Exploring Quantum Field Theories with Qubit Lattice Models

Alexander J. Buser, Tanmoy Bhattacharya A, Shailesh Chandrasekharan A +2 more

Shailesh Chandrasekharan A

To study quantum field theories on a quantum computer, we must begin with Hamiltonians defined on a finite-dimensional Hilbert space and then take appropriate limits. This approach can be seen as a new type of regularization for quantum field theories, which we refer to as qubit regularization. A related finite-dimensional regularization, known as the D-theory approach, was proposed long ago as a general framework for all quantum field theories. In this framework, the dimensionality of the local Hilbert space at each spatial point can increase as needed through an additional flavor index. To reproduce asymptotically free QFTs, most studies assume that qubit-regularized theories require extending the local Hilbert space to infinity. However, contrary to this common belief, recent discoveries in (1+1) dimensions have revealed two examples where asymptotic freedom appears to emerge within a strictly finite-dimensional local Hilbert space through a novel renormalization group (RG) flow. These findings motivate further investigation into whether asymptotically free gauge theories could also emerge within a strictly finite-dimensional local Hilbert space. To support these explorations, we propose an orthonormal basis called the monomer-dimer-tensor-network (MDTN) basis and use it to construct new types of qubit-regularized lattice gauge theories.

Richard C. Brower, David E Berenstein, Hiroki Kawai

The quantum link [1] Hamiltonian was introduced two decades ago a alternative to Wilson's Euclidean lattice QCD with gauge fields represented by bi-linear fermion/anti-fermion operators. When generalized this new microscopic representation of lattice field theories is referred as D-theory [2]. Recast as a Hamiltonian in Minkowski space for real time evolution, D-theory leads naturally to quantum Qubit algorithms. Here to explore digital quantum computing for gauge theories, the simplest example of U(1) compact QED on triangular lattice is defined and gauge invariant kernels for the Suzuki-Trotter expansions are expressed as Qubit circuits capable of being tested on the IMB-Q and other existing Noisy Intermediate Scale Quantum (NISQ) hardware. This is a modest step in exploring the quantum complexity of D-theory to guide future applications to high energy physics and condensed matter quantum field theories.

Anatoli G. Izergin, V. E. Korepin

Vincent Pasquier

Jincheng Zhang

Quantum-Inspired Lattice Field Theory (QILFT) presents a novel theoretical framework for modeling complex systems by integrating quantum field theory principles with lattice geometry. This approach aims to capture the emergent behavior of these systems through the interplay of entanglement and geometric constraints. The core claim is to develop a robust and adaptable model capable of predicting the evolution of complex systems across diverse physical regimes. This work explores the potential of utilizing entanglement as a fundamental building block for a probabilistic field theory, emphasizing its role in generating complex dynamics. We detail the theoretical basis, mathematical formulation, and potential applications of QILFT, highlighting its unique approach to addressing challenges inherent in complex systems modeling.