COVARIANCE APPROACH TO QUANTUM THEORY

J. M. Burgers

Ernst Schmützer

Τ. Padmanabhan

We emphasise the distinction between formal and operational notions of general covariance. Classically, formal covariance implies operational covariance. This is not true in quantum theory. Two observers may not agree on the results of measurement of a tensorial object like Tik (stress tensor) in quantum theory. In particular, one observer might conclude that the measured value is zero while another might attribute non-zero value to it.

Brigitte Falkenburg, Harvey R. Brown, Rom Harré

Rom Harre & Harvey Brown both of the University of Oxford: Introduction I. QUANTUM FIELD THEORY AS AN OBJECT OF PHILOSOPHICAL STUDY: TWO VIEWS: Michael Redhead, University of Cambridge: A philosopher looks at quantum field theory James T. Cushing, University of Notre Dame: Foundational problems in and methodological lessons from quantum field theory II. THE PROBLEMS OF VIRTUAL PARTICLES AND RENORMALIZATION: Robert Weingard, Rutgers University: Virtual particles and the interpretation of quantum field theory Rom Harre: Parsing the amplitudes Paul Teller, University of Illinois: Three problems of renormalization III. COVARIANCE PRINCIPLES IN QUANTUM FIELD THEORY: Gordon N. Fleming, Pennsylvania State University: Hyperplane-dependent quantized fields and Lorentz invariance Tian-yu Cao, Trinity College, Cambridge: Gauge theory and the geometrization of fundamental physics IV. MATHEMATICAL FOUNDATIONS OF QUANTUM FIELD THEORY: Ray F. Streater, King's College, London: Why should anyone want to axiomatize quantum field theory? Simon Saunders, Wolfson College, Oxford: The algebraic notation of quantum field theory.

Jack Cohn

Wooseop Hwang, Bálint Koczor

Abstract CoVariance Root finding with classical shadows (CoVaR) was recently introduced as a new paradigm for training variational quantum circuits. Common approaches, such as variants of the variational quantum eigensolver, aim to optimise a non-linear classical cost function and thus suffer from, e.g. poor local minima, high shot requirements and barren plateaus. In contrast, CoVaR fully exploits powerful classical shadows and finds joint roots of a very large number of covariances using only a logarithmic number of shots and linearly scaling classical computing resources. As a result, CoVaR has been demonstrated to be particularly robust against local traps, however, its main limitation has been that it requires a sufficiently good initial state. We address this limitation by introducing an adiabatic morphing of the target Hamiltonian and demonstrate in a broad range of application examples that CoVaR can successfully prepare eigenstates of the target Hamiltonian when no initial warm start is known. CoVaR succeeds even when Hamiltonian energy gaps are very small—this is in stark contrast to adiabatic evolution and phase estimation algorithms where circuit depths scale inversely with the Hamiltonian energy gaps. On the other hand, when the energy gaps are relatively small then adiabatic CoVaR may converge to higher excited states as opposed to a targeted specific low-lying state. Nevertheless, we exploit this feature of adiabatic CoVaR and demonstrate that it can be used to map out the low lying spectrum of a Hamiltonian which can be useful in practical applications, such as estimating thermal properties or in high-energy physics.