相关论文: Towards complexity of primary-deformed Virasoro ci…

We show that the deformations of Virasoro and super Virasoro algebra, constructed earlier on an abstract mathematical background, emerge after Wick rotation, within an exact treatment of discrete-time free field models on a circle. The…

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 study Nielsen complexity and Fubini-Study complexity for a class of exactly solvable one dimensional spin systems. Our examples include the transverse XY spin chain and its natural extensions, the quantum compass model with and without…

We further advance the study of the notion of computational complexity for 2d CFTs based on a gate set built out of conformal symmetry transformations. Previously, it was shown that by choosing a suitable cost function, the resulting…

Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (=a finite union of hyperplanes) whose Levi-Civita connection is of Dunkl…

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 consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields…

Qubit-efficient optimization studies how large combinatorial problems can be addressed with quantum circuits whose width is far smaller than the number of logical variables. In quadratic unconstrained binary optimization (QUBO), objective…

We approach the question of complexification of the diffeomorphism group of the circle by considering real-analytic maps from the circle into the punctured complex plane with winding number +1. Such complex deformations form an…

We present a framework for the detection and estimation of deformations applied to a grid of sources. Our formalism uses the Hamiltonian formulation of the quantum Fisher information matrix (\textsc{qfim}) as the figure of merit to quantify…

We provide an experimentally measurable local gauge $U(1)$ invariant Fubini-Study (FS) metric for mixed states. Like the FS metric for pure states, it also captures only the quantum part of the uncertainty in the evolution Hamiltonian. We…

In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…

We investigate the quantum aspects of three-dimensional gravity with a positive cosmological constant. The reduced phase space of the three-dimensional de Sitter gravity is obtained as the space which consists of the Kerr-de Sitter…

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 establish the mathematical fundamentals for a unified description of curvature, torsion, and non-metricity 2-forms in the way extending the so-called M\"{o}bius representation of the affine group, which is the method to convert the…

The quantum charged rigid membrane model, which is a higher derivative theory has been considered to explore its gauge symmetries using a recently developed first order formalism \cite{BMP}. Hamiltonian analysis has been performed and the…

The spectrum of conformal weights for the CFT describing the two-dimensional critical $Q$-state Potts model (or its close cousin, the dense loop model) has been known for more than 30 years. However, the exact nature of the corresponding…

Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the…

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field…

Universal compilation is a training process that compiles a trainable unitary into a target unitary and it serves vast potential applications from quantum dynamic simulations to optimal circuits with deep-compressing, device benchmarking,…