Geometric Quantum Machine Learning with Horizontal Quantum Gates

• URL: http://arxiv.org/abs/2406.04418v1
• Date: Thu, 6 Jun 2024 18:04:39 GMT
• Title: Geometric Quantum Machine Learning with Horizontal Quantum Gates
• Authors: Roeland Wiersema, Alexander F. Kemper, Bojko N. Bakalov, Nathan Killoran,
• Abstract summary: 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.
• Score: 41.912613724593875
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the current framework of Geometric Quantum Machine Learning, the canonical method for constructing a variational ansatz that respects the symmetry of some group action is by forcing the circuit to be equivariant, i.e., to commute with the action of the group. This can, however, be an overzealous constraint that greatly limits the expressivity of the circuit, especially in the case of continuous symmetries. We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits, based on homogeneous spaces, relaxing the overly stringent requirement of equivariance. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions orthogonal to those of the symmetry. We show that horizontal quantum gates are much more expressive than equivariant gates, and thus can solve problems that equivariant circuits cannot. For instance, a circuit comprised of horizontal gates can find the ground state of an $\mathrm{SU}(2)$-symmetric model where the ground state spin sector is unknown--a task where equivariant circuits fall short. Moreover, for a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem. Finally, we highlight a particular class of horizontal quantum gates that behave similarly to general $\mathrm{SU}(4)$ gates, while achieving a quadratic reduction in the number of parameters for a generic problem.

Related papers

• Permutation-invariant quantum circuits [4.900041609957432]
  We show the integration of the permutation symmetry as the most restrictive discrete symmetry into quantum circuits. The scaling of the number of parameters is found to be $mathcalO(n3)$, significantly lower than the general case.
  arXiv  Detail & Related papers  (2023-12-22T18:42:48Z)
• 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)
• Simulating scalar field theories on quantum computers with limited resources [62.997667081978825]
  We present a quantum algorithm for implementing $phi4$ lattice scalar field theory on qubit computers. The algorithm allows efficient $phi4$ state preparation for a large range of input parameters in both the normal and broken symmetry phases.
  arXiv  Detail & Related papers  (2022-10-14T17:28:15Z)
• Three-fold way of entanglement dynamics in monitored quantum circuits [68.8204255655161]
  We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles. We obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements.
  arXiv  Detail & Related papers  (2022-01-28T17:21:15Z)
• Quantum simulation of $\phi^4$ theories in qudit systems [53.122045119395594]
  We discuss the implementation of quantum algorithms for lattice $Phi4$ theory on circuit quantum electrodynamics (cQED) system. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates.
  arXiv  Detail & Related papers  (2021-08-30T16:30:33Z)
• 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)
• Entangling power of symmetric two-qubit quantum gates [0.0]
  capacity of a quantum gate to produce entangled states on a bipartite system is quantified in terms of the entangling power. We focus on symmetric two-qubit quantum gates, acting on the symmetric two-qubit space. A geometric description of the local equivalence classes of gates is given in terms of the $mathfraksu(3)$ Lie algebra root vectors.
  arXiv  Detail & Related papers  (2021-07-27T08:06:32Z)
• Noncyclic Geometric Quantum Gates with Smooth Paths via Invariant-based Shortcuts [4.354697470999286]
  We propose a scheme to realize geometric quantum gates with noncyclic and nonadiabatic evolution via invariant-based shortcuts. Our scheme provides a promising way to realize high-fidelity fault-tolerant quantum gates for scalable quantum computation.
  arXiv  Detail & Related papers  (2021-02-01T15:05:29Z)
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms [105.54048699217668]
  A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
  arXiv  Detail & Related papers  (2020-08-03T18:00:05Z)
• Symmetry-adapted variational quantum eigensolver [0.7734726150561086]
  We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm. The symmetry-adapted VQE scheme simply applies the projection operator, which is Hermitian but not unitary, to restore the spatial symmetry.
  arXiv  Detail & Related papers  (2019-12-31T02:13:11Z)

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.