Shailesh Chandrasekharan

Invited theory seminar at the City College of New York

Invited talk at the workshop

Inivited talk at the workshop on Sign problems in QCD and Beyond, organized by Tel Aviv University

Invited Distinguished Lecture/Colloquium

Invited Seminar

Invited Lecture

I was invited to give three lectures on qubit regularization covering two days.

Invited talk at the meeting

Invited Physics Colloquium

Invited online talk

Invited online talk

Online Attendance

Online participation

Invited virtual talk

Invited talk along with Uwe-Jens Wiese

Online talk at the workshop

Online talk

Three lectures at the winter school on "Algorithms for Lattice Gauge Theories and Quantum Spin Systems" held in Kolkata India.

Motivated by the desire to study quantum field theories on a quantum computer, we propose a new type of regularization of quantum field theories where in addition to the usual lattice regularization, quantum field theories are constructed with a finite dimensional Hilbert space per lattice site. This is particularly relevant for studying bosonic field theories using a quantum computer since traditional lattice regularization assumes an infinite dimensional Hilbert space per lattice site and hence difficult to formulate on a quantum computer. Here we show that a two qubit model is sufficient to recover the 3d Wilson-Fisher fixed point and the 4d Gaussian fixed point of the O(3) sigma model. On the other hand in 2d, our qubit model does not seem to have a continuum limit although we have to go to study large lattices to establish this fact. We discuss modifications of our model that could perhaps yield a continuum limit.

Recently it was proposed that conformal dimensions of certain large charge operators satisfy a simple relation with unknown coefficients. In this talk we explain our efforts to test this proposal and compute the unkown coefficients using Monte Carlo calculations. We focus on CFTs that arise at the O(2) and O(4) Wilson-Fisher fixed points as test cases. Since traditional Monte Carlo methods suffer from a severe signal-to-noise ratio problem in the large charge sectors, we use worldline formulations. In the O(2) case we show that the proposed large charge expansion works very well even up to the smallest charge. In the O(4) case, the charged sectors are labeled by the two SU(2) representations $(j_L,j_R)$. Here we introduce and study a drastically simplified alternate model, which we refer to as a "qubit model". We find that the $(j,j)$ sector continues to show excellent agreement with the proposed large charge expansion, again up to small values of $j$. We also present preliminary results on the behavior of the subleading $(j,j-1)$ sector.

The success of the standard model of particle physics is based on the quantum theory of fields where the basic assumptions lead to mathematical infinities. While the theory of renormalization helps us understand why these infinities are in fact harmless, they are still difficult to handle computationally, especially within the strongly interacting sector that describes nuclear physics. Recent effort to overcome these computational bottlenecks using a quantum computer is motivating us to think of new ways to build our universe with qubits. I will discuss the basic ideas and some recent results that suggests that this may indeed be possible.

Conformal field theories (CFTs) are described by a set of dimensionless numbers referred to as conformal dimensions, which are difficult to compute. Recently it was proposed that conformal dimensions of certain large charge operators satisfy a simple relation with unknown coefficients. In this talk we explain our efforts to test this proposal and compute the unkown coefficients using Monte Carlo calculations. We focus on CFTs that arise at the O(2) and O(4) Wilson-Fisher fixed points as test cases. Since traditional Monte Carlo methods suffer from a severe signal-to-noise ratio problem in the large charge sectors, we use worldline formulations. In the O(2) case we show that the large charge expansion works very well even up to the smallest charge. In the O(4) case, the charged sectors are labeled by the two SU(2) representations $(j_L,j_R)$. Here we introduce and study a drastically simplified alternate model, which we refer to as a "qubit model". We find that the $(j,j)$ sector continues to show excellent agreement with the large charge expansion, again up to small values of $j$. We also present preliminary results on the behavior of the subleading $(j,j-1)$ sector, which however suggests a less satisfying scenario.

Motivated by the desire to study quantum field theories on a quantum computer, we propose a new type of regularization of quantum field theories where in addition to the usual lattice regularization, quantum field theories are constructed with a finite dimensional Hilbert space per lattice site. This is particularly relevant for studying bosonic field theories using a quantum computer since traditional lattice regularization assumes an infinite dimensional Hilbert space per lattice site and hence difficult to formulate on a quantum computer. Here we show that a two qubit model is sufficient to recover the 3d Wilson-Fisher fixed point and the 4d Gaussian fixed point of the O(3) sigma model. On the other hand in 2d, the continuum limit of our qubit model is difficult to establish because of asymptotic freedom. Even, if it exists it seems to belong to a different universality class.

