Parallel Quantum Signal Processing Via Polynomial Factorization
Quantum signal processing (QSP) is a methodology for constructing polynomial transformations of a linear operator encoded in a unitary. Applied to an encoding of a state ρ , QSP enables the evaluation of nonlinear functions of the form tr ( P ( ρ ) ) for a polynomial P ( x ) , which encompasses rele...
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| Veröffentlicht in: | Quantum (Vienna, Austria) Jg. 9; S. 1834 |
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| Hauptverfasser: | , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
27.08.2025
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| ISSN: | 2521-327X, 2521-327X |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Quantum signal processing (QSP) is a methodology for constructing polynomial transformations of a linear operator encoded in a unitary. Applied to an encoding of a state ρ , QSP enables the evaluation of nonlinear functions of the form tr ( P ( ρ ) ) for a polynomial P ( x ) , which encompasses relevant properties like entropies and fidelity. However, QSP is a sequential algorithm: implementing a degree- d polynomial necessitates d queries to the encoding, equating to a query depth d . Here, we reduce the depth of these property estimation algorithms by developing Parallel Quantum Signal Processing. Our algorithm parallelizes the computation of tr ( P ( ρ ) ) over k systems and reduces the query depth to d / k , thus enabling a family of time-space tradeoffs for QSP. This furnishes a property estimation algorithm suitable for distributed quantum computers, and is realized at the expense of increasing the number of measurements by a factor O ( poly ( d ) 2 O ( k ) ) . We achieve this result by factorizing P ( x ) into a product of k smaller polynomials of degree O ( d / k ) , which are each implemented in parallel with QSP, and subsequently multiplied together with a swap test to reconstruct P ( x ) . We characterize the achievable class of polynomials by appealing to the fundamental theorem of algebra, and demonstrate application to canonical problems including entropy estimation and partition function evaluation. |
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| ISSN: | 2521-327X 2521-327X |
| DOI: | 10.22331/q-2025-08-27-1834 |