A new quantum lower bound framework proves a tight bound for k-Distinctness.
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Quantum measurements and the Abelian Stabilizer Problem
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abstract
We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor's results. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application of this procedure is a polynomial quantum Fourier transform algorithm for an arbitrary finite Abelian group. The paper also contains a rather detailed introduction to the theory of quantum computation.
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representative citing papers
Quantum algorithms achieve polylogarithmic complexity for Betti number estimation and homology testing via block-encoded Laplacians and cohomological projections, claiming exponential speedups under sparsity assumptions.
A new cultivation protocol prepares reusable logical catalysts as eigenstates of high-period Clifford circuits to implement exact Z^{2^{-b}} phase gates with constant online depth in surface codes.
Recursive grouping of Pauli terms with anti-commuting sign-flip strings reduces compiled T depth by 85.2% and CX depth by 68.9% on a 24-spin Kagome Hamiltonian versus term-by-term controlled rotations.
Explicit reversible quantum oracles for bounded Diophantine systems achieve quadratic speedup with qubit count O((n + d²) log₂ N) and Toffoli depth O(q²).
HBR decomposition quantifies per-phase fidelity loss in quantum compilers, revealing that routing causes up to 60% loss in search circuits while synthesis dominates Hamiltonian simulation, and correctly predicts SDK rankings on both simulation and real hardware.
Generalizes QFT to semisimple algebras and gives poly(n, log d, log(1/ε)) gate algorithms that approximate the transform to error (d^{-1/2} + ε) poly(|A|) on partition, Brauer, and walled Brauer algebras when d is large.
A polylog-sized quantum computer achieves exponential advantage over classical machines in classification and dimension reduction of massive classical data using quantum oracle sketching combined with classical shadows.
Dynamarq is a new scalable benchmarking framework that defines structural features for dynamic quantum circuits and uses statistical models to predict hardware fidelity with transferable parameters.
First end-to-end demonstration of quantum error correction integrated with quantum phase estimation to compute molecular hydrogen ground-state energy to 0.001(13) hartree accuracy on Quantinuum H2-2 hardware.
Search-based approximate diagonalization followed by analytical inversion yields high-precision multi-qubit Clifford+T circuits with 95% fewer non-Clifford gates on real-algorithm benchmarks.
Lattice-surgery scheduling is mapped to 3D path embedding and solved with look-ahead Dijkstra projection, yielding 3.8x lower execution time on quantum phase estimation benchmarks versus greedy scheduling.
Controlled gate networks reduce two-qubit gate counts for linear combinations of unitary operators in quantum circuits, shown in variational calculations, rodeo eigenvalue estimation, and lattice nucleon evolution on real hardware.
Amplitude amplification finds solutions quadratically faster than classical methods and enables quantum estimation of solution counts.
Analog cQED dispersive evolution plus sequential binary threshold tests on a bosonic mode realizes iterative QPE with Heisenberg-limited total time and exponentially suppressed failure probability.
QLS applied to single- and multi-reference linearized coupled cluster shows polylog κ and sublinear sparsity on model systems, supporting prospects of exponential advantage over conjugate gradient.
A rubric-guided GRPO pipeline fine-tunes a 7B LLM to synthesize quantum circuits achieving 3.31x T-gate compression with <1% hardware-constraint violations, validated on IBM and IonQ processors.
LR-SCI-PT with second-order Epstein-Nesbet corrections improves static polarizabilities toward FCI limits for small molecules but preserves the parent pole structure, limiting it to static properties.
QC-AFQMC per-step scaling reduced from O(N^5.5) to O(N^4.5) via Aitken's block transformation for singular Pfaffians and algorithmic differentiation for force bias, with demonstrations on H8 from real quantum data and Li2O4.
The Projector Variational Ansatz (PVA) is a new VQE ansatz that can match ISQ-QSP or ADAPT-VQE structures and converges with shallower circuits than standard ADAPT-VQE in experiments.
Amplitude amplification for Gutzwiller projection (AAGP) achieves a quadratic reduction in projection queries versus postselection, enabling practical preparation of projected BCS states for up to 100-site t-J model simulations.
Replaces sampling-based estimation in NOQE with iterative quantum amplitude estimation to achieve O(1/ε) query complexity for Hamiltonian and overlap matrices.
New boundary condition approach for QLBM using one coherent operation on the full boundary, claimed to use fewer resources asymptotically and practically for bounce-back and specular reflection.
