Universal spectra of noisy parameterized quantum circuits

• URL: http://arxiv.org/abs/2405.11625v1
• Date: Sun, 19 May 2024 17:36:55 GMT
• Title: Universal spectra of noisy parameterized quantum circuits
• Authors: Kristian Wold, Pedro Ribeiro, Sergey Denisov,
• Abstract summary: We implement parameterized circuits, which have been proposed as a means to generate random unitaries on a transmon platform. To retrieve the maps, a machine-learning assisted tomography is used. We find the spectrum of a map to be either an annulus or a disk depending on the circuit depth and detect an annulus-disk transition.
• Score: 1.2617078020344619
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Random unitaries are an important resource for quantum information processing. While their universal properties have been thoroughly analyzed, it is not known what happens to these properties when the unitaries are sampled on the present-day noisy intermediate-scale quantum (NISQ) computers. We implement parameterized circuits, which have been proposed as a means to generate random unitaries, on a transmon platform and model these implementations as quantum maps. To retrieve the maps, a machine-learning assisted tomography is used. We find the spectrum of a map to be either an annulus or a disk depending on the circuit depth and detect an annulus-disk transition. By their spectral properties, the retrieved maps appear to be very similar to a recently introduced ensemble of random maps, for which spectral densities can be analytically evaluated.

Related papers

• Quantum Circuits, Feature Maps, and Expanded Pseudo-Entropy: A Categorical Theoretic Analysis of Encoding Real-World Data into a Quantum Computer [0.0]
  The aim of this paper is to determine the efficacy of an encoding scheme to map real-world data into a quantum circuit. The method calculates the Shannon entropy of each of the data points from a point-cloud, hence, samples from an embedded manifold.
  arXiv  Detail & Related papers  (2024-10-29T14:38:01Z)
• Efficient Quantum Pseudorandomness from Hamiltonian Phase States [41.94295877935867]
  We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem. We show that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We show that our assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives.
  arXiv  Detail & Related papers  (2024-10-10T16:10:10Z)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• 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)
• Realizing Non-Physical Actions through Hermitian-Preserving Map Exponentiation [1.0255759863714506]
  We introduce the Hermitian-preserving mapiation algorithm, which can effectively realize the action of an arbitrary Hermitian-preserving map by encoding its output into a quantum process. Our findings present a pathway for systematically and efficiently implementing non-physical actions with quantum devices.
  arXiv  Detail & Related papers  (2023-08-15T18:00:04Z)
• Majorization-based benchmark of the complexity of quantum processors [105.54048699217668]
  We numerically simulate and characterize the operation of various quantum processors. We identify and assess quantum complexity by comparing the performance of each device against benchmark lines. We find that the majorization-based benchmark holds as long as the circuits' output states have, on average, high purity.
  arXiv  Detail & Related papers  (2023-04-10T23:01:10Z)
• Feature Map for Quantum Data in Classification [2.2940141855172036]
  A quantum feature map corresponds to an instance with a Hilbert space of quantum states by fueling quantum resources to machine learning algorithms. We present a feature map for quantum data as a probabilistic manipulation of quantum states to improve supervised learning algorithms.
  arXiv  Detail & Related papers  (2023-03-28T01:17:08Z)
• Classifying topological neural network quantum states via diffusion maps [0.0]
  We discuss and demonstrate an unsupervised machine-learning procedure to detect topological order in quantum many-body systems. We use a restricted Boltzmann machine to define a variational ansatz for the low-energy spectrum. We show that for the diffusion map, the required similarity measure of quantum states can be defined in terms of the network parameters.
  arXiv  Detail & Related papers  (2023-01-06T19:00:21Z)
• Noisy Quantum Kernel Machines [58.09028887465797]
  An emerging class of quantum learning machines is that based on the paradigm of quantum kernels. We study how dissipation and decoherence affect their performance. We show that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines.
  arXiv  Detail & Related papers  (2022-04-26T09:52:02Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Breaking the waves: asymmetric random periodic features for low-bitrate kernel machines [13.704881067616995]
  We introduce the general framework of asymmetric random periodic features, where the two signals of interest are observed through random periodic features. We prove uniform probabilistic error bounds holding for all signal pairs from an infinite low-complexity set.
  arXiv  Detail & Related papers  (2020-04-14T14:44:54Z)

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.