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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 possible. We derive a theoretical lower bound on the number of C-NOT gates required to decompose an arbitrary isometry from m to n qubits, and give three explicit gate decompositions that achieve this bound up to a factor of about two in the leading order. We also perform some bespoke optimizations for certain cases where m and n are small. In addition, we show how to apply our result for isometries to give decomposition schemes for arbitrary quantum operations and POVMs via Stinesprings theorem. These results will have an impact on experimental efforts to build a quantum computer, enabling them to go further with the same resources.
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 m
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