Top quantum algorithms papers — Winter 2025 edition

In this blog post we share our favourite papers released in the first 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. Fast quantum simulation of electronic structure by spectrum amplification
  • 2. Faster quantum chemistry simulations on a quantum computer with improved tensor factorization and active volume compilation
  • 3. Computing Efficiently in QLDPC Codes
  • 4. The Hitchhiker's Guide to QSP pre-processing
  • 5. Leveraging Atom Loss Errors in Fault Tolerant Quantum Algorithms
• Honourable mentions
• Xanadu papers from Winter 2025

The Top 5

1. Fast quantum simulation of electronic structure by spectrum amplification

Significant reductions in the cost of Hamiltonian simulation using a novel technique (spectrum amplification) combined with even more optimized tensor factorizations.

2. Faster quantum chemistry simulations on a quantum computer with improved tensor factorization and active volume compilation

Major acceleration of electronic structure calculations on a quantum computer via optimized compilation and symmetry-enhanced factorization.

3. Computing Efficiently in QLDPC Codes

Important advancement in making quantum LDPC codes viable in practice for fault-tolerant quantum computing.

4. The Hitchhiker's Guide to QSP pre-processing

A pedagogically accessible review of QSP-processing conventions and methods, including a performance benchmark of different phase-factor finding techniques.

5. Leveraging Atom Loss Errors in Fault Tolerant Quantum Algorithms

Theoretical framework for handling qubit loss errors at a logical level using novel decoding techniques and circuit optimizations.

Honourable mentions

1. 1. Optimizing FTQC Programs through QEC Transpiler and Architecture Codesign

   
   

   

   Performant theoretical and software framework for reducing the cost of Clifford gates in fault-tolerant circuits. 🌮

2. 2. A simple quantum simulation algorithm with near-optimal precision scaling

   

   A creative proposal for a conceptually-novel approach to Hamiltonian simulation using a permutation matrix representation.

3. 3. Correcting and extending Trotterized quantum many-body dynamics

   
   

   

   A hybrid quantum-classical simulation method to reduce quantum resource requirements of Trotter-based simulation using a classical correction ansatz.

Xanadu papers from Winter 2025

Here we share our publications from this winter. You can find the full list on our website.

• Scaling and networking a modular photonic quantum computer

  
  

  

  A quantum computing milestone, demonstrating in practice the unique scalability of photonic quantum computing.

  
  

• Train on classical, deploy on quantum: scaling generative quantum machine learning to a thousand qubits

  
  

  

  A heroic effort to fix the crisis of scalability in quantum machine learning.

  
  

• IQPopt: Fast optimization of instantaneous quantum polynomial circuits in JAX

  
  

  

  A software package for classically training IQP circuits at very large scales; an essential tool for our “train on classical, deploy on quantum” work.

  
  

• Better product formulas for quantum phase estimation

  
  

  

  Improved product formulas with quadratically better error bounds for energy estimating in the low-energy eigenspace.

  
  

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