Approximating Korobov Functions via Quantum Circuits

• URL: http://arxiv.org/abs/2404.14570v4
• Date: Sun, 04 May 2025 14:52:49 GMT
• Title: Approximating Korobov Functions via Quantum Circuits
• Authors: Junaid Aftab, Haizhao Yang,
• Abstract summary: We design quantum circuits capable of approximating d-dimensional functions within the Korobov function space.<n>This is achieved by leveraging the quantum signal processing (QSP) and the linear combination of unitaries (LCU) algorithms.
• Score: 6.460951804337735
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Understanding the capacity of quantum circuits through the lens of approximation theory is essential for evaluating the complexity of quantum circuits required to solve various problems in scientific computation. We design quantum circuits capable of approximating d-dimensional functions within the Korobov function space. This is achieved by leveraging the quantum signal processing (QSP) and the linear combination of unitaries (LCU) algorithms to build quantum circuits that output Chebyshev polynomials. We also present a quantitative analysis of the approximation error rates and evaluates the computational complexity of implementing the proposed circuits. Since the Korobov function space is a subspace of the certain Sobolev spaces, our work develops a theoretical foundation for implementing a large class of functions suitable for applications on a quantum computer.

Related papers

• Circuit Design for a Star-shaped Spin-Qubit Processor via Algebraic Decomposition and Optimal Control [0.0]
  We propose an algorithm for tailored application of optimal-control gates for quantum computing platforms with star-shaped topologies.<n>We show numerically how the resulting circuits can be implemented on a quantum processing unit consisting of a nitrogen-vacancy center in diamond and surrounding nuclear spins.
  arXiv  Detail & Related papers  (2025-06-20T10:47:11Z)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [60.996803677584424]
  Variational Quantum Circuits (VQCs) offer a novel pathway for quantum machine learning.<n>Their practical application is hindered by inherent limitations such as constrained linear expressivity, optimization challenges, and acute sensitivity to quantum hardware noise.<n>This work introduces VQC-MLPNet, a scalable and robust hybrid quantum-classical architecture designed to overcome these obstacles.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• Quantum computer formulation of the FKP-operator eigenvalue problem for probabilistic learning on manifolds [0.0]
  We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifold (PLoM)<n>It involves solving the spectral problem of the high-dimensional Fokker-Planck operator, which remains beyond the reach of classical computing.<n>Explicit formulas for the Laplacian and potential are derived and mapped onto qubits using Pauli matrix expressions.
  arXiv  Detail & Related papers  (2025-02-20T14:05:16Z)
• Expressivity Limits of Quantum Reservoir Computing [0.0]
  We establish a formal connection to parametrized quantum circuit quantum machine learning (PQC-QML)<n>We analytically prove, and numerically corroborate, that in QRC the number of non-linear functions that can be generated from classical data is bounded linearly by the number of input encoding gates.<n>Our results challenge the common assumption that exponential Hilbert space scaling confers a corresponding computational advantage in QRC.
  arXiv  Detail & Related papers  (2025-01-26T13:43:03Z)
• Circuit Implementation of Discrete-Time Quantum Walks on Complex Networks [2.0257616108612373]
  Quantum walks are powerful tools for various graph-based applications. We present a circuit design for implementing discrete-time quantum walks on complex networks.
  arXiv  Detail & Related papers  (2024-08-28T09:11:47Z)
• 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)
• Quantum Compiling with Reinforcement Learning on a Superconducting Processor [55.135709564322624]
  We develop a reinforcement learning-based quantum compiler for a superconducting processor. We demonstrate its capability of discovering novel and hardware-amenable circuits with short lengths. Our study exemplifies the codesign of the software with hardware for efficient quantum compilation.
  arXiv  Detail & Related papers  (2024-06-18T01:49:48Z)
• 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)
• Learning the expressibility of quantum circuit ansatz using transformer [5.368973814856243]
  We propose using a transformer model to predict the expressibility of quantum circuit ansatze. This research can enhance the understanding of the expressibility of quantum circuit ansatze and advance quantum architecture search algorithms.
  arXiv  Detail & Related papers  (2024-05-29T07:34:07Z)
