Top quantum algorithms papers — Winter 2026 edition

In this blog post, we share our favourite papers released in the first quarter of 2026. The selection is based on relevance to quantum algorithms and applications; these are results that we admire and that have been influential to our research. Xanadu papers won’t appear in the selection due to an obvious conflict of interest, but we take the opportunity to share our latest work at the end. And if you haven’t already, make sure to also check out our new Top quantum compilation papers series.

Contents

• The Top 5
  • 1. Classical solution of the FeMo-cofactor model to chemical accuracy and its implications
  • 2. Sparse quantum state preparation with improved Toffoli cost
  • 3. Rapid Dissipative Ground State Preparation at Chemical Transition States
  • 4. Quantum Simulation of Coupled Harmonic Oscillators: From Theory to Implementation
  • 5. A Sublinear-Time Quantum Algorithm for High-Dimensional Reaction Rates
• Honorable mentions
  • 1. Quantum Phaselift
  • 2. Parallel iQCC Enables 200 Qubit Scale Quantum Chemistry on Accelerated Computing Platforms Surpassing Classical Benchmarks in Ruthenium Catalysts
  • 3. Contour-integral based quantum eigenvalue transformation: analysis and applications
• Xanadu papers
  • Quantum algorithm for simulating non-adiabatic dynamics at metallic surfaces
  • Efficient Simulation of Pre-Born-Oppenheimer Dynamics on a Quantum Computer
  • Quantum Simulations for Extreme Ultraviolet Photolithography
  • Quantum algorithm for simulating resonant inelastic X-ray scattering in battery materials
  • Group Fourier filtering of quantum resources in quantum phase space

The Top 5

1. Classical solution of the FeMo-cofactor model to chemical accuracy and its implications

A monumental result demonstrating the classical tractability of the most widely established benchmark for quantum advantage in ground-state energy calculations. While not a quantum algorithms paper, this result will have lasting implications for the future of the field.

2. Sparse quantum state preparation with improved Toffoli cost

Introduces an improvement for a foundational algorithmic subroutine backed by theoretical and numerical analysis.

3. Rapid Dissipative Ground State Preparation at Chemical Transition States

Ingenious approach to compute ground-state energies of classically challenging transition states, using an approach that essentially combines adiabatic and dissipative techniques.

4. Quantum Simulation of Coupled Harmonic Oscillators: From Theory to Implementation

Rare example of a serious practical analysis of an otherwise conceptual quantum algorithm, addressing challenges of initial state preparation and observable extraction.

5. A Sublinear-Time Quantum Algorithm for High-Dimensional Reaction Rates

Quantum algorithm for simulating Fokker-Planck models, claiming an exponential separation in particle number, a quartic speedup in error, and quadratic speedup in evolution time.

Honorable mentions

1. Quantum Phaselift

A quantum version of the phaselift algorithm for computing Loschmidt amplitudes, which may reduce circuit depth in specific use cases.

2. Parallel iQCC Enables 200 Qubit Scale Quantum Chemistry on Accelerated Computing Platforms Surpassing Classical Benchmarks in Ruthenium Catalysts

A dequantization of VQE-type methods using high-performance classical compute, pushing up to systems with 200 qubits. Not strictly a quantum algorithms result, but has important implications for the field.

3. Contour-integral based quantum eigenvalue transformation: analysis and applications

A creative approach to performing quantum eigenvalue transformations using Cauchy’s integral formula that provides asymptotic improvements over previous work for certain types of differential equations.

Xanadu papers

Quantum algorithm for simulating non-adiabatic dynamics at metallic surfaces

A new quantum algorithm for simulating non-adiabatic dynamics at metallic surfaces with unprecedented efficiency. Building on our earlier work on vibronic dynamics, our algorithm is the first of its kind and opens the door to a range of new, technologically relevant applications.

Efficient Simulation of Pre-Born-Oppenheimer Dynamics on a Quantum Computer

A new quantum algorithm for black-box simulation of chemical dynamics with more than an order of magnitude lower cost than previous state-of-the-art, positioning quantum computers to address high-impact industrial and scientific challenges in the discovery of new catalysts.

Quantum Simulations for Extreme Ultraviolet Photolithography

In this collaboration with Mitsubishi Chemical, we propose a new application of quantum computing to extreme ultraviolet lithography, the world’s most advanced method for semiconductor chip fabrication, developing novel algorithms to predict photoabsorption and photoemission spectra.

Quantum algorithm for simulating resonant inelastic X-ray scattering in battery materials

In collaboration with the University of Toronto and the National Research Council of Canada, we expand our portfolio of quantum algorithms for spectroscopy to the more challenging case of RIXS, which involves a nonlinear absorption process. We study its application to diagnosing cathode materials to enable higher-density Li-ion batteries.

Group Fourier filtering of quantum resources in quantum phase space

Work led by our collaborators at LANL, emerging from the 2025 summer school on quantum computing. This paper connects resource theories in quantum phase spaces with tunable filters in Fourier space.

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We hope you enjoyed this selection of top papers. Stay tuned for the Spring 2026 edition! You can sign up to the Xanadu newsletter or follow PennyLane on LinkedIn or Twitter/X to get notified.