Constructs an explicit unitary Q using the quantum Schur transform to coherently map fixed-N first-quantized states to occupation-number form with poly(N,d,log(1/ε)) gate complexity.
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A new quantum ripple-carry addition circuit
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abstract
We present a new linear-depth ripple-carry quantum addition circuit. Previous addition circuits required linearly many ancillary qubits; our new adder uses only a single ancillary qubit. Also, our circuit has lower depth and fewer gates than previous ripple-carry adders.
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representative citing papers
Uses 2D DTQW lattice quantiles and number-theoretic asymptotics to estimate convex integrals with deterministic residual error scaling in T instead of statistical M^{-1/2}.
Presents an end-to-end constraint-aware quantum optimization pipeline using XY-mixer QAOA and Grover Adaptive Search for low-energy defect configurations in doped ZrO2, with QAOA validated against exact enumeration on a high-accuracy QUBO surrogate of MACE energies.
Presents a continuous-time quantum walk over a product space for CVRP that cuts gate complexity to O(n² log n) and shows faster convergence in simulations up to 8 customers.
Explicit quantum-circuit simulation of nonlinear 1D fluid via second-order Carleman-linearized Boltzmann equation and QSVD Taylor ODE solver, with logarithmic scaling analysis.
Explicit reversible quantum oracles for bounded Diophantine systems achieve quadratic speedup with qubit count O((n + d²) log₂ N) and Toffoli depth O(q²).
A coherent quantum rollout oracle is built from O(Nw)-gate rank-select circuits with proven optimality, delivering O(sqrt(k)/eps) query complexity for planning problems and formally verified in Lean.
Quantum algorithms achieve polynomial advantage for synchronization estimation and super-polynomial advantage for no-phase-locking certification in higher-order simplicial Kuramoto models under stated assumptions.
Digital Spreading computes quantum expectations via integer comparisons on superposed states with a pruned Cuccaro architecture, reaching 0.0001% relative error in option pricing simulations.
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
A classically-enriched quantum floating-point variable stores offset and scaling classically, reducing approximation error by up to 89% after repeated additions compared to prior mono-quantum coding.
Quantum algorithm implements Kravchuk transform via su(2) fast-forwarding with logarithmic scaling in dimension and error.
Explicit quantum circuits for elliptic-curve point addition achieve 6.5-10% fewer Toffoli gates and 1.5% more qubits than Babbush et al. for secp256k1, plus a generic prime-field version.
A hot-zone architecture for OQFT on reconfigurable neutral-atom hardware yields tunable latency via 2-4 zones, converging to roughly 500 extra logical ancillae and 128-qubit peak parallelism for half-time performance on 256-2048 bit instances.
A space-efficient quantum ECDLP algorithm uses 5n + 4⌊log₂n⌋ + O(1) logical qubits and O(n³) Toffoli gates, lowering the 256-bit estimate from 2124 to 1333 qubits.
Quantum sieving for SVP in dimension 400 needs ~10^13 physical qubits and ~10^31 years under optimistic assumptions, offering no practical speedup over classical methods.
A quantum Monte Carlo algorithm solves multidimensional Black-Scholes PDEs for option pricing with polynomial complexity in dimension d and accuracy 1/ε, with rigorous error bounds and a claimed speedup over classical Monte Carlo for bounded payoffs.
The paper gives a construction for the partial-oracles search iteration operator restricted to in-place operations via a new reciprocal transform applied to SHA-256 building blocks.
A differentiable tensor-network framework learns CPTP noise channels from single-circuit measurement data on IBM hardware and generalizes the model to unrelated circuits.
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.
An oracle-free Trotter-based quantum algorithm for nonadiabatic molecular dynamics achieves circuit depth advantages over QROM architectures and retains T-gate scalability compared to quantum signal processing.
Quantum integer multiplier with O(log^2 n) circuit depth and T-depth via parallel partial products and binary adder tree in the Clifford+T model.
Heterogeneous quantum architectures with task-specific hardware and QEC encodings deliver up to 138x lower physical-qubit overhead than monolithic baselines for fault-tolerant algorithms, including RSA-2048 factoring at 190k-381k qubits.
TUSQ reduces redundant work in noisy quantum simulations via error tallying, commutation, importance sampling, and depth-first tree traversal with compute/uncompute reuse, reporting large speedups over Qiskit, CUDA-Q, and TQSim on 198 benchmarks.
citing papers explorer
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Efficient Quantum Circuits for Coherent Conversion Between General First- and Second-Quantized Many-Body Representations
Constructs an explicit unitary Q using the quantum Schur transform to coherently map fixed-N first-quantized states to occupation-number form with poly(N,d,log(1/ε)) gate complexity.
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Lattice-quantile estimation of {\pi} and convex-region integrals from coined two-dimensional quantum walks
Uses 2D DTQW lattice quantiles and number-theoretic asymptotics to estimate convex integrals with deterministic residual error scaling in T instead of statistical M^{-1/2}.
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Constraint-Aware Quantum Optimization of Defect Configurations in Doped ZrO2: XY-Mixer QAOA and Grover Adaptive Search
Presents an end-to-end constraint-aware quantum optimization pipeline using XY-mixer QAOA and Grover Adaptive Search for low-energy defect configurations in doped ZrO2, with QAOA validated against exact enumeration on a high-accuracy QUBO surrogate of MACE energies.