Benchmarks on H-chains show an 8th-order formula minimizes cost metrics, but a new 4th-order formula achieves the lowest gate count near chemical accuracy while also lowering RZ-layer depth.
citing papers explorer
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Tight Quantum Lower Bound for k-Distinctness
A new quantum lower bound framework proves a tight bound for k-Distinctness.
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New aspects of quantum topological data analysis: Betti number estimation, and testing and tracking of homology and cohomology classes
Quantum algorithms achieve polylogarithmic complexity for Betti number estimation and homology testing via block-encoded Laplacians and cohomological projections, claiming exponential speedups under sparsity assumptions.
-
Cultivating logical catalysts for fault-tolerant dyadic phase rotations
A new cultivation protocol prepares reusable logical catalysts as eigenstates of high-period Clifford circuits to implement exact Z^{2^{-b}} phase gates with constant online depth in surface codes.
-
Efficient Quantum Circuit Construction of Controlled Time-Evolution for Arbitrary Pauli-Sum Hamiltonians
Recursive grouping of Pauli terms with anti-commuting sign-flip strings reduces compiled T depth by 85.2% and CX depth by 68.9% on a 24-spin Kagome Hamiltonian versus term-by-term controlled rotations.
-
From Hilbert's Tenth Problem to Quantum Speedup: Explicit Oracles for Bounded Diophantine Systems
Explicit reversible quantum oracles for bounded Diophantine systems achieve quadratic speedup with qubit count O((n + d²) log₂ N) and Toffoli depth O(q²).
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Per-Phase Fidelity Attribution for Quantum Compilers using HBR Decomposition
HBR decomposition quantifies per-phase fidelity loss in quantum compilers, revealing that routing causes up to 60% loss in search circuits while synthesis dominates Hamiltonian simulation, and correctly predicts SDK rankings on both simulation and real hardware.
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Efficient Quantum Fourier Transforms For Semisimple Algebras
Generalizes QFT to semisimple algebras and gives poly(n, log d, log(1/ε)) gate algorithms that approximate the transform to error (d^{-1/2} + ε) poly(|A|) on partition, Brauer, and walled Brauer algebras when d is large.
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Exponential quantum advantage in processing massive classical data
A polylog-sized quantum computer achieves exponential advantage over classical machines in classification and dimension reduction of massive classical data using quantum oracle sketching combined with classical shadows.
-
Characterizing and Benchmarking Dynamic Quantum Circuits
Dynamarq is a new scalable benchmarking framework that defines structural features for dynamic quantum circuits and uses statistical models to predict hardware fidelity with transferable parameters.
-
Quantum Error-Corrected Computation of Molecular Energies
First end-to-end demonstration of quantum error correction integrated with quantum phase estimation to compute molecular hydrogen ground-state energy to 0.001(13) hartree accuracy on Quantinuum H2-2 hardware.
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High-Precision Multi-Qubit Clifford+T Synthesis by Unitary Diagonalization
Search-based approximate diagonalization followed by analytical inversion yields high-precision multi-qubit Clifford+T circuits with 95% fewer non-Clifford gates on real-algorithm benchmarks.
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Efficient and high-performance routing of lattice-surgery paths on three-dimensional lattice
Lattice-surgery scheduling is mapped to 3D path embedding and solved with look-ahead Dijkstra projection, yielding 3.8x lower execution time on quantum phase estimation benchmarks versus greedy scheduling.
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Controlled Gate Networks: Theory and Application to Eigenvalue Estimation
Controlled gate networks reduce two-qubit gate counts for linear combinations of unitary operators in quantum circuits, shown in variational calculations, rodeo eigenvalue estimation, and lattice nucleon evolution on real hardware.
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Quantum Amplitude Amplification and Estimation
Amplitude amplification finds solutions quadratically faster than classical methods and enables quantum estimation of solution counts.
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Hardware-native quantum phase estimation with circuit QED
Analog cQED dispersive evolution plus sequential binary threshold tests on a bosonic mode realizes iterative QPE with Heisenberg-limited total time and exponentially suppressed failure probability.
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Quantum linear solvers for quantum chemistry: prospects of exponential quantum advantage
QLS applied to single- and multi-reference linearized coupled cluster shows polylog κ and sublinear sparsity on model systems, supporting prospects of exponential advantage over conjugate gradient.
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RubriQ: Rubric-Guided Group Relative Policy Optimization for Constraint-Aware Quantum Circuit Synthesis
A rubric-guided GRPO pipeline fine-tunes a 7B LLM to synthesize quantum circuits achieving 3.31x T-gate compression with <1% hardware-constraint violations, validated on IBM and IonQ processors.
