Optimal algorithms achieve query complexities Θ(d/ε²) for incoherent access, Θ(d/ε) for coherent access, and Θ(√d/ε) for source-code access in quantum channel certification to unitary, exactly matching prior lower bounds.
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Quantum amplitude amplification and estimation
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Sample complexity for fidelity estimation to a rank-r reference state is O(r²/ε²) with lower bound Ω(r/ε²); O(r²/ε⁴) when unknown state also has rank ≤r.
Quantum algorithm prepares exact Hadamard product state of two function states with N-independent query complexity when either function has finitely many non-zero Fourier coefficients.
A one-ancilla framework for QSAMPLE preparation via GQSP-based selective phase compilation embedded in fixed-point amplitude amplification, improving overlap dependence to inverse square-root minimum overlap.
A quantum multi-level framework achieves near-optimal query complexity for q-Tsallis entropy estimation for q>1 and a speedup for q<1 over classical methods.
A recursive construction preserves O(sqrt(N)) quantum search complexity with local operations on tensor-decomposable partitions, eliminating the need for global diffusion via degeneracy in reflection angles.
On random unimodular lattices, full-sign Gibbs mass of e^{a/n}-edge windows vanishes for c≤1 and converges to a Poisson–Dirichlet partition for c>1; primitive fixed-γ windows have visibility threshold c=γ^{-2} in the high-temperature regime.
AtomTreeSearch embeds a neutral-atom quantum MWIS subroutine inside Monte Carlo Tree Search and matches or exceeds OR-Tools and simulated annealing on TSP instances up to 100 cities.
Coupling-Grouped XY-QAOA enables joint anomaly-feature selection via a constraint-preserving grouped-angle QAOA variant, achieving 45.9-61.3% circuit depth reduction and larger feasible executions (64 qubits at p=2) on IBM Heron hardware compared to standard approaches.
Quantum rejection sampling applied to truncated Klein proposals yields quadratic speedup in dual-attack lattice Gaussian sampling, cutting Kyber attack costs by 9, 4, and 13 bits.
Quantum rejection sampling yields a quadratically faster discrete Gaussian sampler on lattices, enabling two improved versions of quantum dual attacks with trade-offs in speed and memory.
An architecture-aware unitary-synthesis transpiler is claimed to cut CNOT counts by 6-36% and run 39-940x faster than Qiskit/TKET/Pennylane on IQM Garnet and IBM Marrakesh circuits with 3-11 qubits.
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
Quantum algorithm for 1D NLSE via Lax-pair scattering performs time evolution analytically in the scattering domain and reconstructs solutions with QSVT.
QFlow-SD matches canonical UCCSD energies for tested molecules while using substantially fewer qubits via reduced active spaces and constant-depth circuits, with a composite classical-quantum downfolding strategy demonstrated for water.
Tensor-rank quantum and quantum-inspired PINNs solve the Merton HJB PDE with lower error and fewer parameters than classical fully connected PINNs.
Hybrid quantum interior point methods for linear programming have no practical runtime advantage over classical solvers like HiGHS on realistic instances because their quantum lower bounds already exceed classical performance under optimistic assumptions.
citing papers explorer
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Strict Hierarchy for Quantum Channel Certification to Unitary
Optimal algorithms achieve query complexities Θ(d/ε²) for incoherent access, Θ(d/ε) for coherent access, and Θ(√d/ε) for source-code access in quantum channel certification to unitary, exactly matching prior lower bounds.
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Estimating Fidelity to a Reference Quantum State
Sample complexity for fidelity estimation to a rank-r reference state is O(r²/ε²) with lower bound Ω(r/ε²); O(r²/ε⁴) when unknown state also has rank ≤r.
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An efficient quantum Hadamard product algorithm for functions
Quantum algorithm prepares exact Hadamard product state of two function states with N-independent query complexity when either function has finitely many non-zero Fourier coefficients.
