A Rich Type System for Quantum Programs
| Autor: | Sundaram, Aarthi, Rand, Robert, Singhal, Kartik, Lackey, Brad |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We show that Gottesman's semantics (GROUP22, 1998) for Clifford circuits based on the Heisenberg representation can be treated as a type system that can efficiently characterize a common subset of quantum programs. Our applications include (i) certifying whether auxiliary qubits can be safely disposed of, (ii) determining if a system is separable across a given bi-partition, (iii) checking the transversality of a gate with respect to a given stabilizer code, and (iv) typing post-measurement states for computational basis measurements. Further, this type system is extended to accommodate universal quantum computing by deriving types for the $T$-gate, multiply-controlled unitaries such as the Toffoli gate, and some gate injection circuits that use associated magic states. These types allow us to prove a lower bound on the number of $T$ gates necessary to perform a multiply-controlled $Z$ gate. Comment: 49 pages, 3 figures |
| Databáze: | arXiv |
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