Related papers: Path integral optimization as circuit complexity
The search for scale-invariant random geometries is central to the Asymptotic Safety hypothesis for the Euclidean path integral in quantum gravity. In an attempt to uncover new universality classes of scale-invariant random geometries that…
We revisit the fundamentals of Circuit Complexity and the nature of efficient computation from a fresh perspective. We present a framework for understanding Circuit Complexity through the lens of Information Theory with analogies to results…
In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a…
Systems with constraints pose problems when they are quantized. Moreover, the Dirac procedure of quantization prior to reduction is preferred. The projection operator method of quantization, which can be most conveniently described by…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…
Quantum field theory in curved spacetime may be defined either through a manifestly unitary canonical approach or via the manifestly covariant path integral formalism. For gauge theories, these two approaches have produced conflicting…
Motivated by recent studies of quantum computational complexity in quantum field theory and holography, we discuss how weighting certain classes of gates building up a quantum circuit more heavily than others does affect the complexity.…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We use the path integral optimization approach of Caputa, kundu, Miyaji, Takayanagi and Watanabe to find the time slice of geometries dual to vacuum, primary and thermal states in the $T\bar{T}$ deformed two dimensional CFTs. The obtained…
In this work, we introduce a new way to quantify information flow in quantum systems, especially for parameterized quantum circuits. We use a graph representation of the circuits and propose a new distance metric using the mutual…
We construct a path integral based on the coupling of the Liouville action and the Mabuchi K-energy on a one-dimensional complex manifold. To the best of our knowledge this is the first rigorous construction of such an object and this is…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
The core of this thesis is the path-integral formulation of quantum field theory and its ability to describe strongly-coupled quantum many-body systems of finite size. Collective behaviors can be efficiently described in such systems…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q , we construct path integral representation for the quantum mechanical evolution operator kernel of…
Even if path planning can be solved using standard techniques from dynamic programming and control, the problem can also be approached using probabilistic inference. The algorithms that emerge using the latter framework bear some appealing…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
In this work is discussed possibility and actuality of Lagrangian approach to quantum computations. Finite-dimensional Hilbert spaces used in this area provide some challenge for such consideration. The model discussed here can be…
We consider a reduction procedure in Wiener-type path integral for a finite-dimensional mechanical system with a symmetry representing the motion of two interacting scalar particles on a manifold that is the product of the total space of…