Enhancing the Accuracy and Efficiency of Sample-Based Quantum Diagonalization with Phaseless Auxiliary-Field Quantum Monte Carlo
Supplemental Information for 10.1021/acs.jctc.5c01407
Danilov, Don [Department of Chemistry; Rice Univer↗
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Finite temperature auxiliary field quantum Monte Carlo in the canonical ensemble
Finite temperature auxiliary field-based quantum Monte Carlo methods, including determinant quantum Monte Carlo and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates such as superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi–Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble.
Shen, Tong (ORCID:0000000206292468)↗
Exotic $U(1)$ symmetries, duality, and fractons in 3+1-dimensional quantum field theory
We extend our exploration of nonstandard continuum quantum field theories in 2+1 2 + 1 dimensions to 3+1 3 + 1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising dualities. Many of the systems we study have a known lattice construction. In particular, one of them is a known gapless fracton model. The novelty here is in their continuum field theory description. In this paper, we focus on models with a global U(1) U ( 1 ) symmetry and in a followup paper we will study models with a global \mathbb{Z}_N ℤ N symmetry.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states
Understanding real-time dynamics of interacting quantum fields in curved space-time remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime dimensions, subject to a quench modeling a homogeneously expanding gravitational background. The models considered are the scalar λϕ 4 theory and the Schwinger model, i.e. a Dirac fermion coupled to a U(1) gauge field which is equivalent via bosonization to a scalar field with a cosine self-interaction. In the free scalar limit, both theories reproduce known analytical results, providing a nontrivial numerical validation of bosonization in curved spacetime for the Schwinger model. Our central finding is that self-interactions lead to a suppression of gravitational particle production compared to the free-field case, as evidenced by two-point functions and the spectra of produced particles. We further examine the behavior of entanglement generation and find that interactions suppress entanglement growth in the λϕ 4 theory, while in the Schwinger model, the interplay between suppressed particle production and enhanced inter-particle correlations leads to more complex entanglement behavior. Our results pave the way for further explorations of nonperturbative quantum real-time dynamics of interacting scalar and gauge theories in arbitrary gravitational backgrounds.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Self-consistent mean-field quantum approximate optimization
We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.
Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗
Self-consistent mean-field quantum approximate optimization
We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.
Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗
Self-consistent mean-field quantum approximate optimization
We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.
Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗
Determining all thermodynamic transport coefficients for an interacting large N quantum field theory
Thermodynamic transport coefficients can be calculated directly from quantum field theory without requiring analytic continuation to real time. We determine all second-order thermodynamic transport coefficients for the uncharged N-component massless (critical) scalar field theory with quartic interaction in the large N limit, for any value of the coupling. We find that in the large N limit, all thermodynamic transport coefficients for the interacting theory can be expressed analytically in terms of the in-medium mass and sums over modified Bessel functions. We expect our technique to allow a similar determination of all thermodynamic transport coefficients for all theories that are solvable in the large N limit, including certain gauge theories.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Beyond CCSD(T) Accuracy at Lower Scaling with Auxiliary Field Quantum Monte Carlo
We introduce a black-box auxiliary field quantum Monte Carlo (AFQMC) approach to perform highly accurate electronic structure calculations using configuration interaction singles and doubles (CISD) trial states. This method consistently provides more accurate energy estimates than coupled cluster singles and doubles with perturbative triples (CCSD(T)), often regarded as the gold standard in quantum chemistry. This level of precision is achieved at a lower asymptotic computational cost, scaling as O(N 6 ) compared to the O(N 7 ) scaling of CCSD(T). Furthermore, we provide numerical evidence supporting these findings through results for challenging main group and transition metal-containing molecules.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Emergence of quantum-field theory in causal diamonds
The experimental successes of quantum-field theory do not justify using it to describe even a finite fraction of the entanglement entropy of a causal diamond with its exterior, in the limit of large diamonds. Susskind and Uglum and Jacobson conjectured that this divergent entropy could be thought of as a renormalization of Newton’s constant in the Bekenstein–Hawking formula, if we applied that formula to arbitrary causal diamonds. Jacobson showed that this leads to a derivation of the null projection of Einstein’s equations as the hydrodynamic equations of the area law for arbitrary diamonds, a derivation which has the added virtue of demonstrating that the cosmological constant is not an energy density. Using a gauge choice adapted to causal diamond boundaries, we revisit arguments of Carlip and Solodukhin that the proper theory of near horizon states is a (cut-off) (1 + 1)-dimensional conformal field theory, with central charge proportional to the transverse area. This leads to a universal formula for fluctuations of the modular Hamiltonian of a diamond, which we argue is compatible with the explanation of the temperature of de Sitter space in terms of an identification between localized energy and the number of constrained q-bits of the holographic degrees of freedom.
