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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Main Authors: Zane M. Rossi, Jack L. Ceroni, Isaac L. Chuang
Format: Article
Language:English
Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2025-06-01
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.
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publishDate 2025-06-01
publisher Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
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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