Resolves fundamental gap in quantum complexity: determining homology of weighted clique complexes is QMA₁-hard with inverse-polynomial spectral gaps. Uses topological gadget encodings and filtered-Hodge theory for complete hardness proof.

#QuantumComplexity #ComputationalComplexity #Research

Analyzes complexity of redundancy-free quantum Hamiltonians, showing they become tractable at lower inverse temperatures (β∼1/√d vs 1/d) than general Hamiltonians, with NP/QMA-hardness results at higher temperatures.

#QuantumAlgorithms #QuantumComplexity #Research

New framework for unitary complexity reveals surprising links between quantum cryptography and classical computational hardness, showing quantum commitments require solving decade-old complexity theory problems.

#QuantumComplexity #QuantumCryptography #Research

Extends polymorphism-based reductions to entangled CSPs, proving RE-completeness of entangled n-colouring (n≥3) and establishing hardness for quantum constraint problems lacking commutativity gadgets through stable minion homomorphisms.

#QuantumComplexity #QuantumInformation #Research

Proves logarithmic shared EPR pairs preserve QMA(2) computational power, settling part of Aaronson et al.'s open question on quantum prover entanglement.

#QuantumComplexity #QuantumInformation #Research

Study proves computing nonstabilizerness of 2D tensor network states is #P-hard and stabilizer membership is C=P-complete, even at constant bond dimension, establishing fundamental computational barriers for quantum state analysis.

#QuantumComplexity #TensorNetworks #Research

Researchers construct succinct arguments for QMA directly from ideal hash functions, solving a major open problem and showing quantum cryptographic primitives don't require special structured assumptions.

#QuantumCryptography #QuantumComplexity #Research

Proves the commuting local Hamiltonian problem is not BQP-hard by constructing an oracle where BQP ⊄ QIMA. Uses Forrelation query lower bounds to establish exponential separations in commuting verification complexity.

#QuantumComplexity #QuantumAlgorithms #Research

New theoretical result: Quantum-classical simulation complexity doesn't depend on input distribution bias. Whether bits are uniform, biased, or Hamming-weight restricted, polynomial simulation either works for all or none.

#QuantumComplexity #QuantumTheory #Research

First nontrivial quantum lower bounds for triangle listing (Ω(n^3/2)) and multiplicative k-spanner construction via novel recording framework extensions with bidirectional oracle architecture.

#QuantumComplexity #GraphAlgorithms #Research

Degree-balanced frustration-free quantum SAT admits exponential speedup over brute force algorithms, while general quantum 5-SAT remains (Q)SETH-hard—establishing a fine-grained complexity boundary based on constraint distribution.

#QuantumComplexity #QuantumAlgorithms #Research

Settles quantum complexity of identifying hidden symmetries in quantum states, proving O(log|G/H|/√ε) query complexity with state-preparation access versus O(log|G/H|/ε) with copies—establishing quadratic separation and matching lower bounds.

#QuantumAlgorithms #QuantumComplexity #Research

Researchers prove tight Θ(κ√d log(1/ϵ)) query bounds for quantum linear systems solvers, matching upper and lower bounds. This resolves complexity gaps and enables optimal black-box unitary implementation with O(√N) queries.

#QuantumAlgorithms #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

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

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

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

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

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

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