Astronomy & Astrophysics↗
Auxiliary field Quantum Monte Carlo for dilute neutrons on the lattice
We employ constrained path Auxiliary Field Quantum Monte Carlo (AFQMC) in the pursuit of studying physical nuclear systems using a lattice formalism. Since AFQMC has been widely used in the study of condensed-matter systems such as the Hubbard model, we benchmark our method against published results for both one- and two-dimensional Hubbard model calculations. We then turn our attention to cold atomic and nuclear systems. We use an onsite contact interaction that can be tuned in order to reproduce the known scattering length and effective range of a given interaction. Developing this machinery allows us to extend our calculations to study nuclear systems within a lattice formalism. In conclusion, we perform initial calculations for a range of nuclear systems from two- to few-body neutron systems.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Topological symmetry in quantum field theory
We introduce a definition and framework for internal topological symmetries in quantum field theory, including “noninvertible symmetries” and “categorical symmetries”. We outline a calculus of topological defects which takes advantage of well-developed theorems and techniques in topological field theory. Our discussion focuses on finite symmetries, and we give indications for a generalization to other symmetries. We treat quotients and quotient defects (often called “gauging” and “condensation defects”), finite electromagnetic duality, and duality defects, among other topics. We include an appendix on finite homotopy theories, which are often used to encode finite symmetries and for which computations can be carried out using methods of algebraic topology. Throughout we emphasize exposition and examples over a detailed technical treatment.
Mathematics↗
QIS for Applied Quantum Field Theory
Precision predictions in HEP and non-equilibrium dynamics in the early universe require quantum computational technologies. Future quantum devices offer the possibility of performing these, complementing lattice quantum chromodynamics (QCD) studies on classical computers. We are investigating many aspects of the quantum simulation of quantum field theories. Specific topics include simulation-suitable formulations of gauge theories, state preparation, time evolution, extracting HEP-related observables from simulations, quantum error correction (QEC), and entanglement. We are exploring strategies for simulation of scattering in QFTs, and dynamics of the early Universe.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
An algebraic formula for two loop renormalization of scalar quantum field theory
We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending ’t Hooft’s one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizable topologies do not contribute to the renormalization group equations. The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Low-energy effective quantum field theoretic description of excitations about soliton configurations
Solitons are the classical field configurations connecting two trivial vacua. These are also the solutions of classical field equations of motion with particle-like properties. Moreover, they are localized in space, having finite energy, and are stable against decay into radiation. The coherent state description of kink-solitons is discussed in the present article. Further, the relation between topological solitons and occupation numbers corresponding to low momentum excitations are also discussed coherently. The description of the low energy excitations about solitons in quantum field theory is the main theme of this article. Further, a few physical observables, namely some low order correlation functions, are computed up to certain integral forms. Furthermore, we have shown that it is possible to detect the presence of soliton-like classical configurations in many-particle systems from the nature of the one-point function and non-conservation of momentum feature of one-point, two-point and three-point functions in this low-energy effective field theory of these excitations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Symmetry Anomalies, and Duality in Quantum Field Theory (Final Technical Report)
This grant supported work in high energy theoretical physics on quantum field theory by the Principal Investigator Clay Córdova.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Aspects of Large- N f Quantum Field Theories
Presentation for a seminar at Keio University on aspects of large- N f quantum field theories.
74 ATOMIC AND MOLECULAR PHYSICS↗
Quantum field theory of topological spin dynamics
Here, we develop a field theory of quantum magnets and magnetic (semi)metals, which is suitable for the analysis of their universal and topological properties. The systems of interest include collinear, coplanar, and general noncoplanar magnets. At the basic level, we describe the dynamics of magnetic moments using smooth vector fields in the continuum limit. Dzyaloshinskii-Moriya interaction is captured by a non-Abelian vector gauge field, and chiral spin couplings related to topological defects appear as higher-rank antisymmetric tensor gauge fields. We distinguish type-I and type-II magnets by their equilibrium response to the non-Abelian gauge flux, and characterize the resulting lattices of skyrmions and hedgehogs, the spectra of spin waves, and the chiral response to external perturbations. The general spin-orbit coupling of electrons is similarly described by non-Abelian gauge fields, including higher-rank tensors related to the electronic Berry flux. Itinerant electrons and local moments exchange their gauge fluxes through Kondo and Hund interactions. Hence, by utilizing gauge fields, this theory provides a unifying physical picture of “intrinsic” and “topological” anomalous Hall effects, spin-Hall effects, and other correlations between the topological properties of electrons and moments. We predict “topological” magnetoelectric effect in materials prone to hosting hedgehogs. Links to experiments and model calculations are provided by deriving the couplings and gauge fields from generic microscopic models, including the Hubbard model with spin-orbit interactions. Much of the formal analysis is generalized to d spatial dimensions in order to access the $π_{d–1}(S^{d–1})$ homotopy classification of the magnetic hedgehog topological defects, and establish the possibility of novel quantum spin liquids that exhibit a fractional magnetoelectric effect. However, we emphasize the form of all results in the physically relevant $\textit{d}$ = 3 dimensions, and discuss a few applications to topological magnetic conductors like Mn 3 Sn and Pr 2 Ir 2 O 7 .
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