Top quantum algorithms papers — Summer 2025 edition

In this blog post, we share our favourite papers released in the third quarter of 2025. 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.

Contents

• The Top 5
  • 1. Real-Space Chemistry on Quantum Computers: A Fault-Tolerant Algorithm with Adaptive Grids and Transcorrelated Extension
  • 2. Large time-step discretisation of adiabatic quantum dynamics
  • 3. A Classical-Quantum Adder with Constant Workspace and Linear Gates
  • 4. A framework for robust quantum speedups in practical correlated electronic structure and dynamics
  • 5. Quantum Circuit Complexity of Matrix-Product Unitaries
• Honorable mentions
  • 1. Fault-tolerant quantum computations of vibrational wave functions
  • 2. End-to-End Efficient Quantum Thermal and Ground State Preparation Made Simple
  • 3. Quantum algorithm for linear matrix equations
• Xanadu papers from Summer 2025
  • Fast simulations of X-ray absorption spectroscopy for battery materials on a quantum computer
  • Quantum algorithms to detect ODMR-active defects for quantum sensing applications
  • Quantum Simulation of Electron Energy Loss Spectroscopy for Battery Materials

The Top 5

1. Real-Space Chemistry on Quantum Computers: A Fault-Tolerant Algorithm with Adaptive Grids and Transcorrelated Extension

To our knowledge, this is the first strategy to engineer better bases for quantum simulation in first quantization, potentially yielding substantial resource reductions for a variety of quantum algorithms.

2. Large time-step discretisation of adiabatic quantum dynamics

A revival of adiabatic quantum algorithms: this work argues that large time steps and first-order Trotter formulas have much better performance than previously thought!

3. A Classical-Quantum Adder with Constant Workspace and Linear Gates

Classical-quantum addition is an important subroutine that appears in many contexts. This paper provides the new state-of-the-art!

4. A framework for robust quantum speedups in practical correlated electronic structure and dynamics

An intriguing new framework to reason about quantum advantage. If it stands up to scrutiny, it could open opportunities to apply quantum computers in new regimes, including those where classical methods work well!

5. Quantum Circuit Complexity of Matrix-Product Unitaries

Methods for loading matrix product states (MPS) on a quantum computer have been known for a while, but finding circuits that implement a general unitary operator given as a matrix product operator (MPO) has been an open problem until now!

Honorable mentions

1. Fault-tolerant quantum computations of vibrational wave functions

First ever algorithm for a qubitization-based simulation of vibrational Hamiltonians!

2. End-to-End Efficient Quantum Thermal and Ground State Preparation Made Simple

New quantum algorithms for thermal and ground state preparation based on system-bath interactions. Remarkable for requiring only forward evolution and a single-qubit bath.

3. Quantum algorithm for linear matrix equations

A novel quantum algorithm for solving the Sylvester equation. The work stands out for using a block-encoding strategy as opposed to a vector strategy for addressing linear algebra problems.

Xanadu papers from Summer 2025

Fast simulations of X-ray absorption spectroscopy for battery materials on a quantum computer

We continue to advance X-ray absorption spectroscopy as one of the most valuable applications of quantum computing, together with our partners at Volkswagen.

Quantum algorithms to detect ODMR-active defects for quantum sensing applications

New quantum algorithms based on spectroscopy and dynamical techniques, with our partners at Toyota. These allow us to simulate intersystem crossing rates in quantum sensors.

Quantum Simulation of Electron Energy Loss Spectroscopy for Battery Materials

New quantum algorithm for simulating momentum-resolved spectroscopy for battery materials. Joint work with University of Chicago.

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We hope you enjoyed this selection of top papers. Stay tuned for the Fall 2025 edition! You can sign up to the Xanadu newsletter or follow PennyLane on LinkedIn or Twitter/X to get notified.