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We consider the task of breaking down a quantum computation given as an isometry into C-NOTs and single-qubit gates, while keeping the number of C-NOT gates small. Although several decompositions are known for general isometries, here we focus on a method based on Householder reflections that adapts well in the case of sparse isometries. We show how to use this method to decompose an arbitrary isometry before illustrating that the method can lead to significant improvements in the case of sparse isometries. We also discuss the classical complexity of this method and illustrate its effectiveness in the case of sparse state preparation by applying it to randomly chosen sparse states.
We consider the decomposition of arbitrary isometries into a sequence of single-qubit and Controlled-NOT (C-NOT) gates. In many experimental architectures, the C-NOT gate is relatively expensive and hence we aim to keep the number of these as low as
Universal gate sets for quantum computing have been known for decades, yet no universal gate set has been proposed for particle-conserving unitaries, which are the operations of interest in quantum chemistry. In this work, we show that controlled sin
Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of a variati
In a recent breakthrough, Bravyi, Gosset and K{o}nig (BGK) [Science, 2018] proved that simulating constant depth quantum circuits takes classical circuits $Omega(log n)$ depth. In our paper, we first formalise their notion of simulation, which we cal
A general method to mitigate the effect of errors in quantum circuits is outlined. The method is developed in sight of characteristics that an ideal method should possess and to ameliorate an existing method which only mitigates state preparation and