Related papers: Pseudo-randomness and Learning in Quantum Computat…
We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous…
Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which…
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…
Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects…
We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the "frame potential," which is minimized by unitary $k$-designs and measures the $2$-norm…
Random unitary matrices sampled from the uniform Haar ensemble have a number of important applications both in cryptography and in the simulation of a variety of fundamental physical systems. Since the Haar ensemble is very expensive to…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
The Quantitative Group Testing (QGT) is about learning a (hidden) subset $K$ of some large domain $N$ using a sequence of queries, where a result of a query provides information about the size of the intersection of the query with the…
Quantum expanders are a quantum analogue of expanders, and k-tensor product expanders are a generalisation to graphs that randomise k correlated walkers. Here we give an efficient construction of constant-degree, constant-gap quantum…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
Efficient methods for generating pseudo-randomly distributed unitary operators are needed for the practical application of Haar distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical…
The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…
The study of the boundary between classically simulable and computationally complex quantum dynamics is fundamental to understanding which physical resources may enable enhanced information-processing capabilities. We investigate this…
By modeling quantum chaotic dynamics with ensembles of random operators, we explore howmachine learning learning algorithms can be used to detect pseudorandom behavior in qubit systems.We analyze samples consisting of pieces of correlation…
Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics such as benchmarking the performance of quantum circuits, testing for quantum advantage, providing novel insights for many-body…
A unitary t-design is a set of unitaries that is "evenly distributed" in the sense that the average of any t-th order polynomial over the design equals the average over the entire unitary group. In various fields -- e.g. quantum information…
We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…
In this article we develop quantum algorithms for learning and testing juntas, i.e. Boolean functions which depend only on an unknown set of k out of n input variables. Our aim is to develop efficient algorithms: - whose sample complexity…
There is currently a large interest in understanding the potential advantages quantum devices can offer for probabilistic modelling. In this work we investigate, within two different oracle models, the probably approximately correct (PAC)…
We initiate a systematic study of pseudo-deterministic quantum algorithms. These are quantum algorithms that, for any input, output a canonical solution with high probability. Focusing on the query complexity model, our main contributions…