McArdle, Sam and Gilyén, András Pál and Berta, Mario (2026) Quantum State Preparation without Coherent Arithmetic. PHYSICAL REVIEW LETTERS, 136 (24). ISSN 0031-9007
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Abstract
We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum table reads, to encode the function values. Instead, we use a template quantum eigenvalue transformation circuit to convert a low-cost block encoding of the sine function into the desired function. Our method uses only four ancilla qubits (three if the approximating polynomial has definite parity), providing order-of-magnitude qubit count reductions compared to state-of-the-art approaches, while using a similar number of gates if the function can be well represented by a polynomial or Fourier approximation. We demonstrate the algorithmic utility of our method, including preparing Gaussian and Kaiser window states. © 2026 American Physical Society.
| Item Type: | Article |
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| Additional Information: | AWS Center for Quantum Computing, Pasadena, 91125, CA, United States HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary Institute for Quantum Information, RWTH Aachen University, Aachen, Germany Department of Computing, Imperial College London, London, United Kingdom Export Date: 04 September 2026; Cited By: 0; Funding details: AWS Center for Quantum Computing; Engineering and Physical Sciences Research Council, EPSRC, (EP/W032643/1); CODEN: PRLTA |
| Uncontrolled Keywords: | ARTICLE; controlled study; quantum dot; parity; quantum optics; Polynomial approximation; eigenvalues and eigenfunctions; Drug therapy; QUANTUM STATE; arithmetic; Encoding (symbols); Eigen-value; QUBITS; Signal encoding; Quantum state preparation; Function values; Arithmetic circuit; Low-costs; Versatile methods; Block encoding; Ancilla; Sine functions; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 07 Sep 2026 06:55 |
| Last Modified: | 07 Sep 2026 06:55 |
| URI: | https://real.mtak.hu/id/eprint/245556 |
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