNMR is intrinsic to Schmidt spectrum, extending invariance from local unitaries to local isometries. Enables exact evaluation of nonlocal magic resources in many-body quantum systems.
#QuantumComplexity #EntanglementTheory #Research
#QuantumComplexity #EntanglementTheory #Research
Spectral Structure of Bipartite Nonlocal Magic Resource in Quantum States
arxiv.org
June 24, 2026 at 3:24 AM
Canonical encoding framework proves pure-state BNMR is intrinsic to Schmidt spectrum, extending invariance from local unitaries to local isometries. Enables exact evaluation of nonlocal magic resources in many-body quantum systems.
#QuantumComplexity #EntanglementTheory #Research
#QuantumComplexity #EntanglementTheory #Research
This work proves that quantum algorithms with limited adaptivity and parallel queries admit efficient classical simulation on most inputs, providing partial evidence that quantum speedups require inherent input structure.
#QuantumAlgorithms #QuantumComplexity #QuantumAdvantage
#QuantumAlgorithms #QuantumComplexity #QuantumAdvantage
Parallel Quantum Advantage with Limited Adaptivity Requires Structure
arxiv.org
August 21, 2026 at 2:55 AM
This work proves that quantum algorithms with limited adaptivity and parallel queries admit efficient classical simulation on most inputs, providing partial evidence that quantum speedups require inherent input structure.
#QuantumAlgorithms #QuantumComplexity #QuantumAdvantage
#QuantumAlgorithms #QuantumComplexity #QuantumAdvantage
Proves a trichotomy of 2-local Hamiltonian complexity: QMA-complete, StoqMA-complete, or reducible to a new EPR* problem, with phases governed by singlet energy ordering. If EPR* ∈ BPP (conjectured), this completes the full complexity classification.
#QuantumComplexity #LocalHamiltonian #Research
#QuantumComplexity #LocalHamiltonian #Research
Complexity Phase Transition at the EPR Hamiltonian
iq.fp2.dev
April 15, 2026 at 3:10 AM
Proves a trichotomy of 2-local Hamiltonian complexity: QMA-complete, StoqMA-complete, or reducible to a new EPR* problem, with phases governed by singlet energy ordering. If EPR* ∈ BPP (conjectured), this completes the full complexity classification.
#QuantumComplexity #LocalHamiltonian #Research
#QuantumComplexity #LocalHamiltonian #Research
We establish Krylov complexity as a powerful diagnostic of flat-band phase robustness under Carroll-breaking perturbations, revealing sharp dichotomies between vanilla and exotic phases through state-dependent Hilbert space spreading.
#FlatBands #QuantumComplexity #CarrollSymmetry
#FlatBands #QuantumComplexity #CarrollSymmetry
Krylov Complexity as a Probe of Carroll Symmetry Breaking in Flat-Band Systems
arxiv.org
June 5, 2026 at 8:40 AM
We establish Krylov complexity as a powerful diagnostic of flat-band phase robustness under Carroll-breaking perturbations, revealing sharp dichotomies between vanilla and exotic phases through state-dependent Hilbert space spreading.
#FlatBands #QuantumComplexity #CarrollSymmetry
#FlatBands #QuantumComplexity #CarrollSymmetry
New theoretical framework achieves stronger exponential separations between quantum and classical communication complexity of total functions, improving from n^(1/6) to n^(1/2) exponent with polylogarithmic quantum messages.
#QuantumCommunication #QuantumComplexity #Research
#QuantumCommunication #QuantumComplexity #Research
Exponential Separations Between Quantum and Classical Communication Complexity
arxiv.org
September 16, 2026 at 4:40 AM
New theoretical framework achieves stronger exponential separations between quantum and classical communication complexity of total functions, improving from n^(1/6) to n^(1/2) exponent with polylogarithmic quantum messages.
#QuantumCommunication #QuantumComplexity #Research
#QuantumCommunication #QuantumComplexity #Research
Resolves 25-year-old open problems by proving QIP(2), qq-QAM, QAM, and QMA achieve perfect completeness. Introduces endpoint-inward turn-halving transformation that halves message complexity while preserving completeness guarantees.
#QuantumProofs #QuantumComplexity #QuantumInformation
#QuantumProofs #QuantumComplexity #QuantumInformation
Perfect Completeness for Quantum Interactive Proof Systems
arxiv.org
September 15, 2026 at 7:06 PM
Resolves 25-year-old open problems by proving QIP(2), qq-QAM, QAM, and QMA achieve perfect completeness. Introduces endpoint-inward turn-halving transformation that halves message complexity while preserving completeness guarantees.
#QuantumProofs #QuantumComplexity #QuantumInformation
#QuantumProofs #QuantumComplexity #QuantumInformation
Researchers proved QMA=QMA1, demonstrating quantum Merlin-Arthur proof systems can achieve perfect completeness without sacrificing computational power using a universal gate set of Hadamard, Toffoli, and X gates.
#QuantumComplexity #QuantumProofs #Research
#QuantumComplexity #QuantumProofs #Research
QMA Has Perfect Completeness
arxiv.org
September 14, 2026 at 11:54 PM
Researchers proved QMA=QMA1, demonstrating quantum Merlin-Arthur proof systems can achieve perfect completeness without sacrificing computational power using a universal gate set of Hadamard, Toffoli, and X gates.
#QuantumComplexity #QuantumProofs #Research
#QuantumComplexity #QuantumProofs #Research
Resolving a 20-year-old conjecture: oracle separations proved between all consecutive levels of the Fourier hierarchy, establishing that each additional Hadamard layer strictly increases quantum computational power.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Oracle Separations in the Fourier Hierarchy
arxiv.org
September 11, 2026 at 8:35 AM
Resolving a 20-year-old conjecture: oracle separations proved between all consecutive levels of the Fourier hierarchy, establishing that each additional Hadamard layer strictly increases quantum computational power.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Proves three quantum complexity classes are equivalent using dimension-free stability bounds for symmetric tensor states, resolving open conjectures about pure-state quantum proof systems and their relationship to standard QMA.
