Space-bounded quantum state testing via space-efficient quantum singular value transformation
保存先:
| 出版年: | arXiv.org (May 23, 2024), p. n/a |
|---|---|
| 第一著者: | |
| その他の著者: | , |
| 出版事項: |
Cornell University Library, arXiv.org
|
| 主題: | |
| オンライン･アクセス: | Citation/Abstract Full text outside of ProQuest |
| タグ: |
タグなし, このレコードへの初めてのタグを付けませんか!
|
MARC
| LEADER | 00000nab a2200000uu 4500 | ||
|---|---|---|---|
| 001 | 2848591050 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 035 | |a 2848591050 | ||
| 045 | 0 | |b d20240523 | |
| 100 | 1 | |a François Le Gall | |
| 245 | 1 | |a Space-bounded quantum state testing via space-efficient quantum singular value transformation | |
| 260 | |b Cornell University Library, arXiv.org |c May 23, 2024 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a Driven by exploring the power of quantum computation with a limited number of qubits, we present a novel complete characterization for space-bounded quantum computation, which encompasses settings with one-sided error (unitary coRQL) and two-sided error (BQL), approached from a quantum state testing perspective: - The first family of natural complete problems for unitary coRQL, i.e., space-bounded quantum state certification for trace distance and Hilbert-Schmidt distance; - A new family of natural complete problems for BQL, i.e., space-bounded quantum state testing for trace distance, Hilbert-Schmidt distance, and quantum entropy difference. In the space-bounded quantum state testing problem, we consider two logarithmic-qubit quantum circuits (devices) denoted as \(Q_0\) and \(Q_1\), which prepare quantum states \(\rho_0\) and \(\rho_1\), respectively, with access to their ``source code''. Our goal is to decide whether \(\rho_0\) is \(\epsilon_1\)-close to or \(\epsilon_2\)-far from \(\rho_1\) with respect to a specified distance-like measure. Interestingly, unlike time-bounded state testing problems, our results reveal that the space-bounded state testing problems all correspond to the same class. Moreover, our algorithms on the trace distance inspire an algorithmic Holevo-Helstrom measurement, implying QSZK is in QIP(2) with a quantum linear-space honest prover. Our results primarily build upon a space-efficient variant of the quantum singular value transformation (QSVT) introduced by Gilyén, Su, Low, and Wiebe (STOC 2019), which is of independent interest. Our technique provides a unified approach for designing space-bounded quantum algorithms. Specifically, we show that implementing QSVT for any bounded polynomial that approximates a piecewise-smooth function incurs only a constant overhead in terms of the space required for special forms of the projected unitary encoding. | |
| 653 | |a Algorithms | ||
| 653 | |a Quantum computing | ||
| 653 | |a Source code | ||
| 653 | |a Helium | ||
| 653 | |a Polynomials | ||
| 653 | |a Qubits (quantum computing) | ||
| 700 | 1 | |a Liu, Yupan | |
| 700 | 1 | |a Wang, Qisheng | |
| 773 | 0 | |t arXiv.org |g (May 23, 2024), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/2848591050/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/2308.05079 |