Related papers: Circuit complexity for free fermions
We study circuit complexity for a free vector field of a $U(1)$ gauge theory in Coulomb gauge, and Gaussian states. We introduce a quantum circuit model with Gaussian states, including reference and target states. Using the Nielsen's…
We define and calculate versions of complexity for free fermionic quantum field theories in 1+1 and 3+1 dimensions, adopting Nielsen's geodesic perspective in the space of circuits. We do this both by discretizing and identifying…
By using a recent approach proposed by Hackl $et\, al.$ to evaluate the complexity of the free fermionic Gaussian state, we compute the complexity of the Dirac vacuum state as well as the excited state of the Fermi system with a mass…
We consider the circuit complexity of free bosons, or equivalently free fermions, in 1+1 dimensions. Motivated by the results of [1] and [2, 3] who found different behavior in the complexity of free bosons and fermions, in any dimension, we…
We present a general construction of a geometric notion of circuit complexity for Gaussian states (both bosonic and fermionic) in terms of Riemannian geometry. We lay out general conditions that a Riemannian metric function on the space of…
Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a…
We study circuit complexity for conformal field theory states in arbitrary dimensions. Our circuits start from a primary state and move along a unitary representation of the Lorentzian conformal group. Different choices of distance…
We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen's geometric approach as in [1]. The complexity of the coherent states have the same UV divergences as the vacuum state complexity and so we…
Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in $\mathcal{Z}_2$ Even Effective Field Theories ($\mathcal{Z}_2$ EEFTs). We consider a massive…
Motivated by the holographic complexity proposals, in this paper, we investigate the time dependence of the complexity for the Fermionic thermofield double state (TFD) using the Nielsen approach and Fubini-Study (FS) approach separately. In…
In this work, we study the circuit complexity for generalized coherent states in thermal systems by adopting the covariance matrix approach. We focus on the coherent thermal (CT) state, which is non-Gaussian and has a nonvanishing one-point…
We investigate notions of complexity of states in continuous quantum-many body systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the…
We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the $\phi^4$ theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled…
Computation of circuit complexity has gained much attention in the Theoretical Physics community in recent times to gain insights into the chaotic features and random fluctuations of fields in the quantum regime. Recent studies of circuit…
We define circuits given by unitary representations of Lorentzian conformal field theory in 3 and 4 dimensions. Our circuits start from a spinning primary state, allowing us to generalize formulas for the circuit complexity obtained from…
In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions…
We initiate quantitative studies of complexity in (1+1)-dimensional conformal field theories with a view that they provide the simplest setting to find a gravity dual to complexity. Our work pursues a geometric understanding of complexity…
We consider the Bose-Hubbard model in two and three spatial dimensions and numerically compute the quantum circuit complexity of the ground state in the Mott insulator and superfluid phases using a mean field approximation with additional…
We evaluate the complexity of the free scalar field by the operator approach in which the transformation matrix between the second quantization operators of reference state and target state is regarded as the quantum gate. We first examine…
In this paper, we first construct thermofield double states for bosonic string theory in the light-cone gauge. We then obtain a coherent-thermal string state and a thermal-coherent string state. We use the covariance matrix approach to…