Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers

• URL: http://arxiv.org/abs/2210.12732v2
• Date: Wed, 10 May 2023 07:20:38 GMT
• Title: Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Authors: Ze-Hao Huang, Peng He, Li-Jun Lang, Shi-Liang Zhu
• Abstract summary: We propose a general quantum circuit based on the swap test for measuring the quantity $langle psi_1 | A | psi rangle$ of an arbitrary operator $A$ with respect to two quantum states $|psi_1,2rangle$. We apply the circuit, in the field of non-Hermitian physics, to the measurement of generalized expectations with respect to left and right eigenstates of a given non-Hermitian Hamiltonian.
• Score: 5.081241420920605
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a general quantum circuit based on the swap test for measuring the quantity $\langle \psi_1 | A | \psi_2 \rangle$ of an arbitrary operator $A$ with respect to two quantum states $|\psi_{1,2}\rangle$. This quantity is frequently encountered in many fields of physics, and we dub it the generalized expectation as a two-state generalization of the conventional expectation. We apply the circuit, in the field of non-Hermitian physics, to the measurement of generalized expectations with respect to left and right eigenstates of a given non-Hermitian Hamiltonian. To efficiently prepare the left and right eigenstates as the input to the general circuit, we also develop a quantum circuit via effectively rotating the Hamiltonian pair $(H,-H^\dagger)$ in the complex plane. As applications, we demonstrate the validity of these circuits in the prototypical Su-Schrieffer-Heeger model with nonreciprocal hopping by measuring the Bloch and non-Bloch spin textures and the corresponding winding numbers under periodic and open boundary conditions (PBCs and OBCs), respectively. The numerical simulation shows that non-Hermitian spin textures building up these winding numbers can be well captured with high fidelity, and the distinct topological phase transitions between PBCs and OBCs are clearly characterized. We may expect that other non-Hermitian topological invariants composed of non-Hermitian spin textures, such as non-Hermitian Chern numbers, and even significant generalized expectations in other branches of physics would also be measured by our general circuit, providing a different perspective to study novel properties in non-Hermitian as well as other physics realized in qubit systems.

Related papers

• Bethe Ansatz, Quantum Circuits, and the F-basis [40.02298833349518]
  deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the spin-1/2 XXZ model. We show that algebraic Bethe circuits can be derived by a change of basis in the auxiliary space. We demonstrate our approach by presenting new quantum circuits for the inhomogeneous spin-1/2 XXZ model.
  arXiv  Detail & Related papers  (2024-11-04T19:01:41Z)
• Identifying non-Hermitian critical points with quantum metric [2.465888830794301]
  The geometric properties of quantum states are encoded by the quantum geometric tensor. For conventional Hermitian quantum systems, the quantum metric corresponds to the fidelity susceptibility. We extend this wisdom to the non-Hermitian systems for revealing non-Hermitian critical points.
  arXiv  Detail & Related papers  (2024-04-24T03:36:10Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits [37.84307089310829]
  Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit. Despite their promise, the trainability of these algorithms is hindered by barren plateaus. We present a general Lie algebra that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits.
  arXiv  Detail & Related papers  (2023-09-17T18:14:10Z)
• Locality and Exceptional Points in Pseudo-Hermitian Physics [0.0]
  Pseudo-Hermitian operators generalize the concept of Hermiticity. This thesis is devoted to the study of locality in quasi-Hermitian theory. Chiral symmetry and representation theory are used to derive large classes of pseudo-Hermitian operators.
  arXiv  Detail & Related papers  (2023-06-06T22:19:05Z)
• $\mathcal{PT}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities [0.0]
  We present a new set of models with non-Hermiticity generated by splitting a Hermitian term into two Jordan-normal form parts. We find a robust PT threshold that seems insensitive to the size of the quantum spin chain.
  arXiv  Detail & Related papers  (2023-04-20T03:03:58Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• Gaussian initializations help deep variational quantum circuits escape from the barren plateau [87.04438831673063]
  Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks.
  arXiv  Detail & Related papers  (2022-03-17T15:06:40Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• Hunting for the non-Hermitian exceptional points with fidelity susceptibility [1.7205106391379026]
  The fidelity susceptibility has been used to detect quantum phase transitions in the Hermitian quantum many-body systems. Here the fidelity susceptibility $chi$ is generalized to non-Hermitian quantum systems by taking the geometric structure of the Hilbert space into consideration. As examples, we investigate the simplest $mathcalPT$ symmetric $2times2$ Hamiltonian with a single tuning parameter and the non-Hermitian Su-Schriffer-Heeger model.
  arXiv  Detail & Related papers  (2020-09-15T13:21:24Z)
• Emergent $\mathcal{PT}$ symmetry in a double-quantum-dot circuit QED set-up [0.0]
  We show that a non-Hermitian Hamiltonian emerges naturally in a double-quantum-dot-circuit-QED set-up. Our results pave the way for an on-chip realization of a potentially scalable non-Hermitian system.
  arXiv  Detail & Related papers  (2020-04-16T09:08:31Z)

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.