Modular quantum signal processing in many variables
Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum algorithms have been unified with the advent of quantum signal pro...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-06-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-06-18-1776/pdf/ |
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| author | Zane M. Rossi Jack L. Ceroni Isaac L. Chuang |
| author_facet | Zane M. Rossi Jack L. Ceroni Isaac L. Chuang |
| author_sort | Zane M. Rossi |
| collection | DOAJ |
| description | Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum algorithms have been unified with the advent of quantum signal processing (QSP) and quantum singular value transformation (QSVT), an opportunity has appeared to cast these algorithms as modules that can be combined to constitute complex programs. Complicating this, however, is that while QSP/QSVT are often described by the polynomial transforms they apply to the singular values of large linear operators, and the algebraic manipulation of polynomials is simple, the QSP/QSVT protocols realizing analogous manipulations of their embedded polynomials are non-obvious. Here we provide a theory of modular multi-input-output QSP-based superoperators, the basic unit of which we call a $gadget$, and show they can be snapped together with LEGO-like ease at the level of the functions they apply. To demonstrate this ease, we also provide a Python package for assembling gadgets and compiling them to circuits. Viewed alternately, gadgets both enable the efficient block encoding of large families of useful multivariable functions, and substantiate a functional-programming approach to quantum algorithm design in recasting QSP and QSVT as monadic types. |
| format | Article |
| id | doaj-art-dc86fbead26c449d94f9afcb7e0fd4d8 |
| institution | OA Journals |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-dc86fbead26c449d94f9afcb7e0fd4d82025-08-20T02:07:49ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-06-019177610.22331/q-2025-06-18-177610.22331/q-2025-06-18-1776Modular quantum signal processing in many variablesZane M. RossiJack L. CeroniIsaac L. ChuangDespite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum algorithms have been unified with the advent of quantum signal processing (QSP) and quantum singular value transformation (QSVT), an opportunity has appeared to cast these algorithms as modules that can be combined to constitute complex programs. Complicating this, however, is that while QSP/QSVT are often described by the polynomial transforms they apply to the singular values of large linear operators, and the algebraic manipulation of polynomials is simple, the QSP/QSVT protocols realizing analogous manipulations of their embedded polynomials are non-obvious. Here we provide a theory of modular multi-input-output QSP-based superoperators, the basic unit of which we call a $gadget$, and show they can be snapped together with LEGO-like ease at the level of the functions they apply. To demonstrate this ease, we also provide a Python package for assembling gadgets and compiling them to circuits. Viewed alternately, gadgets both enable the efficient block encoding of large families of useful multivariable functions, and substantiate a functional-programming approach to quantum algorithm design in recasting QSP and QSVT as monadic types.https://quantum-journal.org/papers/q-2025-06-18-1776/pdf/ |
| spellingShingle | Zane M. Rossi Jack L. Ceroni Isaac L. Chuang Modular quantum signal processing in many variables Quantum |
| title | Modular quantum signal processing in many variables |
| title_full | Modular quantum signal processing in many variables |
| title_fullStr | Modular quantum signal processing in many variables |
| title_full_unstemmed | Modular quantum signal processing in many variables |
| title_short | Modular quantum signal processing in many variables |
| title_sort | modular quantum signal processing in many variables |
| url | https://quantum-journal.org/papers/q-2025-06-18-1776/pdf/ |
| work_keys_str_mv | AT zanemrossi modularquantumsignalprocessinginmanyvariables AT jacklceroni modularquantumsignalprocessinginmanyvariables AT isaaclchuang modularquantumsignalprocessinginmanyvariables |