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• W3212713369 abstract "We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides an operator-theoretic representation of classical dynamics by combining ergodic theory with quantum information science. The resulting quantum embedding of classical dynamics (QECD) enables efficient simulation of spaces of classical observables with exponentially large dimension using a quadratic number of quantum gates. The QECD framework is based on a quantum feature map that we introduce for representing classical states by density operators on a reproducing kernel Hilbert space, $mathcal{H}$. Furthermore, an embedding of classical observables into self-adjoint operators on $mathcal{H}$ is established, such that quantum mechanical expectation values are consistent with pointwise function evaluation. In this scheme, quantum states and observables evolve unitarily under the lifted action of Koopman evolution operators of the classical system. Moreover, by virtue of the reproducing property of $mathcal{H}$, the quantum system is pointwise-consistent with the underlying classical dynamics. To achieve a quantum computational advantage, we project the state of the quantum system onto a finite-rank density operator on a ${2}^{n}$-dimensional tensor product Hilbert space associated with $n$ qubits. By employing discrete Fourier-Walsh transforms of spectral functions, the evolution operator of the finite-dimensional quantum system is factorized into tensor product form, enabling implementation through an $n$-channel quantum circuit of size $O(n)$ and no interchannel communication. Furthermore, the circuit features a state preparation stage, also of size $O(n)$, and a quantum Fourier transform stage of size $O({n}^{2})$, which makes predictions of observables possible by measurement in the standard computational basis. We prove theoretical convergence results for these predictions in the large-qubit limit, $nensuremath{rightarrow}ensuremath{infty}$. In light of these properties, QECD provides a consistent simulator of the evolution of classical observables, realized through projective quantum measurement, which is able to simulate spaces of classical observables of dimension ${2}^{n}$ using circuits of size $O({n}^{2})$. We demonstrate the consistency of the scheme in prototypical dynamical systems involving periodic and quasiperiodic oscillators on tori. These examples include simulated quantum circuit experiments in Qiskit Aer, as well as actual experiments on the IBM Quantum System One." @default.
• W3212713369 created "2021-11-22" @default.
• W3212713369 creator A5015882134 @default.
• W3212713369 creator A5046278266 @default.
• W3212713369 creator A5065096577 @default.
• W3212713369 creator A5076538541 @default.
• W3212713369 creator A5085374556 @default.
• W3212713369 date "2022-05-03" @default.
• W3212713369 modified "2023-10-17" @default.
• W3212713369 title "Embedding classical dynamics in a quantum computer" @default.
• W3212713369 cites W1582592707 @default.
• W3212713369 cites W1756893185 @default.
• W3212713369 cites W1818380006 @default.
• W3212713369 cites W1965035185 @default.
• W3212713369 cites W1967037487 @default.
• W3212713369 cites W1979991047 @default.
• W3212713369 cites W1997054581 @default.
• W3212713369 cites W2002276939 @default.
• W3212713369 cites W2008158924 @default.
• W3212713369 cites W2014356541 @default.
• W3212713369 cites W2036604884 @default.
• W3212713369 cites W2038345347 @default.
• W3212713369 cites W2039361027 @default.
• W3212713369 cites W2040792108 @default.
• W3212713369 cites W2047278710 @default.
• W3212713369 cites W2049588649 @default.
• W3212713369 cites W2053005188 @default.
• W3212713369 cites W2060806808 @default.
• W3212713369 cites W2067035505 @default.
• W3212713369 cites W2074388175 @default.
• W3212713369 cites W2077180490 @default.
• W3212713369 cites W2081726081 @default.
• W3212713369 cites W2090194301 @default.
• W3212713369 cites W2090857812 @default.
• W3212713369 cites W2092889467 @default.
• W3212713369 cites W2099721081 @default.
• W3212713369 cites W2102540828 @default.
• W3212713369 cites W2111338377 @default.
• W3212713369 cites W2112250505 @default.
• W3212713369 cites W2124358705 @default.
• W3212713369 cites W2128089417 @default.
• W3212713369 cites W2140095548 @default.
• W3212713369 cites W2164954534 @default.
• W3212713369 cites W2179731956 @default.
• W3212713369 cites W2318411205 @default.
• W3212713369 cites W2319450871 @default.
• W3212713369 cites W2324802422 @default.
• W3212713369 cites W2398886555 @default.
• W3212713369 cites W2510030309 @default.
• W3212713369 cites W2559394418 @default.
• W3212713369 cites W2736592352 @default.
• W3212713369 cites W2775659970 @default.
• W3212713369 cites W2781738013 @default.
• W3212713369 cites W2785195724 @default.
• W3212713369 cites W2792946961 @default.
• W3212713369 cites W2795833322 @default.
• W3212713369 cites W2798434869 @default.
• W3212713369 cites W2918226012 @default.
• W3212713369 cites W2941010932 @default.
• W3212713369 cites W2963013180 @default.
• W3212713369 cites W2963111412 @default.
• W3212713369 cites W2963186138 @default.
• W3212713369 cites W2963198496 @default.
• W3212713369 cites W2976645955 @default.
• W3212713369 cites W2990961515 @default.
• W3212713369 cites W3005949189 @default.
• W3212713369 cites W3006164137 @default.
• W3212713369 cites W3006550916 @default.
• W3212713369 cites W3012790144 @default.
• W3212713369 cites W3024243470 @default.
• W3212713369 cites W3038118776 @default.
• W3212713369 cites W3040996531 @default.
• W3212713369 cites W3042830018 @default.
• W3212713369 cites W3085553537 @default.
• W3212713369 cites W3098898877 @default.
• W3212713369 cites W3098932296 @default.
• W3212713369 cites W3099674394 @default.
• W3212713369 cites W3099998929 @default.
• W3212713369 cites W3101122608 @default.
• W3212713369 cites W3101479050 @default.
• W3212713369 cites W3101636216 @default.
• W3212713369 cites W3102057473 @default.
• W3212713369 cites W3102514046 @default.
• W3212713369 cites W3102593705 @default.
• W3212713369 cites W3103179333 @default.
• W3212713369 cites W3104599990 @default.
• W3212713369 cites W3105206907 @default.
• W3212713369 cites W3105971113 @default.
• W3212713369 cites W3109913413 @default.
• W3212713369 cites W3115328420 @default.
• W3212713369 cites W3117414873 @default.
• W3212713369 cites W3126228179 @default.
• W3212713369 cites W3133989388 @default.
• W3212713369 cites W3148410376 @default.
• W3212713369 cites W3175639804 @default.
• W3212713369 cites W4213367101 @default.
• W3212713369 cites W4239340087 @default.
• W3212713369 cites W4239883234 @default.
• W3212713369 cites W4246202617 @default.
• W3212713369 cites W4254857087 @default.

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