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Ancilla-Efficient QSAMPLE Preparation for Reversible Markov Chains
A one-ancilla framework for QSAMPLE preparation via GQSP-based selective phase compilation embedded in fixed-point amplitude amplification, improving overlap dependence to inverse square-root minimum overlap.
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Quantum Multi-Level Estimation of Functionals of Discrete Distributions
A quantum multi-level framework achieves near-optimal query complexity for q-Tsallis entropy estimation for q>1 and a speedup for q<1 over classical methods.
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Quantum Search without Global Diffusion
A recursive construction preserves O(sqrt(N)) quantum search complexity with local operations on tensor-decomposable partitions, eliminating the need for global diffusion via degeneracy in reflection angles.
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Thermal Concentration and Poisson-Dirichlet Edge Statistics for Random-Lattice Gibbs Ensembles
On random unimodular lattices, full-sign Gibbs mass of e^{a/n}-edge windows vanishes for c≤1 and converges to a Poisson–Dirichlet partition for c>1; primitive fixed-γ windows have visibility threshold c=γ^{-2} in the high-temperature regime.
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Quantum-enhanced Monte Carlo Tree Search framework for combinatorial optimization problems
AtomTreeSearch embeds a neutral-atom quantum MWIS subroutine inside Monte Carlo Tree Search and matches or exceeds OR-Tools and simulated annealing on TSP instances up to 100 cities.
-
Coupling-Grouped XY-QAOA for Joint Anomaly-Feature Selection
Coupling-Grouped XY-QAOA enables joint anomaly-feature selection via a constraint-preserving grouped-angle QAOA variant, achieving 45.9-61.3% circuit depth reduction and larger feasible executions (64 qubits at p=2) on IBM Heron hardware compared to standard approaches.
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Improved Dual Attack and Trapdoor Sampling via Quantum Rejection Sampling
Quantum rejection sampling applied to truncated Klein proposals yields quadratic speedup in dual-attack lattice Gaussian sampling, cutting Kyber attack costs by 9, 4, and 13 bits.
-
Quantum algorithm for Discrete Gaussian Sampling
Quantum rejection sampling yields a quadratically faster discrete Gaussian sampler on lattices, enabling two improved versions of quantum dual attacks with trade-offs in speed and memory.
-
Architecture-aware Unitary Synthesis
An architecture-aware unitary-synthesis transpiler is claimed to cut CNOT counts by 6-36% and run 39-940x faster than Qiskit/TKET/Pennylane on IQM Garnet and IBM Marrakesh circuits with 3-11 qubits.
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Numerical approximation of the Koopman-von Neumann equation: Operator learning and quantum computing
Data-driven approximation methods are derived for the unitary Koopman-von Neumann operator, its eigenvalues and eigenfunctions, with explicit quantum-circuit representations for finite-dimensional projections.
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Quantum algorithm for the nonlinear Schr\"odinger equation via the Lax-pair scattering
Quantum algorithm for 1D NLSE via Lax-pair scattering performs time evolution analytically in the scattering domain and reconstructs solutions with QSVT.
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Quantum Flow algorithm: quantum simulations of chemical systems using reduced quantum resources and constant depth quantum circuits
QFlow-SD matches canonical UCCSD energies for tested molecules while using substantially fewer qubits via reduced active spaces and constant-depth circuits, with a composite classical-quantum downfolding strategy demonstrated for water.
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Learning PDEs for Portfolio Optimization with Quantum Physics-Informed Neural Networks
Tensor-rank quantum and quantum-inspired PINNs solve the Merton HJB PDE with lower error and fewer parameters than classical fully connected PINNs.
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Practical lower bounds for hybrid quantum interior point methods in linear programming
Hybrid quantum interior point methods for linear programming have no practical runtime advantage over classical solvers like HiGHS on realistic instances because their quantum lower bounds already exceed classical performance under optimistic assumptions.