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Perturbatively Corrected Linear Response Selected Configuration Interaction
LR-SCI-PT with second-order Epstein-Nesbet corrections improves static polarizabilities toward FCI limits for small molecules but preserves the parent pole structure, limiting it to static properties.
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Quantum-Classical Auxiliary-Field Quantum Monte Carlo at the Edge of Practicability
QC-AFQMC per-step scaling reduced from O(N^5.5) to O(N^4.5) via Aitken's block transformation for singular Pfaffians and algorithmic differentiation for force bias, with demonstrations on H8 from real quantum data and Li2O4.
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Projector Quantum Variational Ansatz
The Projector Variational Ansatz (PVA) is a new VQE ansatz that can match ISQ-QSP or ADAPT-VQE structures and converges with shallower circuits than standard ADAPT-VQE in experiments.
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Scalable Quantum Algorithms for Gutzwiller Projection
Amplitude amplification for Gutzwiller projection (AAGP) achieves a quadratic reduction in projection queries versus postselection, enabling practical preparation of projected BCS states for up to 100-site t-J model simulations.
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Towards Heisenberg Scaling: Measurement-Efficient Non-Orthogonal Quantum Eigensolver
Replaces sampling-based estimation in NOQE with iterative quantum amplitude estimation to achieve O(1/ε) query complexity for Hamiltonian and overlap matrices.
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Efficient and Expressive Boundary Conditions in Quantum Lattice Boltzmann Methods
New boundary condition approach for QLBM using one coherent operation on the full boundary, claimed to use fewer resources asymptotically and practically for bounce-back and specular reflection.
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Evaluating higher-order product formulae for molecular ground-state energy estimation
Benchmarks on H-chains show an 8th-order formula minimizes cost metrics, but a new 4th-order formula achieves the lowest gate count near chemical accuracy while also lowering RZ-layer depth.
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Quantum algorithms for density functional theory with minimal readout
Qubit-efficient quantum algorithm for KS-DFT computes occupied orbitals simultaneously and evaluates total energy via Harris functional without density readout, with a second multi-copy method for self-consistency.
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Point-group symmetry analysis of many-electron wavefunctions on a quantum computer
An ancilla-free method projects many-electron states onto point-group irreps via orbital rotations derived from representation-matrix eigenvectors and demonstrates it on benzene and ferrocene with a 32-qubit IBM hardware run.
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Adiabatic Quantum Phase Estimation
An adiabatic protocol for quantum phase estimation that reaches optimal scaling T = O(1/ε log(1/δ)) by encoding eigenvalues in computational basis populations rather than phases.
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Circuits of Quantum Hashing and Quantum Fourier Transform for a Cactus as a Qubit Connectivity Graph
An O(n^3) algorithm builds quantum hashing and QFT circuits on cactus qubit graphs by solving the shortest non-simple 1-covering path problem in polynomial time.
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Quantum Koopman Algorithms
Quantum Koopman Algorithms define an observable-space quantum framework for simulating linear quantum and nonlinear classical dynamics with polylog gate costs in some cases.
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Near-Optimal Quantum Time Evolution Circuits via Provably Convergent Compression
A recipe for initial points in variational compression of quantum time-evolution operators that provably converges to near-optimal O(N t polylog(N t/ε)) gate complexity for local translationally invariant Hamiltonians.
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$\mathcal{O}(n)$ alternative to Quantum Fourier Transform with efficient neural net classical post-processing
HP-1 circuits achieve O(n) depth while preserving shift invariance and exponentially growing Fisher information, enabling numerical replacement of the QFT in Shor's algorithm with neural net classical post-processing.
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CO-MAP: A Reinforcement Learning Approach to the Qubit Allocation Problem
Reinforcement learning policy for qubit mapping reduces SWAP overhead by 65-85% versus standard quantum compilers on MQTBench and Queko benchmark circuits.
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Practical Log-Depth Quantum State Preparation and Circuit Verification via Tree Tensor Network Compilation
A tree tensor network renormalization decomposes matrix product states into log-depth quantum circuits with a fidelity-depth trade-off parameter, extended to matrix product operators for ancilla-free overlap verification circuits.
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A Transferable Machine Learning Approach to Predict Optimized Orbitals for Electronic Structure Problems
A graph neural network trained on H4 and H6 predicts optimized orbitals for larger unseen H8-H12 systems with O(10-100) milli-Hartree energy errors and provides effective warm-starts for VQE optimization.