#QuantumComplexity #QuantumAlgorithms #Research
#QuantumComplexity #QuantumAlgorithms #Research
Quantum Complexity Collapse: Pure-State Consistency Equals Standard QMA
iq.fp2.dev
September 11, 2026 at 8:20 AM
Proves three quantum complexity classes are equivalent using dimension-free stability bounds for symmetric tensor states, resolving open conjectures about pure-state quantum proof systems and their relationship to standard QMA.
#QuantumComplexity #QuantumAlgorithms #Research
#QuantumComplexity #QuantumAlgorithms #Research
New multiplicative adversary derivation recovers fine-grained quantum query complexity bounds for approximate counting, providing direct analysis of Hamming-weight layer evolution and explicit query-level progress tracking.
#QuantumAlgorithms #QuantumComplexity #QuantumInformation
#QuantumAlgorithms #QuantumComplexity #QuantumInformation
Small-Bias Quantum Approximate Counting via Multiplicative Adversary Method
arxiv.org
September 10, 2026 at 5:07 AM
New multiplicative adversary derivation recovers fine-grained quantum query complexity bounds for approximate counting, providing direct analysis of Hamming-weight layer evolution and explicit query-level progress tracking.
#QuantumAlgorithms #QuantumComplexity #QuantumInformation
#QuantumAlgorithms #QuantumComplexity #QuantumInformation
Theoretical study showing promise problems behave fundamentally differently from languages in relativized settings. Improves upper bound on Quantum-Classical Polynomial Hierarchy and proves self-lowness of PromiseBQP under robust oracle access.
#QuantumComplexity #TheoreticalCS #Research
#QuantumComplexity #TheoreticalCS #Research
Promise Problems and Relativization in Quantum Complexity Theory
arxiv.org
September 9, 2026 at 7:40 PM
Theoretical study showing promise problems behave fundamentally differently from languages in relativized settings. Improves upper bound on Quantum-Classical Polynomial Hierarchy and proves self-lowness of PromiseBQP under robust oracle access.
#QuantumComplexity #TheoreticalCS #Research
#QuantumComplexity #TheoreticalCS #Research
Quantitative lower bounds established on semidefinite program complexity for approximating separable quantum state properties, improving previous quasipolynomial bounds and providing insights into entanglement certification hardness.
#QuantumComplexity #QuantumInformation #Research
#QuantumComplexity #QuantumInformation #Research
Semidefinite Extension Complexity Bounds for Separable Quantum States
arxiv.org
September 9, 2026 at 7:27 AM
Quantitative lower bounds established on semidefinite program complexity for approximating separable quantum state properties, improving previous quasipolynomial bounds and providing insights into entanglement certification hardness.
#QuantumComplexity #QuantumInformation #Research
#QuantumComplexity #QuantumInformation #Research
We prove quantum algorithms achieve quadratic speedup for counting positive Bernoulli distributions, establishing near-matching bounds: Õ(√ρ/(Δϵ)) upper and Ω(√ρ/(Δϵ)) lower via novel Boolean-over-average-case composition theorem.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Quantum Approximate Counting with Bernoulli Oracles
iq.fp2.dev
September 9, 2026 at 12:00 PM
We prove quantum algorithms achieve quadratic speedup for counting positive Bernoulli distributions, establishing near-matching bounds: Õ(√ρ/(Δϵ)) upper and Ω(√ρ/(Δϵ)) lower via novel Boolean-over-average-case composition theorem.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Establishes upper and lower bounds for sample complexity of the generalized hidden shift problem over arbitrary finite groups using quantum information theory and representation-theoretic techniques.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Sample Complexity of Generalized Hidden Shift Problem Over Finite Groups
arxiv.org
September 9, 2026 at 5:06 AM
Establishes upper and lower bounds for sample complexity of the generalized hidden shift problem over arbitrary finite groups using quantum information theory and representation-theoretic techniques.
#QuantumAlgorithms #QuantumComplexity #Research
#QuantumAlgorithms #QuantumComplexity #Research
Constant-depth quantum circuits and controlled fanout gates are equivalent for symmetric Boolean functions. The required fanout size is precisely determined by the function's transition radius, unifying prior quantum circuit complexity results.
#QuantumCircuits #QuantumComplexity #Research
#QuantumCircuits #QuantumComplexity #Research
Fanout Complexity of Symmetric Boolean Functions in QAC0
arxiv.org
September 7, 2026 at 12:15 PM
Constant-depth quantum circuits and controlled fanout gates are equivalent for symmetric Boolean functions. The required fanout size is precisely determined by the function's transition radius, unifying prior quantum circuit complexity results.
#QuantumCircuits #QuantumComplexity #Research
#QuantumCircuits #QuantumComplexity #Research
Researchers establish universal bounds linking entanglement spectrum structure to quantum nonstabilizerness, revealing that spectral non-uniformity and entropy distribution independently govern quantum complexity in many-body systems.
#QuantumEntanglement #QuantumComplexity #Research
#QuantumEntanglement #QuantumComplexity #Research
Unified Spectral Framework for Entanglement and Nonlocal Nonstabilizerness
arxiv.org
September 3, 2026 at 8:07 AM
Researchers establish universal bounds linking entanglement spectrum structure to quantum nonstabilizerness, revealing that spectral non-uniformity and entropy distribution independently govern quantum complexity in many-body systems.
#QuantumEntanglement #QuantumComplexity #Research
#QuantumEntanglement #QuantumComplexity #Research