QuICS seminar

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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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.

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].

We present the first leveled fully homomorphic encryption scheme for quantum circuits with classical keys. The scheme allows a classical client to blindly delegate a quantum computation to a quantum server: an honest server is able to run the computation while a malicious server is unable to learn any information about the computation. We show that it is possible to construct such a scheme directly from a quantum secure classical homomorphic encryption scheme with certain properties.

A linear optical approach to quantum computing offers highly coherent qubits, high fidelity single qubit gates, and probabilistic entangling operations that can be implemented using well-known quantum optical methods.

The past decade of research in quantum information theory has witnessed  extraordinary progress in understanding communication over quantum channels, due in large part to quantum generalizations of the classical Renyi relative entropy. One generalization is known as the sandwiched Renyi relative entropy and finds its use in characterizing asymptotic behavior in quantum hypothesis testing. It has also found use in establishing strong converse theorems (fundamental communication capacity limitations) for a variety of quantum communication tasks.

Finding ways to connect quantum systems in a controlled and flexible fashion lies at the core of constructing quantum information processing systems. Superconducting quantum circuits present a particularly promising platform for engineering quantum systems from the ground up: the strong light-matter interactions in these circuits can readily be used to realize interactions between different components. There remain interesting questions, however, about what types of interactions we can realize.

The Hartree-Fock problem provides the conceptual and mathematical underpinning of a large portion of quantum chemistry. As efforts in quantum technology aim to enhance computational chemistry algorithms, the fundamental Hartree-Fock problem is a natural target. While quantum computers and quantum simulation offer many prospects for the future of modern chemistry, the Hartree-Fock problem is not a likely candidate.

Buhrman, Cleve and Wigderson (STOC'98) observed that for every Boolean function f : {-1, 1}^n to {-1, 1}, the two-party bounded-error quantum communication complexity of 2-bit distributed versions of f is O(Q(f) log n), where Q(f) denotes the bounded-error quantum query complexity of f. This is in contrast to the classical randomized analogue of this statement, where the log n factor is absent. A natural question is if this O(log n) factor can be avoided. Aaronson and Ambainis (FOCS'03) showed that this factor is avoidable when f = OR.

Interference is an essential part of quantum mechanics.  However, an important class of Hamiltonians considered are those with "no sign problem", where all off-diagonal matrix elements of the Hamiltonian are non-negative.  This means that the ground state wave function can be chosen to have all amplitudes real and positive.  In a sense, no destructive interference is possible for these Hamiltonians so that they are "almost classical", and there are several simulation algorithms which work well in practice on classical computers today.  In this talk, I'll discuss what ha