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MasterThesis_Helena_Monso_Mas.pdf (1.04 MB)

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Treball de fi de màster

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2026-09

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cc-by-nc-nd (c) Monsó Mas, Helena, 2026
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/231726

Probabilistic Simulation of Deep Quantum Circuits and Applications to Shor’s Algorithm

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The simulation of deep quantum circuits is traditionally bottlenecked by the exponential scaling of the Hilbert space. This thesis presents a classical simulation framework that circumvents this barrier by mapping quantum states to classical probability distributions using informationally complete positive operator-valued measures (IC-POVMs). By leveraging an autoregressive transformer architecture, this work redefines quantum simulation as a highdimensional generative modeling task, utilizing the self-attention mechanism to capture non-local multi-qubit correlations. To rigorously benchmark the model against volume-law entanglement, the circuits are generated dynamically using uncompiled logical primitives, including the Cuccaro ripple-carry adder routed through the Vedral-Barenco-Ekert (VBE) modular exponentiation architecture. Evaluated via a variance-stabilized mixed Monte Carlo framework, the transformer successfully simulated a 25-qubit quantum Fourier transform (QFT) applied to an entangled 1D cluster state, maintaining a classical fidelity of Fc > 0.99 over 325 gates. Furthermore, the model executed the complete, uncompiled Shor’s algorithm to factor N = 15. Across a depth of 301 gates and 22 qubits, the network sustained a classical fidelity of Fc > 0.97. These results demonstrate that attention-based neural networks can robustly track complex, reversible quantum arithmetic without suffering exponential error accumulation, thereby establishing a stricter classical baseline for proving practical quantum advantage.

Descripció

Màster Oficial de Ciència i Tecnologia Quàntiques / Quantum Science and Technology, Facultat de Física, Universitat de Barcelona. Curs: 2025-2026. Tutors: Edward Jiang, Tim Heightman, Antonio Acín

Recurs relacionat

Matèries

Ordinadors quàntics, Treballs de fi de màster

Matèries (anglès)

Quantum computers, Master's thesis

Citació

Col·leccions

Màster Oficial - Ciència i Tecnologia Quàntiques / Quantum Science and Technology

Citació

MONSÓ MAS, Helena. Probabilistic Simulation of Deep Quantum Circuits and Applications to Shor’s Algorithm. [consulted: 2 of October of 2026]. Available at: https://hdl.handle.net/2445/231726

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