Complexity in two-point measurement schemes

• URL: http://arxiv.org/abs/2311.07892v1
• Date: Tue, 14 Nov 2023 04:00:31 GMT
• Title: Complexity in two-point measurement schemes
• Authors: Ankit Gill, Kunal Pal, Kuntal Pal, Tapobrata Sarkar
• Abstract summary: We show that the probability distribution associated with the change of an observable in a two-point measurement protocol with a perturbation can be written as an auto-correlation function. We probe how the evolved state spreads in the corresponding conjugate space. We show that the complexity saturates for large values of the parameter only when the pre-quench Hamiltonian is chaotic.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the characteristic function of the probability distribution associated with the change of an observable in a two-point measurement protocol with a perturbation can be written as an auto-correlation function between an initial state and a certain unitary evolved state by an effective unitary operator. Using this identification, we probe how the evolved state spreads in the corresponding conjugate space, by defining a notion of the complexity of the spread of this evolved state. For a sudden quench scenario, where the parameters of an initial Hamiltonian (taken as the observable measured in the two-point measurement protocol) are suddenly changed to a new set of values, we first obtain the corresponding Krylov basis vectors and the associated Lanczos coefficients for an initial pure state, and obtain the spread complexity. Interestingly, we find that in such a protocol, the Lanczos coefficients can be related to various cost functions used in the geometric formulation of circuit complexity, for example the one used to define Fubini-Study complexity. We illustrate the evolution of spread complexity both analytically, by using Lie algebraic techniques, and by performing numerical computations. This is done for cases when the Hamiltonian before and after the quench are taken as different combinations of chaotic and integrable spin chains. We show that the complexity saturates for large values of the parameter only when the pre-quench Hamiltonian is chaotic. Further, in these examples we also discuss the important role played by the initial state which is determined by the time-evolved perturbation operator.

Related papers

• Generalization of Modular Spread Complexity for Non-Hermitian Density Matrices [0.0]
  In this work we generalize the concept of modular spread complexity to the cases where the reduced density matrix is non-Hermitian. We define the quantity pseudo-capacity which generalizes capacity of entanglement, and corresponds to the early modular-time measure of pseudo-modular complexity. We show some analytical calculations for 2-level systems and 4-qubit models and then do numerical investigations on the quantum phase transition of transverse field Ising model.
  arXiv  Detail & Related papers  (2024-10-07T17:59:16Z)
• Exploring entanglement in finite-size quantum systems with degenerate ground state [0.0]
  We develop an approach for characterizing non-local quantum correlations in spin systems with exactly or nearly degenerate ground states. We generate a finite set of their random linear combinations with Haar measure, which guarantees that these combinations are uniformly distributed in the space spanned by the initial eigenstates. We elaborate on the problem of estimating observables on the basis of the single-shot measurements of numerous degenerate eigenstates.
  arXiv  Detail & Related papers  (2024-10-01T08:56:34Z)
• Complex Scaling Method applied to the study of the Swanson Hamiltonian in the broken PT-symmetry phase [0.0]
  We study the non-PT symmetry phase of the Swanson Hamiltonian in the framework of the Complex Scaling Method. We apply the formalism of the response function to analyse the time evolution of different initial wave packages.
  arXiv  Detail & Related papers  (2024-05-07T18:21:09Z)
• Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies [58.179981892921056]
  This work introduces a novel principle for disentanglement we call mechanism sparsity regularization. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors. We show that the latent factors can be recovered by regularizing the learned causal graph to be sparse.
  arXiv  Detail & Related papers  (2024-01-10T02:38:21Z)
• Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution [44.99833362998488]
  We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate quantum systems classically. We prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias. We show that a different scheme based on the solution of an optimization problem at each time step is free from such problems.
  arXiv  Detail & Related papers  (2023-05-23T17:38:10Z)
• Time evolution of spread complexity and statistics of work done in quantum quenches [0.0]
  Lanczos coefficients corresponding to evolution under the post-quench Hamiltonian. Average work done on the system, its variance, as well as the higher order cumulants.
  arXiv  Detail & Related papers  (2023-04-19T13:21:32Z)
• Extremal jumps of circuit complexity of unitary evolutions generated by random Hamiltonians [0.0]
  We investigate circuit complexity of unitaries generated by time evolution of randomly chosen strongly interacting Hamiltonians in finite dimensional Hilbert spaces. We prove that the complexity of $exp(-it H)$ exhibits a surprising behaviour -- with high probability it reaches the maximal allowed value on the same time scale as needed to escape the neighborhood of the identity consisting of unitaries with trivial (zero) complexity.
  arXiv  Detail & Related papers  (2023-03-30T17:05:06Z)
• Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
  We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom. We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
  arXiv  Detail & Related papers  (2023-03-13T13:06:40Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Interplay between transport and quantum coherences in free fermionic systems [58.720142291102135]
  We study the quench dynamics in free fermionic systems. In particular, we identify a function, that we dub emphtransition map, which takes the value of the stationary current as input and gives the value of correlation as output.
  arXiv  Detail & Related papers  (2021-03-24T17:47:53Z)
• Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
  The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy. In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
  arXiv  Detail & Related papers  (2020-07-31T19:23:26Z)

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.