Top quantum algorithms papers — Fall 2025 edition

In this blog post, we share our favourite papers released in the fourth 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. The Grand Challenge of Quantum Applications
  • 2. Block encoding with low gate count for second-quantized Hamiltonians
  • 3. Multi-qubit Toffoli with exponentially fewer T gates
  • 4. The FLuid Allocation of Surface code Qubits (FLASQ) cost model for early fault-tolerant quantum algorithms
  • 5. Verifiable Quantum Advantage via Optimized DQI Circuits
• Honorable mentions
  • 1. Quantum matrix arithmetics with Hamiltonian evolution
  • 2. A Quantum Algorithm for the Finite Element Method
  • 3. End-to-end quantum algorithms for tensor problems
• Xanadu papers from Fall 2025
  • Unitary synthesis with optimal brick wall circuits
  • Realistic GKP stabilizer states enable universal quantum computation
  • Fault-tolerant transformations of spacetime codes
  • Quantum compilation framework for data loading

The Top 5

1. The Grand Challenge of Quantum Applications

A must-read "instant-classic" perspective on the landscape of quantum applications research, highlighting the path from abstract algorithms to practical impact.

2. Block encoding with low gate count for second-quantized Hamiltonians

A new technique for block-encoding second quantized Hamiltonians with cost and subnormalization factor both scaling as the square root of the number of interaction terms.

3. Multi-qubit Toffoli with exponentially fewer T gates

This paper shows that an n-qubit Toffoli can approximately be implemented in O(\log (1/\varepsilon)) T-gates, exponentially fewer than previous lower bounds for exact synthesis.

4. The FLuid Allocation of Surface code Qubits (FLASQ) cost model for early fault-tolerant quantum algorithms

Introduces a cost model for estimating realistic spacetime overheads for a 2D surface-code layout, lowering the barrier of entry for quantum algorithm specialists.

5. Verifiable Quantum Advantage via Optimized DQI Circuits

Establishes DQI for Optimal Polynomial Intersection as a candidate for verifiable quantum advantage, with ~6e6 gate cost.

Honorable mentions

1. Quantum matrix arithmetics with Hamiltonian evolution

Versatile algorithmic primitive to encode operators A as "Hamiltonian block encodings"—time evolution operators of Hermitian block-encodings.

2. A Quantum Algorithm for the Finite Element Method

Tour de Force that develops a general quantum algorithm for a widely applicable numerical method to solve differential equations.

3. End-to-end quantum algorithms for tensor problems

Intriguing work on tensor problems with quartic speedup, going from asymptotic to explicit circuits with resource estimates. Non-obvious avenue for potential use cases.

Xanadu papers from Fall 2025

Unitary synthesis with optimal brick wall circuits

A unitary synthesis framework that uses the optimal number of parameters and two-qubit gates.

Realistic GKP stabilizer states enable universal quantum computation

This work demonstrates that imperfect GKP states can actually be leveraged to apply non-Clifford gates using only linear optical elements.

Fault-tolerant transformations of spacetime codes

A framework based on homological algebra that establishes a general way to find equivalence between spacetime codes—in particular, how to transform any Clifford circuit into an MBQC protocol while preserving its fault-tolerant properties.

Quantum compilation framework for data loading

A general approach for identifying the best methods to load data on a quantum computer, leveraging resource estimation in PennyLane.

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