8 research outputs found
Preparing thermal states of quantum systems by dimension reduction
We present an algorithm that prepares thermal Gibbs states of one dimensional
quantum systems on a quantum computer without any memory overhead, and in a
time significantly shorter than other known alternatives. Specifically, the
time complexity is dominated by the quantity , where is the
size of the system, is a bound on the operator norm of the local terms
of the Hamiltonian (coupling energy), and is the temperature. Given other
results on the complexity of thermalization, this overall scaling is likely
optimal. For higher dimensions, our algorithm lowers the known scaling of the
time complexity with the dimension of the system by one.Comment: Published version. Minor editorial changes, one new reference added.
4 pages, 1 figur
Anyonic entanglement renormalization
We introduce a family of variational ansatz states for chains of anyons which
optimally exploits the structure of the anyonic Hilbert space. This ansatz is
the natural analog of the multi-scale entanglement renormalization ansatz for
spin chains. In particular, it has the same interpretation as a coarse-graining
procedure and is expected to accurately describe critical systems with
algebraically decaying correlations. We numerically investigate the validity of
this ansatz using the anyonic golden chain and its relatives as a testbed. This
demonstrates the power of entanglement renormalization in a setting with
non-abelian exchange statistics, extending previous work on qudits, bosons and
fermions in two dimensions.Comment: 19 pages, 10 figures, v2: extended, updated to match published
versio
Coarse grained belief propagation for simulation of interacting quantum systems at all temperatures
We continue our numerical study of quantum belief propagation initiated in
[Phys. Rev. A, 77 (2008), p. 052318]. We demonstrate how the method can be
expressed in terms of an effective thermal potential that materializes when the
system presents quantum correlations, but is insensitive to classical
correlations. The thermal potential provides an efficient means to assess the
precision of belief propagation on graphs with no loops. We illustrate these
concepts using the one-dimensional quantum Ising model and compare our results
with exact solutions. We also use the method to study the transverse field
quantum Ising spin glass for which we obtain a phase diagram that is largely in
agreement with the one obtained in [arXiv:0706.4391] using a different
approach. Finally, we introduce the coarse grained belief propagation (CGBP)
algorithm to improve belief propagation at low temperatures. This method
combines the reliability of belief propagation at high temperatures with the
ability of entanglement renormalization to efficiently describe low energy
subspaces of quantum systems with local interactions. With CGBP, thermodynamic
properties of quantum systems can be calculated with a high degree of accuracy
at all temperatures.Comment: updated references and acknowledgement
Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs
Belief propagation -- a powerful heuristic method to solve inference problems
involving a large number of random variables -- was recently generalized to
quantum theory. Like its classical counterpart, this algorithm is exact on
trees when the appropriate independence conditions are met and is expected to
provide reliable approximations when operated on loopy graphs. In this paper,
we benchmark the performances of loopy quantum belief propagation (QBP) in the
context of finite-tempereture quantum many-body physics. Our results indicate
that QBP provides reliable estimates of the high-temperature correlation
function when the typical loop size in the graph is large. As such, it is
suitable e.g. for the study of quantum spin glasses on Bethe lattices and the
decoding of sparse quantum error correction codes.Comment: 5 pages, 4 figure
General Issues Connecting Flavor Symmetry and Supersymmetry
We motivate and construct supersymmetric theories with continuous flavor
symmetry, under which the electroweak Higgs doublets transform non-trivially.
Flavor symmetry is spontaneously broken at a large mass scale in a sector of
gauge-singlet fields; the light Higgs multiplets naturally emerge as special
linear combinations that avoid acquiring the generic large mass. Couplings of
the light Higgs doublets to light moduli fields from the singlet sector could
lead to important effects in the phenomenology of the Higgs sector.Comment: 5 page
Simulation of Strongly Correlated Quantum Many-Body Systems
In this thesis, we address the problem of solving for the properties of interacting quantum many-body systems in thermal equilibrium. The complexity of this problem increases exponentially with system size, limiting exact numerical simulations to very small systems. To tackle more complex systems, one needs to use heuristic algorithms that approximate solutions to these systems. Belief propagation is one such algorithm that we discuss in chapters 2 and 3. Using belief propagation, we demonstrate that it is possible to solve for static properties of highly correlated quantum many-body systems for certain geometries at all temperatures. In chapter 4, we generalize the multiscale renormalization ansatz to the anyonic setting to solve for the ground state properties of anyonic quantum many-body systems. The algorithms we present in chapters 2, 3, and 4 are very successful in certain settings, but they are not applicable to the most general quantum mechanical systems. For this, we propose using quantum computers as we discuss in chapter 5. The dimension reduction algorithm we consider in chapter 5 enables us to prepare thermal states of any quantum many-body system on a quantum computer faster than any previously known algorithm. Using these thermal states as the initialization of a quantum computer, one can study both static and dynamic properties of quantum systems without any memory overhead
Simulation of Strongly Correlated Quantum Many-Body Systems
Copyright notice and joint work: Chapters 1, 2, and 3 contain material from [1], [2] and [3], and are joint work with David Poulin. Chapter 4 is from [3] and is joint work with Robert König. Chapter 5 contains material from [4] and is joint work with Sergio Boixo. copyrighted by the American Physical Society. All articles referenced above are c ○ 201