• A circuit-generated quantum subspace algorithm for the variational quantum eigensolver [0.0]
  We propose combining quantum subspace techniques with the variational quantum eigensolver (VQE) In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies.
  arXiv  Detail & Related papers  (2024-04-09T18:00:01Z)
• Shallow Quantum Circuit Implementation of Symmetric Functions with Limited Ancillary Qubits [5.9862846364925115]
  In quantum computation, optimizing depth and number of ancillary qubits in quantum circuits is crucial. This paper presents an innovative approach to implementing arbitrary symmetric Boolean functions using poly-logarithmic depth quantum circuits. The key technique involves a novel poly-logarithmic depth quantum circuit designed to compute Hamming weight without the need for ancillary qubits.
  arXiv  Detail & Related papers  (2024-04-09T06:30:54Z)
• Quantum computing topological invariants of two-dimensional quantum matter [0.0]
  We present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. First algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. Second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits.
  arXiv  Detail & Related papers  (2024-04-09T06:22:50Z)
• Quantum computation of conical intersections on a programmable superconducting quantum processor [10.064448021157139]
  Conical intersections (CIs) are pivotal in many photochemical processes. We present the first successful realization of a hybrid quantum-classical state-average complete active space self-consistent method.
  arXiv  Detail & Related papers  (2024-02-20T04:12:40Z)
• Analysis of arbitrary superconducting quantum circuits accompanied by a Python package: SQcircuit [0.0]
  Superconducting quantum circuits are a promising hardware platform for realizing a fault-tolerant quantum computer. We develop a framework to construct a superconducting quantum circuit's quantized Hamiltonian from its physical description. We implement the methods described in this work in an open-source Python package SQcircuit.
  arXiv  Detail & Related papers  (2022-06-16T17:24:51Z)
• Quantum circuit debugging and sensitivity analysis via local inversions [62.997667081978825]
  We present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most. We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
  arXiv  Detail & Related papers  (2022-04-12T19:39:31Z)
• Quantum circuits for the preparation of spin eigenfunctions on quantum computers [63.52264764099532]
  Hamiltonian symmetries are an important instrument to classify relevant many-particle wavefunctions. This work presents quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers.
  arXiv  Detail & Related papers  (2022-02-19T00:21:46Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Quantum amplitude damping for solving homogeneous linear differential equations: A noninterferometric algorithm [0.0]
  This work proposes a novel approach by using the Quantum Amplitude Damping operation as a resource, in order to construct an efficient quantum algorithm for solving homogeneous LDEs. We show that such an open quantum system-inspired circuitry allows for constructing the real exponential terms in the solution in a non-interferometric.
  arXiv  Detail & Related papers  (2021-11-10T11:25:32Z)
• Characterizing quantum circuits with qubit functional configurations [0.0]
  We propose a theory of characterizing quantum circuits with qubit functional configurations. We demonstrate the theory's application to the hardware-efficient ansatzes of variational quantum algorithms.
  arXiv  Detail & Related papers  (2021-10-05T22:42:14Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• On exploring the potential of quantum auto-encoder for learning quantum systems [60.909817434753315]
  We devise three effective QAE-based learning protocols to address three classically computational hard learning problems. Our work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.
  arXiv  Detail & Related papers  (2021-06-29T14:01:40Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum Simulation of Light-Front Parton Correlators [0.0]
  The physics of high-energy colliders relies on the knowledge of non-perturbative parton correlators. We propose a quantum algorithm to perform a quantum simulation of these type of correlators.
  arXiv  Detail & Related papers  (2020-11-02T19:38:33Z)
• Efficient simulatability of continuous-variable circuits with large Wigner negativity [62.997667081978825]
  Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures. We identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable. We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.
  arXiv  Detail & Related papers  (2020-05-25T11:03:42Z)

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.