276 research outputs found
Systematic DFT Frames: Principle, Eigenvalues Structure, and Applications
Motivated by a host of recent applications requiring some amount of
redundancy, frames are becoming a standard tool in the signal processing
toolbox. In this paper, we study a specific class of frames, known as discrete
Fourier transform (DFT) codes, and introduce the notion of systematic frames
for this class. This is encouraged by a new application of frames, namely,
distributed source coding that uses DFT codes for compression. Studying their
extreme eigenvalues, we show that, unlike DFT frames, systematic DFT frames are
not necessarily tight. Then, we come up with conditions for which these frames
can be tight. In either case, the best and worst systematic frames are
established in the minimum mean-squared reconstruction error sense. Eigenvalues
of DFT frames and their subframes play a pivotal role in this work.
Particularly, we derive some bounds on the extreme eigenvalues DFT subframes
which are used to prove most of the results; these bounds are valuable
independently
Quantum simulations of Fermionic Hamiltonians with efficient encoding and ansatz schemes
We propose a computational protocol for quantum simulations of Fermionic
Hamiltonians on a quantum computer, enabling calculations which were previously
not feasible with conventional encoding and ansatses of variational quantum
eigensolvers (VQE). We combine a qubit-efficient encoding scheme mapping Slater
determinants onto qubits with a modified qubit-coupled cluster ansatz and
noise-mitigation techniques. Our strategy leads to a substantial improvement in
the scaling of circuit gate counts and to a decrease in the number of required
variational parameters, thus increasing the resilience to noise. We present
results for spin defects of interest for quantum technologies, going beyond
minimum models for the negatively charged nitrogen vacancy center in diamond
and the double vacancy in 4H silicon carbide (4H-SiC) and tackling a defect as
complex as negatively charged silicon vacancy in 4H-SiC for the first time.Comment: 36 pages, 8 figure
Practical Quantum Chemistry on Near Term Quantum Computers
Solutions to the time-independent Schrödinger equation for molecular systems allow chemical properties to be studied without the direct need for the material. However, the dimension of this problem grows exponentially with the size of the quantum system under consideration making conventional treatment intractable. Quantum computers can efficiently represent and evolve quantum states. Their use offers a possible way to perform simulations on molecules previously impossible to model. However, given the constraints of current quantum computers even studying small systems is limited by the number of qubits, circuit depth and runtime of a chosen quantum algorithm. The work in this thesis is to explore and provide new tools to make chemical simulation more practical on near-term devices. First, the unitary partitioning measurement reduction strategy is explored. This reduces the runtime of the variational quantum eigensolver algorithm (VQE). We then apply this reduction technique to the contextual subspace method, which approximates a problem by introducing artificial symmetries based on the solution of noncontextual version of the problem that reduces the number of qubits required for simulation. We provide a modification to the original algorithm that makes an exponentially scaling part of the technique quadratic. Finally, we develop the projection-based embedding (PBE) technique to allow chemical systems to be studied using state-of-the-art classical methods in conjuncture with quantum computing protocols in a multiscale hierarchy. This allows molecular problems much larger than conventionally studied on quantum hardware to be approached
Cellular, Wide-Area, and Non-Terrestrial IoT: A Survey on 5G Advances and the Road Towards 6G
The next wave of wireless technologies is proliferating in connecting things
among themselves as well as to humans. In the era of the Internet of things
(IoT), billions of sensors, machines, vehicles, drones, and robots will be
connected, making the world around us smarter. The IoT will encompass devices
that must wirelessly communicate a diverse set of data gathered from the
environment for myriad new applications. The ultimate goal is to extract
insights from this data and develop solutions that improve quality of life and
generate new revenue. Providing large-scale, long-lasting, reliable, and near
real-time connectivity is the major challenge in enabling a smart connected
world. This paper provides a comprehensive survey on existing and emerging
communication solutions for serving IoT applications in the context of
cellular, wide-area, as well as non-terrestrial networks. Specifically,
wireless technology enhancements for providing IoT access in fifth-generation
(5G) and beyond cellular networks, and communication networks over the
unlicensed spectrum are presented. Aligned with the main key performance
indicators of 5G and beyond 5G networks, we investigate solutions and standards
that enable energy efficiency, reliability, low latency, and scalability
(connection density) of current and future IoT networks. The solutions include
grant-free access and channel coding for short-packet communications,
non-orthogonal multiple access, and on-device intelligence. Further, a vision
of new paradigm shifts in communication networks in the 2030s is provided, and
the integration of the associated new technologies like artificial
intelligence, non-terrestrial networks, and new spectra is elaborated. Finally,
future research directions toward beyond 5G IoT networks are pointed out.Comment: Submitted for review to IEEE CS&
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