Geometric Formalization of Natural Language in Binary Representation and Its Implementation as Quantum Control Operations - REV. 2.3
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| author | Medesani, Massimo |
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| contents | <div> <div> <p><strong>Abstract</strong></p> <p>This work presents a unified, formal framework for translating natural language commands into executable quantum operations on superconducting qubit processors. We establish a rigorous geometric and algebraic structure for natural language, wherein sentences are embedded in a semantic vector space and encoded in binary representations. This formalism is then explicitly bridged to physical quantum control by defining a protocol to extract machine-interpretable <strong>quantum tokens</strong>—encoded as triples <span><span>(θ,ϕ,axis)</span><span><span><span>(</span><span>θ</span><span>,</span><span>ϕ</span><span>,</span><span><span>axis</span></span><span>)</span></span></span></span>—from linguistically specified gate operations.</p> <p>The core technical contribution is a deterministic, hardware-aware mapping that converts these abstract tokens into the precise microwave pulse parameters <span><span>(I(t),Q(t),ωd,τ)</span><span><span><span>(</span><span>I</span><span>(</span><span>t</span><span>)</span><span>,</span><span>Q</span><span>(</span><span>t</span><span>)</span><span>,</span><span><span>ω</span><span><span><span><span><span><span><span>d</span></span></span></span><span></span></span></span></span></span><span>,</span><span>τ</span><span>)</span></span></span></span> required to drive single-qubit rotations on a transmon-type qubit. By leveraging the standard circuit QED control Hamiltonian <span><span>H~d=−Ω2V0s(t)(Iσx+Qσy)</span><span><span><span><span><span><span><span><span><span>H</span></span><span><span>~</span></span></span></span></span></span><span><span><span><span><span><span><span>d</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>−</span><span><span><span><span><span><span><span><span>2</span></span></span><span><span><span>Ω</span></span></span></span><span></span></span></span></span></span><span><span>V</span><span><span><span><span><span><span><span>0</span></span></span></span><span></span></span></span></span></span><span>s</span><span>(</span><span>t</span><span>)</span><span>(</span><span>I</span><span><span>σ</span><span><span><span><span><span><span><span>x</span></span></span></span><span></span></span></span></span></span><span>+</span></span><span><span>Q</span><span><span>σ</span><span><span><span><span><span><span><span>y</span></span></span></span><span></span></span></span></span></span><span>)</span></span></span></span>, we demonstrate how tailored in-phase and quadrature microwave pulses physically implement the intended unitary evolution <span><span>U=exp(−iθ2(cosϕ σx+sinϕ σy))</span><span><span><span>U</span><span>=</span></span><span><span>exp</span><span>(</span><span>−</span><span>i</span><span><span><span><span><span><span><span><span>2</span></span></span><span><span><span><span>θ</span></span></span></span></span><span></span></span></span></span></span><span>(</span><span>cos</span><span>ϕ</span><span> </span><span><span>σ</span><span><span><span><span><span><span><span>x</span></span></span></span><span></span></span></span></span></span><span>+</span></span><span><span>sin</span><span>ϕ</span><span> </span><span><span>σ</span><span><span><span><span><span><span><span>y</span></span></span></span><span></span></span></span></span></span><span>))</span></span></span></span>, resulting in a targeted rotation on the Bloch sphere.</p> <p>We further prove a <strong>Uniqueness Correspondence Theorem</strong>, guaranteeing a surjective, bijective, and injective mapping pipeline from the set of well-formed linguistic commands, through token and parameter spaces, to the set of single-qubit unitary operations, thereby ensuring semantic consistency and operational determinism. A complete binary encoding scheme for quantum commands is provided, illustrating the end-to-end pipeline from a command string to a calibrated microwave waveform.</p> <p>This work provides a foundational, mathematically rigorous interface between high-level algorithmic instructions and the physical layer of quantum control, with direct applications in automated quantum compilers, error-corrected gate synthesis, and human-quantum machine interaction platforms. The formalism is generalizable to multi-qubit operations and adaptable to other qubit modalities, offering a template for standardizing quantum hardware control abstraction.