Top quantum compilation papers — Summer 2026 edition

Welcome to the Summer edition of our top papers series on quantum compilation and fault-tolerant architectures! The following are our favorite papers of the season, selected for their potential to advance practical quantum computing. Several of this season's results show how much the cost of a quantum algorithm depends on its compilation and error-correction architecture. Let’s get into it!

Contents

• Top papers
  • 1. Computing 256-bit elliptic curve discrete logarithms in 26 days on a fault-tolerant trapped-ion quantum computer with 20,000 qubits
  • 2. High-rate qLDPC processors and Quantum LDPC codes with design rate 1/5 and good performance below 1000 physical qubits
  • 3. Suppressing errors in analog logical rotation gates via balanced fusion
  • 4. A Platform-aware Compilation Framework for Fault-tolerant Quantum Computation
  • 5. Lifted surgery: Fast processing with QLDPC codes
• Honourable Mentions
  • 1. Borrowed Identities: Malleable Distillation Factories and a Unified Numerical Search
  • 2. Compiling the 2D Fermi-Hubbard ground-state energy estimation algorithm for active volume quantum architectures
  • 3. Low-cost algorithm-to-execution framework for surface-code quantum computing
• Xanadu Papers
  • 1. Practical Estimation of Trotter Error for Hamiltonian Simulation
  • 2. Theory and practice of Trotter product formulas for quantum chemistry
  • 3. Spectral Born machines: classically trainable quantum generative models for discrete data
  • 4. Improved constant factors for qubitized Hamiltonian simulation
  • 5. Spectral Theory of Semisimple Bivariate Bicycle Codes

Top papers

1. Computing 256-bit elliptic curve discrete logarithms in 26 days on a fault-tolerant trapped-ion quantum computer with 20,000 qubits

Detailed compilation of Shor's algorithm into trapped-ion measurement schedules, including routing, transport, and loss. The projected 26-day computation has a 63% success probability under the paper's noise and hardware assumptions.

2. High-rate qLDPC processors and Quantum LDPC codes with design rate 1/5 and good performance below 1000 physical qubits

Mitten codes pair 20% encoding rates with reusable logical operations. The second paper shows strong simulated memory performance below 1,000 physical qubits; both studies exclude idling errors.

3. Suppressing errors in analog logical rotation gates via balanced fusion

Balanced fusion improves leading rotation error from O(p\varphi) to O(p\varphi^{3/2}), with p being the physical error rate and \varphi the target angle. Useful progress for early fault-tolerant simulation.

4. A Platform-aware Compilation Framework for Fault-tolerant Quantum Computation

Connects logical circuits to hardware-specific compilation, comparing three connectivity regimes and introducing transversal active volume. The framework makes physical-qubit, runtime, and classical-processing costs easier to compare across platforms.

5. Lifted surgery: Fast processing with QLDPC codes

Code symmetries enable fast, parallel qLDPC measurements. For the [[90, 8, 10]] radial code, simulations give comparable performance to standard surgery with ten times fewer syndrome rounds.

Honourable Mentions

1. Borrowed Identities: Malleable Distillation Factories and a Unified Numerical Search

Builds magic-state factories from circuits that preserve one chosen input state. A single parent circuit can yield different resource types at compile time, simplifying searches and offering useful flexibility.

2. Compiling the 2D Fermi-Hubbard ground-state energy estimation algorithm for active volume quantum architectures

Architecture-aware compilation reduces active volume by up to 3.9× versus a non-Clifford-optimized baseline. For a 20×20 Fermi-Hubbard lattice, it also roughly halves the Toffoli count.

3. Low-cost algorithm-to-execution framework for surface-code quantum computing

Links surface-code layout and resource supply to an algorithm's execution needs. Tailored layouts reduce modeled routing latency across twenty benchmarks, with spacetime savings in thirteen; complete physical schedules remain future work.

Xanadu Papers

1. Practical Estimation of Trotter Error for Hamiltonian Simulation

Novel theoretical and numerical developments for tight Trotter-error estimation at unprecedented scale.

2. Theory and practice of Trotter product formulas for quantum chemistry

Introduces SPRINT, a novel framework for the construction of advanced product formulas that reduce costs for electronic structure Hamiltonians; achieving a 4.5× Toffoli reduction on the benchmarked Li₄Mn₂O system.

3. Spectral Born machines: classically trainable quantum generative models for discrete data

Classically trainable quantum generative models, demonstrated with a 190-qubit model and over a million parameters on RNA sequences.

4. Improved constant factors for qubitized Hamiltonian simulation

Tighter QSP degree bounds reduce established Hamiltonian-simulation overhead estimates by about 1.36× in the large-time regime. A useful constant-factor improvement to a widely used primitive.

5. Spectral Theory of Semisimple Bivariate Bicycle Codes

An algebraic treatment of semisimple bivariate bicycle codes using Frobenius orbits, yielding logical dimensions, distance lower bounds, and explicit constructions. A useful complement to numerical code discovery.

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We hope you enjoyed our Summer selection of top quantum compilation papers. Stay tuned for the Fall 2026 edition! You can sign up to the Xanadu newsletter or follow PennyLane on LinkedIn or Twitter/X to get notified. If you haven’t already, make sure to check out our series on top quantum algorithms papers.