Top quantum algorithms papers — Spring 2025 edition

In this blog post, we share our favourite papers released in the second 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. A comprehensive framework to simulate real-time chemical dynamics on a fault-tolerant quantum computer
  • 2. How to factor 2048 bit RSA integers with less than a million noisy qubits
  • 3. Quantum Simulation of Dynamical Response Functions of Equilibrium States
  • 4. A log-depth in-place quantum Fourier transform that rarely needs ancillas
  • 5. Productionizing Quantum Mass Production
• Honorable mentions
  • 1. Quantum simulation with sum-of-squares spectral amplification
  • 2. Demonstration of logical quantum phase estimation for X-ray absorption spectra
  • 3. In the shadow of the Hadamard test: Using the garbage state for good and further modifications
• Xanadu papers from Winter 2025
  • Integrated photonic source of Gottesman–Kitaev–Preskill qubits
  • Simulating near-infrared spectroscopy on a quantum computer for enhanced chemical detection
  • Logical channels in approximate Gottesman-Kitaev-Preskill error correction
  • The stellar decomposition of Gaussian quantum states
  • Constant-time hybrid compilation of Shor's algorithm with quantum just-in-time compilation

The Top 5

1. A comprehensive framework to simulate real-time chemical dynamics on a fault-tolerant quantum computer

Great strides in the development of algorithms for applications of quantum computing in quantum dynamics.

2. How to factor 2048 bit RSA integers with less than a million noisy qubits

Substantial reduction in quantum computing resources for factoring by combining a number of recent algorithmic developments in the field.

3. Quantum Simulation of Dynamical Response Functions of Equilibrium States

Circumventing the need for the exact preparation of equilibrium states for estimating response functions on a quantum computer.

4. A log-depth in-place quantum Fourier transform that rarely needs ancillas

Introduces the idea of “optimistic quantum circuits” that achieve good approximations on most inputs (but not all), thereby reducing the cost of implementation.

5. Productionizing Quantum Mass Production

Significant reduction of Clifford operations in quantum read-only memory (QROM).

Honorable mentions

1. Quantum simulation with sum-of-squares spectral amplification

2. Demonstration of logical quantum phase estimation for X-ray absorption spectra

3. In the shadow of the Hadamard test: Using the garbage state for good and further modifications

Xanadu papers from Winter 2025

Integrated photonic source of Gottesman–Kitaev–Preskill qubits

Simulating near-infrared spectroscopy on a quantum computer for enhanced chemical detection

Logical channels in approximate Gottesman-Kitaev-Preskill error correction

The stellar decomposition of Gaussian quantum states

Constant-time hybrid compilation of Shor's algorithm with quantum just-in-time compilation

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