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Quantum

Efficiently simulable quantum circuits with large entanglement, magic, and non-Gaussianity via code-compiled tensor networks

Aydin Deger, Stergios Koutsioumpas, Mark A. Webster, Hasan Sayginel, Joschka Roffe, Dan E. Browne

Featured July 16, 2026

Original Paper

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Simply

Scientists found a clever way to make complex quantum circuits, which usually need huge supercomputers, easy to simulate using regular computers by "compiling" them with error-correcting codes, keeping the simulation cost low.

In depth
The paper introduces code-compiled quantum circuits (CCQCs), a novel class of quantum circuits that appear classically hard to simulate due to high entanglement and non-Clifford gates. However, by leveraging quantum error-correcting codes as a compilation tool, these complex logical operations are transformed into simple physical operations—single-qubit gates and qubit relabelings. This "compilation" ensures that the classical simulation cost, particularly with Matrix Product States (MPS), remains low and bounded by the initial encoding step, regardless of the circuit's depth or the complexity of its logical gates.

Key Takeaways

  • 1
    Code-Compiled Quantum Circuits (CCQCs) enable efficient classical simulation of quantum circuits that otherwise exhibit high entanglement, magic, and non-Gaussianity.
  • 2
    The simulation cost for CCQCs using Matrix Product States (MPS) is primarily determined by the initial encoding step, with subsequent complex logical operations compiling to simple physical gates that do not increase bond dimension.
  • 3
    CCQCs provide a valuable tool for quantum hardware benchmarking, offering a classically simulable reference for complex, non-Clifford logical circuits to estimate device fidelity.

Conceptual Flow

HIGH LEVEL
1
Compiling Complex Quantum Logic

The paper shows how to turn tricky, spread-out quantum instructions into simple, local ones using a special "code" as a translator.

Complex Logical Circuit
Translate with Code
Simple Physical Circuit
2
Simulating Hard Problems Easily

This new method allows regular computers to simulate quantum circuits that look very complicated and entangled, which usually only super-quantum computers can handle.

Hard Quantum Problem
Use New Method
Easy Computer Simulation