On variants of multivariate quantum signal processing and their
characterizations
- URL: http://arxiv.org/abs/2312.09072v1
- Date: Thu, 14 Dec 2023 16:06:58 GMT
- Title: On variants of multivariate quantum signal processing and their
characterizations
- Authors: Bal\'azs N\'emeth, Blanka K\"ov\'er, Bogl\'arka Kulcs\'ar, Roland
Botond Mikl\'osi, Andr\'as Gily\'en
- Abstract summary: Quantum signal processing (QSP) is a highly successful algorithmic primitive in quantum computing.
We show that Haah's characterization of general QSP can be extended to homogeneous bivariable (commuting) quantum signal processing.
We also show a similar result for an alternative inhomogeneous variant when the degree in one of the variables is at most 1, but construct a counterexample where both variables have degree 2.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum signal processing (QSP) is a highly successful algorithmic primitive
in quantum computing which leads to conceptually simple and efficient quantum
algorithms using the block-encoding framework of quantum linear algebra.
Multivariate variants of quantum signal processing (MQSP) could be a valuable
tool in extending earlier results via implementing multivariate (matrix)
polynomials. However, MQSP remains much less understood than its single-variate
version lacking a clear characterization of "achievable" multivariate
polynomials. We show that Haah's characterization of general univariate QSP can
be extended to homogeneous bivariate (commuting) quantum signal processing. We
also show a similar result for an alternative inhomogeneous variant when the
degree in one of the variables is at most 1, but construct a counterexample
where both variables have degree 2, which in turn refutes an earlier
characterization proposed / conjectured by Rossi and Chuang for a related
restricted class of MQSP. Finally, we describe homogeneous multivariate
(non-commuting) QSP variants that break away from the earlier two-dimensional
treatment limited by its reliance on Jordan-like decompositions, and might
ultimately lead to the development of novel quantum algorithms.
Related papers
- Benchmarking Variational Quantum Eigensolvers for Entanglement Detection in Many-Body Hamiltonian Ground States [37.69303106863453]
Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage.
We use a specific class of VQA named variational quantum eigensolvers (VQEs) to benchmark them at entanglement witnessing and entangled ground state detection.
Quantum circuits whose structure is inspired by the Hamiltonian interactions presented better results on cost function estimation than problem-agnostic circuits.
arXiv Detail & Related papers (2024-07-05T12:06:40Z) - Evaluation of phase shifts for non-relativistic elastic scattering using quantum computers [39.58317527488534]
This work reports the development of an algorithm that makes it possible to obtain phase shifts for generic non-relativistic elastic scattering processes on a quantum computer.
arXiv Detail & Related papers (2024-07-04T21:11:05Z) - Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application.
We analyse the generation of random states in PQCs under restrictions on the qubits connectivities.
We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
arXiv Detail & Related papers (2024-05-03T17:32:55Z) - The Power of Unentangled Quantum Proofs with Non-negative Amplitudes [55.90795112399611]
We study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $textQMA+(2)$.
In particular, we design global protocols for small set expansion, unique games, and PCP verification.
We show that QMA(2) is equal to $textQMA+(2)$ provided the gap of the latter is a sufficiently large constant.
arXiv Detail & Related papers (2024-02-29T01:35:46Z) - Variational-quantum-eigensolver-inspired optimization for spin-chain work extraction [39.58317527488534]
Energy extraction from quantum sources is a key task to develop new quantum devices such as quantum batteries.
One of the main issues to fully extract energy from the quantum source is the assumption that any unitary operation can be done on the system.
We propose an approach to optimize the extractable energy inspired by the variational quantum eigensolver (VQE) algorithm.
arXiv Detail & Related papers (2023-10-11T15:59:54Z) - Modular quantum signal processing in many variables [0.0]
We show that modular multi-input-based QSP-based superoperators can be snapped together with LEGO-like ease at the level of the functions they apply.
We also provide a Python package for assembling gadgets and compiling them to circuits.
arXiv Detail & Related papers (2023-09-28T17:58:51Z) - Quantum signal processing with continuous variables [0.0]
Quantum singular value transformation (QSVT) enables the application of functions to singular values of near arbitrary linear operators embedded in unitary transforms.
We show that one can recover a QSP-type ansatz, and show its ability to approximate near arbitrary transformations.
We discuss various experimental uses of this construction, as well as prospects for expanded relevance of QSP-like ans"atze to other Lie groups.
arXiv Detail & Related papers (2023-04-27T17:50:16Z) - Multivariable quantum signal processing (M-QSP): prophecies of the
two-headed oracle [0.0]
Recent work shows that quantum signal processing (QSP) and its multi-qubit lifted version, quantum singular value transformation (QSVT)
QSVT transforms and improve the presentation of most quantum algorithms.
arXiv Detail & Related papers (2022-05-12T17:58:59Z) - Quantum algorithms for grid-based variational time evolution [36.136619420474766]
We propose a variational quantum algorithm for performing quantum dynamics in first quantization.
Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
arXiv Detail & Related papers (2022-03-04T19:00:45Z) - A Grand Unification of Quantum Algorithms [0.0]
A number of quantum algorithms were recently tied together by a technique known as the quantum singular value transformation.
This paper provides a tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform.
We then employ QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation.
arXiv Detail & Related papers (2021-05-06T17:46:33Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.