Symmetric derivatives of parametrized quantum circuits

• URL: http://arxiv.org/abs/2312.06752v1
• Date: Mon, 11 Dec 2023 19:00:00 GMT
• Title: Symmetric derivatives of parametrized quantum circuits
• Authors: David Wierichs and Richard D. P. East and Mart\'in Larocca and M. Cerezo and Nathan Killoran
• Abstract summary: We introduce the concept of projected derivatives of parametrized quantum circuits. We show that the covariant derivative gives rise to the quantum Fisher information and quantum natural gradient.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Symmetries are crucial for tailoring parametrized quantum circuits to applications, due to their capability to capture the essence of physical systems. In this work, we shift the focus away from incorporating symmetries in the circuit design and towards symmetry-aware training of variational quantum algorithms. For this, we introduce the concept of projected derivatives of parametrized quantum circuits, in particular the equivariant and covariant derivatives. We show that the covariant derivative gives rise to the quantum Fisher information and quantum natural gradient. This provides an operational meaning for the covariant derivative, and allows us to extend the quantum natural gradient to all continuous symmetry groups. Connecting to traditional particle physics, we confirm that our covariant derivative is the same as the one introduced in physical gauge theory. This work provides tools for tailoring variational quantum algorithms to symmetries by incorporating them locally in derivatives, rather than into the design of the circuit.

Related papers

• Physical consequences of Lindbladian invariance transformations [44.99833362998488]
  We show that symmetry transformations can be exploited, on their own, to optimize practical physical tasks. In particular, we show how they can be used to change the measurable values of physical quantities regarding the exchange of energy and/or information with the environment.
  arXiv  Detail & Related papers  (2024-07-02T18:22:11Z)
• Geometric Quantum Machine Learning with Horizontal Quantum Gates [41.912613724593875]
  We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions to those of the symmetry. For a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem.
  arXiv  Detail & Related papers  (2024-06-06T18:04:39Z)
• All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks [0.0]
  Variational algorithms require architectures that naturally constrain the optimisation space to run efficiently. We propose the use of spin networks, a form of directed tensor network invariant under a group transformation, to devise SU(2) equivariant quantum circuit ans"atze. By changing to the basis that block diagonalises SU(2) group action, these networks provide a natural building block for constructing parameterised equivariant quantum circuits.
  arXiv  Detail & Related papers  (2023-09-13T18:38:41Z)
• A Bottom-up Approach to Constructing Symmetric Variational Quantum Circuits [0.0]
  We show how to construct symmetric quantum circuits using representation theory. We show how to derive the particle-conserving exchange gates, which are commonly used in constructing hardware-efficient quantum circuits.
  arXiv  Detail & Related papers  (2023-08-17T10:57:15Z)
• Symmetry enhanced variational quantum imaginary time evolution [1.6872254218310017]
  We provide guidance for constructing parameterized quantum circuits according to the locality and symmetries of the Hamiltonian. Our approach can be used to implement the unitary and anti-unitary symmetries of a quantum system. Numerical results confirm that the symmetry-enhanced circuits outperform the frequently-used parametrized circuits in the literature.
  arXiv  Detail & Related papers  (2023-07-25T16:00:34Z)
• Generalized quantum geometric tensor for excited states using the path integral approach [0.0]
  The quantum geometric tensor encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral formalism that can handle both the ground and excited states. We then generalize the quantum geometric tensor to incorporate variations of the system parameters and the phase-space coordinates.
  arXiv  Detail & Related papers  (2023-05-19T08:50:46Z)
• Order-invariant two-photon quantum correlations in PT-symmetric interferometers [62.997667081978825]
  Multiphoton correlations in linear photonic quantum networks are governed by matrix permanents. We show that the overall multiphoton behavior of a network from its individual building blocks typically defies intuition. Our results underline new ways in which quantum correlations may be preserved in counterintuitive ways even in small-scale non-Hermitian networks.
  arXiv  Detail & Related papers  (2023-02-23T09:43:49Z)
• Efficient estimation of trainability for variational quantum circuits [43.028111013960206]
  We find an efficient method to compute the cost function and its variance for a wide class of variational quantum circuits. This method can be used to certify trainability for variational quantum circuits and explore design strategies that can overcome the barren plateau problem.
  arXiv  Detail & Related papers  (2023-02-09T14:05:18Z)
• Variational waveguide QED simulators [58.720142291102135]
  Waveguide QED simulators are made by quantum emitters interacting with one-dimensional photonic band-gap materials. Here, we demonstrate how these interactions can be a resource to develop more efficient variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-02-03T18:55:08Z)
• Exploiting symmetry in variational quantum machine learning [0.5541644538483947]
  Variational quantum machine learning is an extensively studied application of near-term quantum computers. We show how a standard gateset can be transformed into an equivariant gateset that respects the symmetries of the problem at hand. We benchmark the proposed methods on two toy problems that feature a non-trivial symmetry and observe a substantial increase in generalization performance.
  arXiv  Detail & Related papers  (2022-05-12T17:01:41Z)
• 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)

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.