Related papers: Circuit Complexity From Supersymmetric Quantum Fie…
Modern understanding of symmetry in quantum field theory includes both invertible and non-invertible operations. Motivated by this, we extend Nielsen's geometric approach to quantum circuit complexity to incorporate non-invertible gates.…
In this work, we explore the effects of a quantum quench on the circuit complexity for a quenched quantum field theory having weakly coupled quartic interaction. We use the invariant operator method, under a perturbative framework, for…
Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy…
Inspired by the close relationship between Kolmogorov complexity and unsupervised machine learning, we explore quantum circuit complexity, an important concept in quantum computation and quantum information science, as a pivot to understand…
Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics. While extensively studied in closed systems, its characterization and behaviors in…
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…
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…
The quantum mechanics of superconducting circuits is derived by starting from a classical Hamiltonian dynamical system describing a dissipationless circuit, usually made of capacitive and inductive elements. However, standard approaches to…
We study circuit complexity for free fermionic field theories and Gaussian states. Our definition of circuit complexity is based on the notion of geodesic distance on the Lie group of special orthogonal transformations equipped with a…
The current noisy intermediate-scale quantum (NISQ) era is characterized by substantial errors and noise, which limit the practical feasibility of deep, many-qubit circuits. To address these constraints, quantum circuit cutting has emerged…
According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the…
We describe correlations functions of topological quantum mechanics (TQM) in terms of Morse theory. We review the basics of topological field theories and discuss geometric and algebraic interpretations of TQM. We prove that correlators in…
We consider a specific instance of a superconducting circuit, the so-called charge-qubit, consisting of a capacitor and a Josephson junction. Starting from the microscopic description of the latter in terms of two tunneling BCS models in…
In the rapidly evolving field of quantum computing, quantifying circuit complexity remains a critical challenge. This paper introduces Character Complexity, a novel measure that bridges Group-theoretic concepts with practical quantum…
We extend Nielsen's formulation of quantum circuit complexity to include intrinsically non-invertible operations. Such gates arise from fusion with topological defect operators and remove a basic limitation of symmetry-based circuits: the…
Quantum circuit complexity has played a central role in recent advances in holography and many-body physics. Within quantum field theory, it has typically been studied in a Lorentzian (real-time) framework. In a departure from standard…
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…
In Nielsen's geometric approach to quantum complexity, the introduction of a suitable geometrical space, based on the Lie group formed by fundamental operators, facilitates the identification of complexity through geodesic distance in the…
We formulate Nielsen's geometric approach to complexity in the context of two dimensional conformal field theories, where series of conformal transformations are interpreted as unitary circuits. We show that the complexity functional can be…
The implementation of physical symmetries into problem descriptions allows for the reduction of parameters and computational complexity. We show the integration of the permutation symmetry as the most restrictive discrete symmetry into…