Quantum Sensors for the Generating Functional of Interacting Quantum Field Theories

Abstract

Difficult problems described in terms of interacting quantum fields evolving in real time or out of equilibrium are abound in condensed-matter and high-energy physics. Addressing such problems via controlled experiments in atomic, molecular, and optical physics would be a breakthrough in the field of quantum simulations. In this work, we present a quantum-sensing protocol to measure the generating functional of an interacting quantum field theory and, with it, all the relevant information about its in or out of equilibrium phenomena. Our protocol can be understood as a collective interferometric scheme based on a generalization of the notion of Schwinger sources in quantum field theories, which make it possible to probe the generating functional. We show that our scheme can be realized in crystals of trapped ions acting as analog quantum simulators of self-interacting scalar quantum field theories. CONTENTS

Gross–Neveu–Wilson model and correlated symmetry-protected topological phases

“…By setting the model parameters in the vicinity of a second-order quantum phase transition, the relevant length scales fulfill ξ l d, and one recovers universal features that are independent of the microscopic lattice details, and can be described by a continuum QFT. In this section, we exploit the above mapping (59) to explore the phase diagram of the N = 1 lattice GNW model by importing some of the condensed-matter and quantuminformation techniques described in [71]. In particular, we will use the numerical matrix-product-state results to benchmark the large-N predictions.…”

“…9, which describes an exact solution that becomes valid in the strong-coupling limit g 2 1. From the parameter correspondence (59), this regime corresponds to the strongly-interacting Hubbard model, where one expects to find super-exchange interactions between the fermions [94]. In this case, these superexchange can be described in terms of an orbital Ising model with ferromagnetic coupling J = −2/g 2 a, and subjected to a transverse magnetic field B = 2(m + 1/a).…”

General methods for digital quantum simulation of gauge theories

“…QPE [30] has been used to compute linear response [6]. Another intriguing idea uses quantum sensors to implement generating functionals [44]. A second problem arises from state contamination.…”

Multi-bit quantum digital signature based on temporal quantum ghost imaging

“…The classical protocols of digital signatures commonly employ the public-key encryption and provide the computational-assumption security for legitimate users. For example, the security of the famous Rivest-Shamir-Adleman protocol [1] is based on the reasonable capabilities in the computation of factorizing large integers, and such security is susceptible to algorithmic breakthroughs, large-scale computational resources and the emerging technologies of quantum computation [2][3][4]. In contrast, quantum digital signature (QDS), which was firstly proposed in 2001 [5], is robust against attackers with unrestricted capabilities in the computation, since QDS offers the information-theoretical security by fundamental principles of quantum mechanics.…”