Determining non-Hermitian parent Hamiltonian from a single eigenstate

• URL: http://arxiv.org/abs/2408.15781v1
• Date: Wed, 28 Aug 2024 13:23:47 GMT
• Title: Determining non-Hermitian parent Hamiltonian from a single eigenstate
• Authors: Xu-Dan Xie, Zheng-Yuan Xue, Dan-Bo Zhang,
• Abstract summary: We show that it can be sufficient to determine a non-Hermitian Hamiltonian from a single right or left eigenstate. Our scheme favours non-Hermitian Hamiltonian learning on experimental quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A quantum state for being an eigenstate of some local Hamiltonian should be constraint by zero energy variance and consequently, the constraint is rather strong that a single eigenstate may uniquely determine the Hamiltonian. For non-Hermitian systems, it is natural to expect that determining the Hamiltonian requires a pair of both left and right eigenstates. Here, we observe that it can be sufficient to determine a non-Hermitian Hamiltonian from a single right or left eigenstate. Our approach is based on the quantum covariance matrix, where the solution of Hamiltonian corresponds to the complex null vector. Our scheme favours non-Hermitian Hamiltonian learning on experimental quantum systems, as only the right eigenstates there can be accessed. Furthermore, we use numerical simulations to examine the effects of measurement errors and show the stability of our scheme.

Related papers

• Quantifying non-Hermiticity using single- and many-particle quantum properties [14.37149160708975]
  The non-Hermitian paradigm of quantum systems displays salient features drastically different from Hermitian counterparts. We propose a formalism that quantifies the (dis-)similarity of these right and left ensembles, for single- as well as many-particle quantum properties. Our findings can be instrumental in unveiling new exotic quantum phases of non-Hermitian quantum many-body systems.
  arXiv  Detail & Related papers  (2024-06-19T13:04:47Z)
• Coherence generation with Hamiltonians [44.99833362998488]
  We explore methods to generate quantum coherence through unitary evolutions. This quantity is defined as the maximum derivative of coherence that can be achieved by a Hamiltonian. We identify the quantum states that lead to the largest coherence derivative induced by the Hamiltonian.
  arXiv  Detail & Related papers  (2024-02-27T15:06:40Z)
• Twirling Operations to Produce Energy Eigenstates of a Hamiltonian by Classically Emulated Quantum Simulation [0.0]
  We propose a simple procedure to produce energy eigenstates of a Hamiltonian with discrete eigenvalues. We use ancilla qubits and quantum entanglement to separate an energy eigenstate from the other energy eigenstates.
  arXiv  Detail & Related papers  (2023-09-10T04:10:36Z)
• Recovery of a generic local Hamiltonian from a degenerate steady state [11.567029926262476]
  Hamiltonian Learning (HL) is essential for validating quantum systems in quantum computing. HL success depends on the Hamiltonian model and steady state. We analyze HL for a specific type of steady state composed of eigenstates with degenerate mixing weight.
  arXiv  Detail & Related papers  (2023-09-01T08:40:50Z)
• Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix [0.0]
  We provide a systematical and efficient way to construct non-Hermitian Hamiltonian from a single pair of biorthogonal eigenstates. Our work sheds light on future exploration on non-Hermitian physics.
  arXiv  Detail & Related papers  (2023-07-06T16:27:22Z)
• A hybrid quantum algorithm to detect conical intersections [39.58317527488534]
  We show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path. We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule.
  arXiv  Detail & Related papers  (2023-04-12T18:00:01Z)
• 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)
• A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations [31.761854762513337]
  Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hybrid approach.
  arXiv  Detail & Related papers  (2021-09-16T13:53:12Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Hamiltonian operator approximation for energy measurement and ground state preparation [23.87373187143897]
  We show how to approximate the Hamiltonian operator as a sum of propagators using a differential representation. The proposed approach, named Hamiltonian operator approximation (HOA), is designed to benefit analog quantum simulators.
  arXiv  Detail & Related papers  (2020-09-07T18:11:00Z)
• How to define quantum mean-field solvable Hamiltonians using Lie algebras [0.0]
  We define what mean-field theory is, independently of a Hamiltonian realization in a particular set of operators. We then formulate a criterion for a Hamiltonian to be mean-field solvable. For the electronic Hamiltonians, our approach reveals the existence of mean-field solvable Hamiltonians of higher fermionic operator powers than quadratic.
  arXiv  Detail & Related papers  (2020-08-15T03:01:33Z)

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.