Efficient characterization of general Gottesman-Kitaev-Preskill qubits

• URL: http://arxiv.org/abs/2604.17303v1
• Date: Sun, 19 Apr 2026 07:36:55 GMT
• Title: Efficient characterization of general Gottesman-Kitaev-Preskill qubits
• Abstract summary: We introduce a family of positive semidefinite Hermitian operators, one for each point on the logical Bloch sphere.<n>We show that the expectation value of each operator serves as a witness of non-Gaussianity.<n>We show that the truncated finite-dimensional counterparts of these operators yield physical approximations of arbitrary logical GKP states as their ground states.
• Score: 0.3437656066916039
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Practical utilization of Gottesman-Kitaev-Preskill (GKP) qubits requires not only the preparation of logical basis states, but also the ability to prepare and evaluate arbitrary logical qubit superpositions. Currently, this is typically done via quantum state tomography, which is resource-intensive. We introduce a family of positive semidefinite Hermitian operators, one for each point on the logical Bloch sphere, whose unique zero-eigenvalue ground states are the corresponding ideal GKP qubit states. We show that the expectation value of each operator serves as a witness of non-Gaussianity, and corresponds to twice the logical infidelity for states in the ideal logical GKP subspace. Furthermore, the truncated finite-dimensional counterparts of these operators yield physical approximations of arbitrary logical GKP states as their ground states. The evaluation of the proposed operators requires only three quadrature measurements, making this framework practical for both the experimental characterization and numerical optimization of GKP state preparation circuits.

Related papers

• Realistic GKP stabilizer states enable universal quantum computation [0.0]
  Physical Gottesman-Kitaev-Preskill (GKP) states are inherently noisy as ideal ones would require infinite energy.<n>This work demonstrates that imperfect GKP stabilizer states can be leveraged in order to apply non-Clifford gates using only linear optical elements.
  arXiv  Detail & Related papers  (2025-11-05T21:42:54Z)
• Euclidean-Monte-Carlo-informed ground-state preparation for quantum simulation of scalar field theory [0.0]
  We present a fully classical pipeline for generating efficient quantum circuits for preparing the ground state of a quantum field theory in 1+1 dimensions.<n>The work opens the way to systematically applying classically obtained knowledge of states to prepare accurate initial states in quantum field of theories of interest in nature.
  arXiv  Detail & Related papers  (2025-06-02T23:02:45Z)
• Generalization of Bohmian Mechanics and Quantum Gravity Effective Action [55.2480439325792]
  We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG)<n>This is done by replacing the dBB equations of motion with the effective action equations of motion, which is beneficial even in the non-gravitational case.<n>Another advantage of the effective action formalism is that one can obtain the field configurations in the case of a quantum field theory.
  arXiv  Detail & Related papers  (2025-05-06T08:38:03Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• The vacuum provides quantum advantage to otherwise simulatable architectures [49.1574468325115]
  We consider a computational model composed of ideal Gottesman-Kitaev-Preskill stabilizer states. We provide an algorithm to calculate the probability density function of the measurement outcomes.
  arXiv  Detail & Related papers  (2022-05-19T18:03:17Z)
• Threshold size for the emergence of a classical-like behaviour [68.8204255655161]
  We design a procedure to estimate the minimum size beyond which a system is amenable to a classical-like description. The specific case of a magnetic system is considered, with details of a gedanken experiment presented and thoroughly commented.
  arXiv  Detail & Related papers  (2022-03-25T11:31:14Z)
• Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits [68.8204255655161]
  We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements. For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems can be employed to assess the simulatability.
  arXiv  Detail & Related papers  (2022-03-21T17:57:02Z)
• Coherent states for fractional powers of the harmonic oscillator Hamiltonian [0.0]
  This article is inspired by special and general relativistic systems that can have Hamiltonians involving square roots. We discuss two approaches for finding suitable coherent states for this system.
  arXiv  Detail & Related papers  (2021-09-13T16:25:49Z)
• Local optimization on pure Gaussian state manifolds [63.76263875368856]
  We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm. The method is based on notions of descent gradient attuned to the local geometry. We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
  arXiv  Detail & Related papers  (2020-09-24T18:00:36Z)
• Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement [0.6091702876917281]
  An adaptive method for quantum state fidelity estimation in bipartite higher dimensional systems is established. The state verifier operators that stabilize Bell-type entangled states are constructed explicitly. Together with an error operator in the computational basis, one can estimate the lower and upper bounds on the state fidelity for Bell-type entangled states.
  arXiv  Detail & Related papers  (2020-09-16T15:17:52Z)

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.