notes:2026-08-18
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| notes:2026-08-18 [August 18, 2026 at 11:52] – Ivan Janevski | notes:2026-08-18 [August 18, 2026 at 11:53] (current) – Ivan Janevski | ||
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| - | # Quantum computing modalities, physical systems, and encodings | + | # Notes 2026-08-18 |
| - | ## General picture | + | ## (Quantum 1) Quantum computing modalities, physical systems, and encodings |
| + | |||
| + | ### General picture | ||
| It is useful to distinguish several levels: | It is useful to distinguish several levels: | ||
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| --- | --- | ||
| - | ## Physical platforms | + | ### Physical platforms |
| Major physical approaches include: | Major physical approaches include: | ||
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| --- | --- | ||
| - | # Transmon qubit | + | ## Transmon qubit |
| The transmon Hamiltonian is | The transmon Hamiltonian is | ||
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| --- | --- | ||
| - | # Bosonic systems | + | ## Bosonic systems |
| A bosonic mode has Fock space | A bosonic mode has Fock space | ||
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| --- | --- | ||
| - | # Cat code | + | ## Cat code |
| A coherent state satisfies | A coherent state satisfies | ||
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| --- | --- | ||
| - | # GKP code | + | ## GKP code |
| The GKP code uses oscillator quadratures | The GKP code uses oscillator quadratures | ||
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| --- | --- | ||
| - | # Binomial code | + | ## Binomial code |
| Binomial codes construct logical states from selected finite superpositions of Fock states. | Binomial codes construct logical states from selected finite superpositions of Fock states. | ||
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| --- | --- | ||
| - | # Photonic quantum computing | + | ## Photonic quantum computing |
| " | " | ||
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| --- | --- | ||
| - | # Dual-rail encoding | + | ## Dual-rail encoding |
| Dual rail encodes one logical qubit into the **single-excitation subspace of two distinguishable modes or subsystems**. | Dual rail encodes one logical qubit into the **single-excitation subspace of two distinguishable modes or subsystems**. | ||
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| --- | --- | ||
| - | # Schwinger-boson representation | + | ## Schwinger-boson representation |
| Two bosonic modes naturally realize the algebra $\mathfrak{su}(2)$. | Two bosonic modes naturally realize the algebra $\mathfrak{su}(2)$. | ||
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| --- | --- | ||
| - | # Dual rail versus cat | + | ## Dual rail versus cat |
| Both can start from bosonic Hilbert spaces, but they use them very differently. | Both can start from bosonic Hilbert spaces, but they use them very differently. | ||
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| --- | --- | ||
| - | # Dual rail and leakage | + | ## Dual rail and leakage |
| For two ideal two-level systems, | For two ideal two-level systems, | ||
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| --- | --- | ||
| - | # Dual rail versus repetition code | + | ## Dual rail versus repetition code |
| Dual rail: | Dual rail: | ||
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| --- | --- | ||
| - | # Why use a larger Hilbert space? | + | ## Why use a larger Hilbert space? |
| Encoding often increases the physical Hilbert-space dimension. | Encoding often increases the physical Hilbert-space dimension. | ||
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| --- | --- | ||
| - | # Overall taxonomy | + | ## Overall taxonomy |
| The most useful classification separates **hardware** from **encoding**: | The most useful classification separates **hardware** from **encoding**: | ||
notes/2026-08-18.1787053923.md.gz · Last modified: by Ivan Janevski