Qubit Regularization and Qubit Embedding Algebras

• URL: http://arxiv.org/abs/2112.02090v1
• Date: Fri, 3 Dec 2021 18:56:31 GMT
• Title: Qubit Regularization and Qubit Embedding Algebras
• Authors: Hanqing Liu and Shailesh Chandrasekharan
• Abstract summary: We show a systematic procedure to derive QEAs for the O(N) lattice spin models and the SU(N) lattice gauge theories. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.
• Score: 4.3799421495439175
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the O(N) lattice spin models and the SU(N) lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far more richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.

Related papers

• Relational Quantum Geometry [0.0]
  We identify non-commutative or quantum geometry as a mathematical framework which unifies three objects. We first provide a rigorous account of the extended phase space, and demonstrate that it can be regarded as a classical principal bundle with a Poisson manifold base. We conclude that the quantum orbifold is equivalent to the G-framed algebra proposed in prior work.
  arXiv  Detail & Related papers  (2024-10-14T19:29:27Z)
• Galois Symmetries in the Classification and Quantification of Quantum Entanglement [0.0]
  We present a new interpretation of entanglement classification by revealing a profound connection to Galois groups. This work bridges the mathematical elegance of Galois theory with the complexities of quantum mechanics, opening pathways for advances in quantum computing and information theory.
  arXiv  Detail & Related papers  (2024-10-10T20:58:23Z)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• The Ultraviolet Structure of Quantum Field Theories. Part 1: Quantum Mechanics [0.0]
  This paper fires the opening salvo in the systematic construction of the lattice-continuum correspondence. The focus will be on quantum field theory in (0+1)D, i.e. quantum mechanics.
  arXiv  Detail & Related papers  (2021-05-24T18:00:06Z)
• Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
  We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
  arXiv  Detail & Related papers  (2020-11-12T18:49:11Z)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Functorial evolution of quantum fields [0.0]
  We show how familiar notions from Relativity and quantum causality can be recovered in a purely order-theoretic way. We formulate theory-independent notions of fields over causal orders in a compositional, functorial way. We introduce notions of symmetry and cellular automata, which we show to subsume existing definitions of Quantum Cellular Automata.
  arXiv  Detail & Related papers  (2020-03-30T08:39:22Z)
• Lattice Gauge Theory for a Quantum Computer [0.0]
  Hamiltonian was introduced two decades ago as an alternative to Wilson's Euclidean lattice QCD with gauge fields represented by bi-linear fermion/anti-fermion operators. D-theory leads naturally to quantum Qubit algorithms. Digital quantum computing for gauge theories, the simplest example of U(1) compact QED on triangular lattice is defined.
  arXiv  Detail & Related papers  (2020-02-24T01:16:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.