Date: 9/21/2022
Time: 10:30 (Taipei time)
Venue: Zoom [Registration] is required
Zoom link: https://us02web.zoom.us/j/83736741073?pwd=MWVkU29rTFpkcUdtYitDTGVwa3VtUT09
Speaker: Dr. C.N. (Miranda) Cheng (University of Amsterdam)
Host: Prof. Ying-Jer Kao (Department of Physics, NTU)
Title: Learning Quantum Field Theory with Equivariant Continuous Flows.
Abstract: Machine learning has the potential of becoming, among other things, a major computational tools in physics, making possible what was not. Specifically, I will summarise my recent work which aims to use a continuous flow model to help ameliorate the numerical difficulties in sampling in lattice field theories, which for instance hampers high-precision computations in LQCD. I will focus on the case study of the phi^4 theory in 2 dimensions. The talk will be based on 2110.02673 and 2207.00283 with de Haan, Gerdes, Rainone, and Bondesan.
Date: 10/12/2022
Time: 9:30 (Taipei time)
Venue: Zoom [Registration] is required
Zoom link: https://us02web.zoom.us/j/83736741073?pwd=MWVkU29rTFpkcUdtYitDTGVwa3VtUT09
Speaker: Yu-An Chen (UMD)
Host: Prof. Ying-Jer Kao (Department of Physics, NTU)
Title: Pauli stabilizer models of twisted quantum doubles, and a new quantum cellular automaton.
Abstract:
In 2d, we construct a Pauli stabilizer model for every Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z_4 toric code. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes—in fact, exhausting all Abelian anyon theories that admit a gapped boundary.
In 3d, we use this technique to construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (U(1)_2 Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on 2^n-dimensional qudits that feature surface anyons described by U(1)_{2^n} Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.
References:
PRX QUANTUM 3, 010353 (2022) (https://doi.org/10.1103/PRXQuantum.3.010353)
PRX Quantum 3, 030326 (2022) (https://doi.org/10.1103/PRXQuantum.3.030326)
Date: 10/26/2022
Time: 9:30 (Taipei time)
Venue: Zoom [Registration] is required
Zoom link: https://us02web.zoom.us/j/86867205231?pwd=OTJVTURuVU9FVzkzR01kMVUwcGVvZz09
Speaker: Dr. Tsung-Cheng Peter Lu (Perimeter Institute)
Host: Prof. Yi-Ping Huang (Department of Physics, NTHU)
Title: Measurement as a shortcut to long-range entangled quantum matter
Abstract: The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback (``adaptive circuits'') can evade such restrictions. We introduce three classes of local adaptive circuits that enable low-depth preparation of long-range entangled quantum matter characterized by gapped topological orders and conformal field theories (CFTs). The three classes are inspired by distinct physical insights, including tensor-network constructions, multiscale entanglement renormalization ansatz (MERA), and parton constructions. A large class of topological orders, including chiral topological order, can be prepared in constant depth or time, and one-dimensional CFT states and non-abelian topological orders with both solvable and non-solvable groups can be prepared in depth scaling logarithmically with system size. We also build on a recently discovered correspondence between symmetry-protected topological phases and long-range entanglement to derive efficient protocols for preparing symmetry-enriched topological order and arbitrary CSS (Calderbank-Shor-Steane) codes. Our work illustrates the practical and conceptual versatility of measurement for state preparation.
Date: 11/2/2022
Time: 10:30 (Taipei time)
Venue: Zoom [Registration] is required
Zoom link: https://us02web.zoom.us/j/86867205231?pwd=OTJVTURuVU9FVzkzR01kMVUwcGVvZz09
Speaker: Dr. Roman Krčmár (Institute of Physics, SAV)
Host: Prof. Ying-Jer Kao (Department of Physics, NTU)
Title: Ising ferromagnets and antiferromagnets in an imaginary magnetic field.
Abstract:
We will present results of our study of classical Ising spin-1/2 models on the 2D square lattice with ferromagnetic or antiferro- magnetic nearest-neighbor interactions, under the effect of a pure imaginary magnetic field. The transformations of the complex Boltzmann weights of spin configurations onto symmetric vertex models which leads to real (positive or negative) Boltzmann weights will be presented. This enables us to apply accurate numerical methods based on the real space renormalization, namely the corner transfer matrix renormalization group (CTMRG) and the higher-order tensor renormalization group (HOTRG). For the 2D antiferromagnet, the curve of critical points related to the symmetry breaking of magnetizations was calculated. The critical exponent β and the central charge c are shown to be constant along the critical line, equal to their values β = 1/8 and c = 1/2 for the 2D Ising in a zero magnetic field. The 2D ferromagnets behave in analogy with their 1D counterparts defined on a chain of sites, namely there exists a transient temperature which splits the temperature range into its high-temperature and low-temperature parts. The free energy and the magnetization are well defined in the high-temperature region. In the low-temperature region, the free energy exhibits singularities at the Yang-Lee zeros of the partition function and the magnetization is also ill-defined: it varies chaotically with the size of the system. The transient temperature is determined as a function of the imaginary magnetic field by using the fact that from the high- temperature side both the first derivative of the free energy with respect to the temperature and the magnetization diverge at this temperature.
Work was published in Physical Review E 105 054112 (2022).
Date: 11/30/2022
Time: 9:30 (Taipei time)
Venue: Zoom [Registration] is required
Zoom link: https://us02web.zoom.us/j/86867205231?pwd=OTJVTURuVU9FVzkzR01kMVUwcGVvZz09
Speaker: PhD student Hsin-Yuan Huang (Robert)
Host: Prof. Yi-Ping Huang (Department of Physics, NTHU)
Title: Provably efficient machine learning for quantum many-body problems.
Abstract: Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.
Date: 12/07/2022
Time: 10:00 (Taipei time)
Venue: Zoom [Registration] is required
Zoom link: https://us02web.zoom.us/j/86867205231?pwd=OTJVTURuVU9FVzkzR01kMVUwcGVvZz09
Speaker: Dr. Miles Stoudenmire (Flatiron Institute)
Host: Prof. Ying-Jer Kao (Department of Physics, NTU)
Title: Disentangling Interacting Systems with Gaussian Tensor Networks.
Abstract: Gaussian tensor networks are a special class of quantum circuits which are also single-particle basis transformations and map an entangled, non-interacting fermionic state to an unentangled state. We show that Gaussian tensor networks can be useful for interacting systems too. Although they no longer bring the system to an unentangled state in the presence of interactions, applying them to an interacting system can greatly reduce its entanglement. The basis transformation defined by a Gaussian tensor network can be applied to the Hamiltonian before doing any many-body computations, avoiding working with the original, highly-entangled state. We explore applications of different types of Gaussian tensor networks to impurity model systems and consider applications to computing ground state and dynamical properties.
Date: 12/14/2022
Time: 10:30 (Taipei time)
Venue: Zoom [Registration] is required
Zoom link: https://us02web.zoom.us/j/86867205231?pwd=OTJVTURuVU9FVzkzR01kMVUwcGVvZz09
Speaker: Dr. Garnet Chan (Caltech)
Host: Prof. Ying-Jer Kao (Department of Physics, NTU)
Title: Recent progress in the ab initio description of high temperature superconductors.
Abstract: I will discuss recent work towards a fully first principles description of the cuprates using quantum embedding methods.