Quantum Lunch: Quantum Circuits for Isometries – University of Copenhagen

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Quantum Lunch: Quantum Circuits for Isometries

Title: Quantum Circuits for Isometries

Speaker: Raban Iten

Abstract: Every quantum operation can be decomposed into a sequence of single-qubit and Controlled-Not (C-NOT) gates. In many experimental architectures, single-qubit gates are relatively ‘cheap’ to perform compared to C-NOTs (for instance, being less susceptible to noise), and hence it is desirable to minimize the number of C-NOT gates required to implement a circuit. I will consider the task of constructing an arbitrary isometry from m qubits to n qubits, while trying to minimize the number of C-NOT gates required.  I will show a lower bound and then give an explicit gate decomposition that gets within a factor of about two of this bound. Through Stinespring’s theorem this points to a C-NOT-efficient way to perform an arbitrary quantum operation.