Related papers: Pseudo-randomness and Learning in Quantum Computat…

Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in…

We prove that local random quantum circuits acting on n qubits composed of O(t^{10} n^2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design…

The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically…

Neural networks have achieved impressive breakthroughs in both industry and academia. How to effectively develop neural networks on quantum computing devices is a challenging open problem. Here, we propose a new quantum neural network model…

Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements. In this…

Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including…

Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum…

Bell sampling is a simple yet powerful measurement primitive that has recently attracted a lot of attention, and has proven to be a valuable tool in studying stabiliser states. Unfortunately, however, it is known that Bell sampling fails…

As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…

We introduce the Non-commutative Subset Convolution - a convolution of functions useful when working with determinant-based algorithms. In order to compute it efficiently, we take advantage of Clifford algebras, a generalization of…

Quantum computing is a promising candidate for accelerating machine learning tasks. Limited by the control accuracy of current quantum hardware, reducing the consumption of quantum resources is the key to achieving quantum advantage. Here,…

We present an algorithm for performing quantum process tomography on an unknown $n$-qubit unitary $C$ from the Clifford group. Our algorithm uses Bell basis measurements to deterministically learn $C$ with $4n + 3$ queries, which is the…

Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum…

This paper explores the representation of quantum computing in terms of unitary reflections (unitary transformations that leave invariant a hyperplane of a vector space). The symmetries of qubit systems are found to be supported by…

Unitary $k$-designs are central to quantum information and quantum many-body physics as efficient proxies for Haar-random dynamics. We study how chaotic Hamiltonian evolution can generate unitary $k$-designs. Standard approaches typically…

For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…

Uniformly random unitaries, i.e. unitaries drawn from the Haar measure, have many useful properties, but cannot be implemented efficiently. This has motivated a long line of research into random unitaries that "look" sufficiently Haar…

This paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in…

It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…

Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose…