Modular quantum signal processing in many variables
arXiv:2309.16665 · doi:10.22331/q-2025-06-18-1776
Abstract
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.
15 pages + 9 figures + 4 tables + 45 pages supplement. Updated and edited for Quantum journal. For codebase, see https://github.com/ichuang/pyqsp/tree/beta
References in corpus (32)
- Quantum algorithms: an overview
- Hamiltonian Simulation by Qubitization
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- Quantum advantage in learning from experiments
- Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
- Theoretical framework for quantum networks
- Quantum Circuits Architecture
- Hamiltonian simulation with nearly optimal dependence on all parameters
- Quantum algorithms for algebraic problems
- Quantum Channels with Memory
- Fixed-point quantum search with an optimal number of queries
- A different kind of quantum search
- Efficient phase-factor evaluation in quantum signal processing
- The methodology of resonant equiangular composite quantum gates
- A functional quantum programming language
- Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning
- Product Decomposition of Periodic Functions in Quantum Signal Processing
- On the energy landscape of symmetric quantum signal processing
- Optimal arbitrarily accurate composite pulse sequences
- Finding Angles for Quantum Signal Processing with Machine Precision
- Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle
- Further analysis of some symmetric and antisymmetric composite pulses for tackling pulse strength errors
- Approximating Fractional Time Quantum Evolution
- Polylogarithmic-depth controlled-NOT gates without ancilla qubits
- Power and limitations of single-qubit native quantum neural networks
- Nested composite NOT gates for quantum computation
- Infinite quantum signal processing
- How Much Structure Is Needed for Huge Quantum Speedups?
- Higher-order quantum transformations of Hamiltonian dynamics
- Error Correction of Quantum Algorithms: Arbitrarily Accurate Recovery Of Noisy Quantum Signal Processing
- A CS guide to the quantum singular value transformation
- A Quantum Algorithm for Functions of Multiple Commuting Hermitian Matrices