</p> </div> </div> <div> </div> <div> <div> <div> <div> </div> <div> </div> </div> </div> </div> <div> <div> </div> </div> <div> <div> </div> <div> </div> </div> <div> <div> </div> </div> <div> <div> </div> <div> </div> </div> <div> <div> </div> </div> <div> <div> </div> <div> </div> </div> <div> <div> </div> </div> <div> <div> </div> <div> </div> </div> <div> <div> <div> <div> <div> <div> </div> </div> </div> <div> </div> </div> </div> </div> <div> <div> </div> <div> </div> </div> <div> <div> <div> </div> <div> </div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18071714 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Geometric Formalization of Natural Language in Binary Representation and Its Implementation as Quantum Control Operations - REV. 2.3 Medesani, Massimo <div> <div> <p><strong>Abstract</strong></p> <p>This work presents a unified, formal framework for translating natural language commands into executable quantum operations on superconducting qubit processors. We establish a rigorous geometric and algebraic structure for natural language, wherein sentences are embedded in a semantic vector space and encoded in binary representations. This formalism is then explicitly bridged to physical quantum control by defining a protocol to extract machine-interpretable <strong>quantum tokens</strong>—encoded as triples <span><span>(θ,ϕ,axis)</span><span><span><span>(</span><span>θ</span><span>,</span><span>ϕ</span><span>,</span><span><span>axis</span></span><span>)</span></span></span></span>—from linguistically specified gate operations.</p> <p>The core technical contribution is a deterministic, hardware-aware mapping that converts these abstract tokens into the precise microwave pulse parameters <span><span>(I(t),Q(t),ωd,τ)</span><span><span><span>(</span><span>I</span><span>(</span><span>t</span><span>)</span><span>,</span><span>Q</span><span>(</span><span>t</span><span>)</span><span>,</span><span><span>ω</span><span><span><span><span><span><span><span>d</span></span></span></span><span></span></span></span></span></span><span>,</span><span>τ</span><span>)</span></span></span></span> required to drive single-qubit rotations on a transmon-type qubit. By leveraging the standard circuit QED control Hamiltonian <span><span>H~d=−Ω2V0s(t)(Iσx+Qσy)</span><span><span><span><span><span><span><span><span><span>H</span></span><span><span>~</span></span></span></span></span></span><span><span><span><span><span><span><span>d</span></span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>−</span><span><span><span><span><span><span><span><span>2</span></span></span><span><span><span>Ω</span></span></span></span><span></span></span></span></span></span><span><span>V</span><span><span><span><span><span><span><span>0</span></span></span></span><span></span></span></span></span></span><span>s</span><span>(</span><span>t</span><span>)</span><span>(</span><span>I</span><span><span>σ</span><span><span><span><span><span><span><span>x</span></span></span></span><span></span></span></span></span></span><span>+</span></span><span><span>Q</span><span><span>σ</span><span><span><span><span><span><span><span>y</span></span></span></span><span></span></span></span></span></span><span>)</span></span></span></span>, we demonstrate how tailored in-phase and quadrature microwave pulses physically implement the intended unitary evolution <span><span>U=exp(−iθ2(cosϕ σx+sinϕ σy))</span><span><span><span>U</span><span>=</span></span><span><span>exp</span><span>(</span><span>−</span><span>i</span><span><span><span><span><span><span><span><span>2</span></span></span><span><span><span><span>θ</span></span></span></span></span><span></span></span></span></span></span><span>(</span><span>cos</span><span>ϕ</span><span> </span><span><span>σ</span><span><span><span><span><span><span><span>x</span></span></span></span><span></span></span></span></span></span><span>+</span></span><span><span>sin</span><span>ϕ</span><span> </span><span><span>σ</span><span><span><span><span><span><span><span>y</span></span></span></span><span></span></span></span></span></span><span>))</span></span></span></span>, resulting in a targeted rotation on the Bloch sphere.</p> <p>We further prove a <strong>Uniqueness Correspondence Theorem</strong>, guaranteeing a surjective, bijective, and injective mapping pipeline from the set of well-formed linguistic commands, through token and parameter spaces, to the set of single-qubit unitary operations, thereby ensuring semantic consistency and operational determinism. A complete binary encoding scheme for quantum commands is provided, illustrating the end-to-end pipeline from a command string to a calibrated microwave waveform.</p> <p>This work provides a foundational, mathematically rigorous interface between high-level algorithmic instructions and the physical layer of quantum control, with direct applications in automated quantum compilers, error-corrected gate synthesis, and human-quantum machine interaction platforms. The formalism is generalizable to multi-qubit operations and adaptable to other qubit modalities, offering a template for standardizing quantum hardware control abstraction.</p> </div> </div> <div> </div> <div> <div> <div> <div> </div> <div> </div> </div> </div> </div> <div> <div> </div> </div> <div> <div> </div> <div> </div> </div> <div> <div> </div> </div> <div> <div> </div> <div> </div> </div> <div> <div> </div> </div> <div> <div> </div> <div> </div> </div> <div> <div> </div> </div> <div> <div> </div> <div> </div> </div> <div> <div> <div> <div> <div> <div> </div> </div> </div> <div> </div> </div> </div> </div> <div> <div> </div> <div> </div> </div> <div> <div> <div> </div> <div> </div> </div> </div> |
| title | Geometric Formalization of Natural Language in Binary Representation and Its Implementation as Quantum Control Operations - REV. 2.3 |
| url | https://doi.org/10.5281/zenodo.18071714 |