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Fault-Tolerant Quantum Computing with Trapped Ions: The Walking Cat Architecture
A trapped-ion architecture based on LDPC codes and cat-state factories achieves 110 logical qubits and one million T gates per day using 2514 physical qubits, with estimates for Heisenberg model simulation on 100 sites in one month using 10000 qubits.
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Split-Evolution Quantum Phase Estimation for Particle-Conserving Hamiltonians
SE-QPE replaces controlled evolution in QPE with CSWAP-based interference, cutting CX and T costs for particle-conserving chemistry Hamiltonians while matching canonical phase outcomes.
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Worst-case Harrow-Hassidim-Lloyd algorithm with average-case correct quantum Fourier transform
A strengthened average-case QFT verification condition that controls inter-eigenspace coherences guarantees worst-case correctness of the HHL algorithm in natural settings.
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Generative Circuit Design for Quantum-Selected Configuration Interaction
A Transformer policy optimizes quantum circuit ansatzes for QSCI, yielding up to 98% reduction in two-qubit gates while reaching chemical accuracy on N2 and competitive compactness with classical methods.
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Hybrid Quantum-Classical Algorithm for Hamiltonian Simulation
Hybrid algorithm classically diagonalizes Hamiltonian tensor factors to construct block-encodings for quantum simulation via QSVD, with extensions for commuting time-dependent cases.
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Exponentially cheaper coherent phase estimation via uncontrolled unitaries
Uncontrolled unitaries plus controlled preparations replace controlled unitaries in phase estimation, cutting two-qubit gates exponentially when eigenstate preparation is known.
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Exponential Scaling Barriers for Variational Quantum Eigensolvers
Adaptive VQE exhibits exponential growth in iterations and circuit depth with system size, accurately predicted by classical Rényi entropy on molecules with 4-10 orbitals.
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Deterministic Ground State Preparation via Power-Cosine Filtering of Time Evolution Operators
A single-ancilla Power-Cosine QSP filter on time-evolution operators achieves deterministic many-body ground state preparation with exponential excited-state suppression and O(Δ^{-2} log(1/ε)) depth scaling.
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Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra
QFAMES is a quantum algorithm that identifies clusters of closely spaced dominant eigenvalues and their multiplicities in quantum Hamiltonians under physically motivated assumptions, enabling observable estimation within energy clusters.
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The Constant Geometric Speed Schedule for Adiabatic State Preparation
The constant geometric speed (CGS) schedule achieves optimal Δ^{-1} scaling for adiabatic evolution time when path length L is gap-independent, using a segmented protocol that requires only a global gap lower bound, as shown in numerical tests on search and molecular systems.
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Adiabatic preparation of thermal states and entropy-noise relation on noisy quantum computers
Adiabatic evolution prepares local thermal states from initial Gibbs states while conserving entropy density in the thermodynamic limit, with mirror-circuit benchmarking of hardware noise entropy demonstrated experimentally on a 5x4 Ising model.
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Hybrid quantum-classical framework for Betti number estimation with applications to topological data analysis
Hybrid quantum-classical method for Betti number estimation that combines classical simplex enumeration with quantum processing and claims polynomial-to-exponential speedups over existing quantum algorithms at the cost of extra ancilla qubits.
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SAQR-QC: A Logic for Scalable but Approximate Quantitative Reasoning about Quantum Circuits
SAQR-QC is a new logic for scalable approximate quantitative reasoning about quantum circuits via local qubit operations and controlled precision loss, demonstrated on GHZ circuits and quantum phase estimation.
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Tensor-Programmable Quantum Circuits for Solving Differential Equations
A quantum solver for PDEs is introduced via flexible matrix product operator representations with mid-circuit measurements and state-dependent norm correction to handle non-unitary dynamics.
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From barren plateaus through fertile valleys: Conic extensions of parameterised quantum circuits
Conic extensions of parameterized quantum circuits enable jumps from barren plateaus to fertile valleys via non-unitary operations and ancilla, reducing optimal jump selection to a generalized eigenvalue problem and improving QAOA sampling in simulations.
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Quantum Data Fitting Algorithm for Non-sparse Matrices
Quantum data fitting algorithm for non-sparse N x N Hermitian matrices achieves O(κ² √N polylog(N) / (ε log κ)) runtime via QSVE, eigenvalue sign recovery, and regularization.