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Quantum walk-based optimisation for capacitated vehicle routing with homogeneous and heterogeneous fleets
Presents a continuous-time quantum walk over a product space for CVRP that cuts gate complexity to O(n² log n) and shows faster convergence in simulations up to 8 customers.
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Explicit Quantum Circuit Simulation of Nonlinear 1-Dimensional Fluid with Carleman-linearized Boltzmann Method
Explicit quantum-circuit simulation of nonlinear 1D fluid via second-order Carleman-linearized Boltzmann equation and QSVD Taylor ODE solver, with logarithmic scaling analysis.
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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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Coherent Rollout Oracles for Finite-Horizon Sequential Decision Problems
A coherent quantum rollout oracle is built from O(Nw)-gate rank-select circuits with proven optimality, delivering O(sqrt(k)/eps) query complexity for planning problems and formally verified in Lean.
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Efficient Quantum Algorithms for Higher-Order Coupled Oscillators
Quantum algorithms achieve polynomial advantage for synchronization estimation and super-polynomial advantage for no-phase-locking certification in higher-order simplicial Kuramoto models under stated assumptions.
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A Digital Spreading Framework for Quantum Expectation Computation Without Rotation Gates or Arithmetic Circuits
Digital Spreading computes quantum expectations via integer comparisons on superposed states with a pruned Cuccaro architecture, reaching 0.0001% relative error in option pricing simulations.
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Magic state cultivation: growing T states as cheap as CNOT gates
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
-
Hybrid quantum floating-point method for sharp arithmetic
A classically-enriched quantum floating-point variable stores offset and scaling classically, reducing approximation error by up to 89% after repeated additions compared to prior mono-quantum coding.
-
Quantum Kravchuk Transform using $\mathfrak{su}(2)$ fast-forwarding
Quantum algorithm implements Kravchuk transform via su(2) fast-forwarding with logarithmic scaling in dimension and error.
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Optimized Point Addition Circuits for Elliptic Curve Discrete Logarithms
Explicit quantum circuits for elliptic-curve point addition achieve 6.5-10% fewer Toffoli gates and 1.5% more qubits than Babbush et al. for secp256k1, plus a generic prime-field version.
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Towards Deploying Optimistic Quantum Fourier Transforms: An Architecture-Algorithm Co-Design Study
A hot-zone architecture for OQFT on reconfigurable neutral-atom hardware yields tunable latency via 2-4 zones, converging to roughly 500 extra logical ancillae and 128-qubit peak parallelism for half-time performance on 256-2048 bit instances.
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Space-Efficient Quantum Algorithm for Elliptic Curve Discrete Logarithms with Resource Estimation
A space-efficient quantum ECDLP algorithm uses 5n + 4⌊log₂n⌋ + O(1) logical qubits and O(n³) Toffoli gates, lowering the 256-bit estimate from 2124 to 1333 qubits.
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On the practicality of quantum sieving algorithms for the shortest vector problem
Quantum sieving for SVP in dimension 400 needs ~10^13 physical qubits and ~10^31 years under optimistic assumptions, offering no practical speedup over classical methods.
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Quantum Monte Carlo algorithm for option pricing and its complexity analysis
A quantum Monte Carlo algorithm solves multidimensional Black-Scholes PDEs for option pricing with polynomial complexity in dimension d and accuracy 1/ε, with rigorous error bounds and a claimed speedup over classical Monte Carlo for bounded payoffs.
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Partial oracles quantum algorithm framework -- Part I: Analysis of in-place operations
The paper gives a construction for the partial-oracles search iteration operator restricted to in-place operations via a new reciprocal transform applied to SHA-256 building blocks.
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Quantum hardware noise learning via differentiable Kraus representation on tensor networks
A differentiable tensor-network framework learns CPTP noise channels from single-circuit measurement data on IBM hardware and generalizes the model to unrelated circuits.
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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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An Oracle-Free Quantum Algorithm for Nonadiabatic Quantum Molecular Dynamics
An oracle-free Trotter-based quantum algorithm for nonadiabatic molecular dynamics achieves circuit depth advantages over QROM architectures and retains T-gate scalability compared to quantum signal processing.
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A Polylogarithmic-Depth Quantum Multiplier
Quantum integer multiplier with O(log^2 n) circuit depth and T-depth via parallel partial products and binary adder tree in the Clifford+T model.
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Heterogeneous architectures enable a 138x reduction in physical qubit requirements for fault-tolerant quantum computing under detailed accounting
Heterogeneous quantum architectures with task-specific hardware and QEC encodings deliver up to 138x lower physical-qubit overhead than monolithic baselines for fault-tolerant algorithms, including RSA-2048 factoring at 190k-381k qubits.
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Noisy Quantum Simulation Using Tracking, Uncomputation and Sampling
TUSQ reduces redundant work in noisy quantum simulations via error tallying, commutation, importance sampling, and depth-first tree traversal with compute/uncompute reuse, reporting large speedups over Qiskit, CUDA-Q, and TQSim on 198 benchmarks.
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A Fully Quantum Algorithm for Image Edge Detection
A fully quantum gradient-based edge detection algorithm using NEQR encoding, cyclic shifts for neighbor superpositions, direction-aware alignment, and a Quantum Partitioning Algorithm for in-place thresholding, with claimed resource optimizations.
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Quantum Model for CVRPTW
A Grover-search-based quantum model for CVRPTW that encodes constraints with only linear additional decision qubits relative to TSP formulations.