Entanglement at finite temperature
Entanglement is a critical resource for a useful quantum computer. There is a not a consensus on whether large-scale entanglement is physically possible, and entanglement on mixed states at non-zero temperature is poorly understood. We discuss theoretical and computable bounds on how much entropy a quantum system can tolerate and still be useful for computation, and some directions for further exploration. This is not a research talk, but rather a review of interesting results.
Extraction of many-body Chern number from a single wave function
The quantized Hall conductivity of integer and fractional quantum Hall (IQH and FQH) states is directly related to a topological invariant, the many-body Chern number. The conventional calculation of this invariant in interacting systems requires a family of many-body wave functions parameterized by twist angles in order to calculate the Berry curvature. In this work, we demonstrate how to extract the Chern number given a single many-body wave function, without knowledge of the Hamiltonian.
Implementing a fast, unbounded quantum fanout gate using power-law interactions
The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/r^α in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets.
Quantum Machine Learning: prospects and challenges
We will review recent work on Quantum Machine Learning and discuss the prospects and challenges of applying this new exciting computing paradigm to machine learning applications. We will also discuss a very recent implementation of our quantum classification algorithms on quantum hardware.
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The multi-terminal Josephson effect
Junctions of more than two superconducting terminals are required for implementing braiding operations on Majorana fermions. Moreover, such multi-terminal Josephson Junctions (JJ) were predicted to support topological state and host zero-energy quasiparticles. Unlike conventional two-terminal JJs where the value of critical current is a number, the multi-terminal JJs exhibit a novel feature – the critical current contour (CCC).
The importance of the spectral gap in estimating ground-state energies
The field of quantum Hamiltonian complexity lies at the intersection of quantum many-body physics and computational complexity theory, with deep implications to both fields. The main object of study is the LocalHamiltonian problem, which is concerned with estimating the ground-state energy of a local Hamiltonian. A major challenge in the field is to understand the complexity of the LocalHamiltonian problem in more physically natural parameter regimes.
Dynamics of Confined Domain Walls in a Quantum Simulator
Confinement is a ubiquitous mechanism in nature, whereby particles feel an attractive force that increases without bound as they separate. A prominent example is color confinement in particle physics, in which baryons and mesons are produced by quark confinement. Analogously, confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. We report the observation of magnetic domain wall confinement in an interacting spin chain with a trapped-ion quantum simulator.
Quantum advantage for computations with limited space
Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical quantum advantage, and later demonstrate it experimentally. I will discuss space-restricted computations, where input is a read-only memory and only one (qu)bit can be computed on. We show that any n-bit symmetric Boolean function can be implemented exactly through the use of quantum signal processing as a space-restricted quantum computation using O(n^2) gates.
Density functionals, Kohn-Sham potentials, and Green’s functions from a quantum computer
Solving quantum chemistry problems on the quantum computer faces several hurdles in practical implementation [1]. Nevertheless, even incremental improvements in finding exact solutions for quantum chemistry can lead to real improvements in everyday life, so exploring the capabilities for quantum computers is worthwhile. In this talk, I discuss how to export solutions from a quantum computer to a classical user as a machine learned model [2,3].
Faster Digital Quantum Simulation by Symmetry Protection
Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection.