Quantum signal processing over SU(N)

• URL: http://arxiv.org/abs/2311.03949v2
• Date: Mon, 1 Jul 2024 12:53:37 GMT
• Title: Quantum signal processing over SU(N)
• Authors: Lorenzo Laneve,
• Abstract summary: Quantum signal processing (QSP) and the quantum singular value transformation (QSVT) are pivotal tools for simplifying the development of quantum algorithms. These techniques leverage transformations on the eigenvalues or singular values of block-encoded matrices, achieved with the use of just one control qubit. In this work, we extend the original QSP ansatz by introducing multiple control qubits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum signal processing (QSP) and the quantum singular value transformation (QSVT) are pivotal tools for simplifying the development of quantum algorithms. These techniques leverage polynomial transformations on the eigenvalues or singular values of block-encoded matrices, achieved with the use of just one control qubit. In contexts where the control qubit is used to extract information about the eigenvalues or singular values, the amount of extractable information is limited to one bit per protocol. In this work, we extend the original QSP ansatz by introducing multiple control qubits. We show that, much like in the single-qubit case, nearly any vector of polynomials can be implemented with a multi-qubit QSP ansatz, and the gate complexity scales polynomially with the dimension of such states. Moreover, assuming that powers of the matrix to transform are easily implementable - as in Shor's algorithm - we can achieve polynomial transformations with degrees that scale exponentially with the number of control qubits. This work aims to provide a partial characterization of the polynomials that can be implemented using this approach, with phase estimation schemes and discrete logarithm serving as illustrative examples.

Related papers

• Polynomial time constructive decision algorithm for multivariable quantum signal processing [0.7332146059733189]
  Multivariable quantum signal processing (M-QSP) is proposed. M-QSP interleaves signal operators corresponding to each variable with signal processing operators. A classical algorithm is proposed to determine whether a given pair of Laurents can be implemented by M-QSP.
  arXiv  Detail & Related papers  (2024-10-03T09:30:35Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Multivariable QSP and Bosonic Quantum Simulation using Iterated Quantum Signal Processing [0.5097809301149342]
  We provide a form of Modular Quantum Signal Processing that we call iterated quantum signal processing. This method applies quantum signal processing to the outputs of other quantum signal processing steps. We discuss how these ideas can be used to construct phase functions relevant for quantum simulation.
  arXiv  Detail & Related papers  (2024-08-06T15:27:43Z)
• On multivariate polynomials achievable with quantum signal processing [0.9208007322096533]
  Quantum signal processing (QSP) is a framework which was proven to unify and simplify a large number of known quantum algorithms. This work uses a slightly different formalism than what is found in the literature, and uses it to find simpler necessary conditions for decomposability.
  arXiv  Detail & Related papers  (2024-07-30T13:40:11Z)
• Quantum Signal Processing and Quantum Singular Value Transformation on $U(N)$ [8.264300525515097]
  Quantum signal processing and quantum value transformation are powerful tools to implement transformations of block-encoded matrices on quantum computers. We propose a framework which realizes multiples simultaneously from a block-encoded input. We also give an algorithm to construct the quantum circuit that gives the desired transformation.
  arXiv  Detail & Related papers  (2024-07-19T14:15:20Z)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• 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)
• Determining the ability for universal quantum computing: Testing controllability via dimensional expressivity [39.58317527488534]
  Controllability tests can be used in the design of quantum devices to reduce the number of external controls. We devise a hybrid quantum-classical algorithm based on a parametrized quantum circuit.
  arXiv  Detail & Related papers  (2023-08-01T15:33:41Z)
• Calculating the many-body density of states on a digital quantum computer [58.720142291102135]
  We implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer. We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18bits.
  arXiv  Detail & Related papers  (2023-03-23T17:46:28Z)
• Graph test of controllability in qubit arrays: A systematic way to determine the minimum number of external controls [62.997667081978825]
  We show how to leverage an alternative approach, based on a graph representation of the Hamiltonian, to determine controllability of arrays of coupled qubits. We find that the number of controls can be reduced from five to one for complex qubit-qubit couplings.
  arXiv  Detail & Related papers  (2022-12-09T12:59:44Z)

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.