We test the recent proposal for computing conformal dimensions using a large charge expansion using Monte Carlo methods. We focus on the O(2) and the O(4) Wilson-Fisher fixed points as test cases. Unfortunately, traditional Monte Carlo methods suffer from a severe signal-to-noise ratio problem in the large charge sectors. To overcome this bottleneck we use worldline formulations. In the O(2) case we show that conformal dimensions of charge $q$ operators obey a simple formula predicted by the large charge expansion. In the O(4) case, the charged sectors are labeled by the two SU(2) representations $(j_L,j_R)$. Since the traditional model continues to be difficult to explore in the large $(j_L, j_R)$ sectors, we study a drastically simplified alternate model, which we refer to as a "qubit regularization” of the original model. Such simpler formulations of scalar quantum field theories have become interesting recently from the perspective of quantum computing. Here we again find that the $(j,j)$ sector continues to show excellent agreement with the predicted large charge expansion up to small values of $j$. However, preliminary results on the behavior of the next subleading sector $(j,j-1)$ suggests a less satisfying scenario.

In order to test the recent proposal for computing conformal dimensions using a large charge expansion, we explore Monte Carlo methods to compute them. We focus on the O(2) and the O(4) Wilson-Fisher fixed points as test cases. Unfortunately, traditional Monte Carlo methods suffer from a severe signal-to-noise ratio problem in the large charge sectors. To overcome this bottleneck we use worldline formulations. In the O(2) case we show that conformal dimensions of charge $q$ operators obey a simple formula predicted by the large charge expansion. In the O(4) case, the charged sectors are labeled by the two SU(2) representations $(j_L,j_R)$. Since the traditional model continues to be difficult to explore in the large $(j_L, j_R)$ sectors, we study a drastically simplified alternate model, which we refer to as a "qubit" formulation. Such simpler formulations of quantum field theories have become interesting recently from the perspective of quantum computing. Here we find that while the $(j,j)$ sector continues to show excellent agreement with the predicted large charge expansion up to small values of $j$, the behavior of the next subleading sector $(j,j-1)$ is far from satisfying.

Using Monte Carlo methods we explore how well does the recent proposal for computing conformal dimensions, using a large charge expansion, work. We focus on the O(2) and the O(4) Wilson-Fisher fixed points as test cases. Since the traditional Monte Carlo approach suffers from a severe signal-to-noise ratio problem in the large charge sectors, we use worldline formulations that eliminate such problems. In particular we argue that the O(4) model can be simplified drastically by studying what we refer to as a "qubit" formulation. Such simpler formulations of quantum field theories have become interesting recently from the perspective of quantum computing. Using our studies we confirm that the conformal dimensions of both conformal field theories with O(2) and O(4) symmetries obey a simple formula predicted by the large charge expansion. We also compute the two leading universal low energy constants in both cases , that play an important role in the large charge expansion.

Ever more efficient numerical methods, such as quantum Monte Carlo sampling of expanded classes of known sign-problem-free models and tensor network methods, have enabled unbiased studies of a number of exotic phases and continuous phase transitions, such as those involving topological phases and emergent gauge fields. The phenomena of interest often arise in simple looking designer models, which are attractive to a wide variety of theorists, including those who study condensed matter, high energy physics, and quantum information. This broad appeal stems from the fact that these models can be viewed as interesting models of materials, as regularizations of strongly coupled quantum field theories, or as playgrounds to study highly entangled quantum systems.

This interdisciplinary workshop thus aims to bring together researchers with the goal of facilitating an exchange of ideas for understanding these models using diverse numerical methods and from the field-theoretic point of view.

Understanding strongly coupled quantum systems has become a unifying theme for both condensed matter and particle physcists. The possibility of finding that Higgs could be a composite particle that emerges from a new strongly interacting sector is encouraging particle physicists to explore a variety of gauge theories. At the same time the discovery of many materials that show strong correlation effects is forcing condensed matter physicists to look for explanations that go beyond the standard paradigms, including emergent gauge fields, non-Fermi liquids and topological phases. Interestingly, the challenges that the two communities face are quite similar and the goal of the workshop is to bring together experts from both communities to facilitate discussion. Topics of common interest include phase structure and dynamics in strongly coupled systems, especially in the vicinity of quantum critical points. Questions related to these topics appear in the study of quantum antiferromagnets, superconductors, metal-insulator transitions, dense nuclear matter, conformal and near conformal gauge theories, holographic models, and topological field theories. Through the exchange of ideas involving theoretical insights and advances in computational algorithms, and by exploring the possibility of developing quantum simulators to study the underlying problems, the hope is to initiate future collaborations between the two communities and to encourage younger scientists to see their work within a broader framework.