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
- 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) - Krylov Complexity and Dynamical Phase Transition in the quenched LMG model [0.0]
We explore the Krylov complexity in quantum states following a quench in the Lipkin-Meshkov-Glick model.
Our results reveal that the long-term averaged Krylov complexity acts as an order parameter for this model.
A matching dynamic behavior is observed in both bases when the initial state possesses a specific symmetry.
arXiv Detail & Related papers (2023-12-08T19:11:55Z) - 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 [0.11719282046304676]
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) - Sinkhorn Natural Gradient for Generative Models [125.89871274202439]
We propose a novel Sinkhorn Natural Gradient (SiNG) algorithm which acts as a steepest descent method on the probability space endowed with the Sinkhorn divergence.
We show that the Sinkhorn information matrix (SIM), a key component of SiNG, has an explicit expression and can be evaluated accurately in complexity that scales logarithmically.
In our experiments, we quantitatively compare SiNG with state-of-the-art SGD-type solvers on generative tasks to demonstrate its efficiency and efficacy of our method.
arXiv Detail & Related papers (2020-11-09T02:51:17Z) - Adding machine learning within Hamiltonians: Renormalization group
transformations, symmetry breaking and restoration [0.0]
We include the predictive function of a neural network, designed for phase classification, as a conjugate variable coupled to an external field within the Hamiltonian of a system.
Results show that the field can induce an order-disorder phase transition by breaking or restoring the symmetry.
We conclude by discussing how the method provides an essential step toward bridging machine learning and physics.
arXiv Detail & Related papers (2020-09-30T18:44:18Z) - 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.