49 research outputs found
Non-Abelian Braiding of Lattice Bosons
We report on a numerical experiment in which we use time-dependent potentials
to braid non-abelian quasiparticles. We consider lattice bosons in a uniform
magnetic field within the fractional quantum Hall regime, where , the
ratio of particles to flux quanta, is near 1/2, 1 or 3/2. We introduce
time-dependent potentials which move quasiparticle excitations around one
another, explicitly simulating a braiding operation which could implement part
of a gate in a quantum computation. We find that different braids do not
commute for near and , with Berry matrices respectively
consistent with Ising and Fibonacci anyons. Near , the braids commute.Comment: 5 pages, 1 figur
Exact Parent Hamiltonian for the Quantum Hall States in a Optical Lattice
We study lattice models of charged particles in uniform magnetic fields. We
show how longer range hopping can be engineered to produce a massively
degenerate manifold of single-particle ground states with wavefunctions
identical to those making up the lowest Landau level of continuum electrons in
a magnetic field. We find that in the presence of local interactions, and at
the appropriate filling factors, Laughlin's fractional quantum Hall
wavefunction is an exact many-body ground state of our lattice model. The
hopping matrix elements in our model fall off as a Gaussian, and when the flux
per plaquette is small compared to the fundamental flux quantum one only needs
to include nearest and next nearest neighbor hoppings. We suggest how to
realize this model using atoms in optical lattices, and describe observable
consequences of the resulting fractional quantum Hall physics.Comment: 4 pages, 3 figures. Published versio
S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case
A new analytic treatment of three-dimensional homogeneous Bose and Fermi
gases in the unitary limit of negative infinite scattering length is presented,
based on the S-matrix approach to statistical mechanics we recently developed.
The unitary limit occurs at a fixed point of the renormalization group with
dynamical exponent z=2 where the S-matrix equals -1. For fermions we find T_c
/T_F is approximately 0.1. For bosons we present evidence that the gas does not
collapse, but rather has a critical point that is a strongly interacting form
of Bose-Einstein condensation. This bosonic critical point occurs at n lambda^3
approximately 1.3 where n is the density and lambda the thermal wavelength,
which is lower than the ideal gas value of 2.61.Comment: 26 pages, 16 figure
Quantum Simulation of Tunneling in Small Systems
A number of quantum algorithms have been performed on small quantum
computers; these include Shor's prime factorization algorithm, error
correction, Grover's search algorithm and a number of analog and digital
quantum simulations. Because of the number of gates and qubits necessary,
however, digital quantum particle simulations remain untested. A contributing
factor to the system size required is the number of ancillary qubits needed to
implement matrix exponentials of the potential operator. Here, we show that a
set of tunneling problems may be investigated with no ancillary qubits and a
cost of one single-qubit operator per time step for the potential evolution. We
show that physically interesting simulations of tunneling using 2 qubits (i.e.
on 4 lattice point grids) may be performed with 40 single and two-qubit gates.
Approximately 70 to 140 gates are needed to see interesting tunneling dynamics
in three-qubit (8 lattice point) simulations.Comment: 4 pages, 2 figure
Effect of Doublon-Holon Binding on Mott transition---Variational Monte Carlo Study of Two-Dimensional Bose Hubbard Models
To understand the mechanism of Mott transitions in case of no magnetic
influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard
model at unit filling are studied on the square and triangular lattices, using
a variational Monte Carlo method. In trial many-body wave functions, we
introduce various types of attractive correlation factors between a
doubly-occupied site (doublon, D) and an empty site (holon, H), which play a
central role for Mott transitions, in addition to the onsite repulsive
(Gutzwiller) factor. By optimizing distance-dependent parameters, we study
various properties of this type of wave functions. With a hint from the Mott
transition arising in a completely D-H bound state, we propose an improved
picture of Mott transitions, by introducing two characteristic length scales,
the D-H binding length and the minimum D-D exclusion length
. Generally, a Mott transition occurs when becomes
comparable to . In the conductive (superfluid) state, domains of
D-H pairs overlap with each other (); thereby D and
H can propagate independently as density carriers by successively exchanging
the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors
have little importance for the Mott transition.Comment: 16 pages, 22 figures, submitted to J. Phys. Soc. Jp
Simulating Dirac fermions with Abelian and non-Abelian gauge fields in optical lattices
In this work we present an optical lattice setup to realize a full Dirac
Hamiltonian in 2+1 dimensions. We show how all possible external potentials
coupled to the Dirac field can arise from perturbations of the existing
couplings of the honeycomb lattice model, without the need of additional laser
fields. This greatly simplifies the proposed implementations, requiring only
spatial modulations of the intensity of the laser beams. We finally suggest
several experiments to observe the properties of the Dirac field in the setup
Simulating the exchange of Majorana zero modes with a photonic system
The realization of Majorana zero modes is in the centre of intense theoretical and experimental investigations. Unfortunately, their exchange that can reveal their exotic statistics needs manipulations that are still beyond our experimental capabilities. Here we take an alternative approach. Through the Jordan-Wigner transformation, the Kitaev's chain supporting two Majorana zero modes is mapped to the spin-1/2 chain. We experimentally simulated the spin system and its evolution with a photonic quantum simulator. This allows us to probe the geometric phase, which corresponds to the exchange of two Majorana zero modes positioned at the ends of a three-site chain. Finally, we demonstrate the immunity of quantum information encoded in the Majorana zero modes against local errors through the simulator. Our photonic simulator opens the way for the efficient realization and manipulation of Majorana zero modes in complex architectures
Building a Quantum Engineering Undergraduate Program
Contribution: A roadmap is provided for building a quantum engineering education program to satisfy U.S. national and international workforce needs.
Background: The rapidly growing quantum information science and engineering (QISE) industry will require both quantum-aware and quantum-proficient engineers at the bachelor\u27s level.
Research Question: What is the best way to provide a flexible framework that can be tailored for the full academic ecosystem?
Methodology: A workshop of 480 QISE researchers from across academia, government, industry, and national laboratories was convened to draw on best practices; representative authors developed this roadmap.
Findings: 1) For quantum-aware engineers, design of a first quantum engineering course, accessible to all STEM students, is described; 2) for the education and training of quantum-proficient engineers, both a quantum engineering minor accessible to all STEM majors, and a quantum track directly integrated into individual engineering majors are detailed, requiring only three to four newly developed courses complementing existing STEM classes; 3) a conceptual QISE course for implementation at any postsecondary institution, including community colleges and military schools, is delineated; 4) QISE presents extraordinary opportunities to work toward rectifying issues of inclusivity and equity that continue to be pervasive within engineering. A plan to do so is presented, as well as how quantum engineering education offers an excellent set of education research opportunities; and 5) a hands-on training plan on quantum hardware is outlined, a key component of any quantum engineering program, with a variety of technologies, including optics, atoms and ions, cryogenic and solid-state technologies, nanofabrication, and control and readout electronics