**12 pm, October 20, 2020**

**Speaker: Xavier Gitiaux, GMU Department of Computer Science; Ian Morris, GMU Department of Physics and Astronomy**

Topic: SWAP Test for Arbitrary Number of Quantum States

Location: Zoom

QSEC’s quantum computing subgroup will organize and host a seminar series throughout the upcoming semester. These events are free and open to the public. For any questions, contact qsec@gmu.edu.

The upcoming seminar on Tuesday October 20 will be given by Mr. Xavier Gitiaux of GMU Computer Science and Mr. Ian Morris of GMU Physics and Astronomy. This work is jointly advised by GMU Professors Ming Tian of Physics and Maria Emelianenko of Math. Below is the abstract of the talk and meeting information:

**Title: SWAP Test for Arbitrary Number of Quantum States**

**Abstract**

SWAP test is a useful primitive in quantum computing: for example, it allows estimating the inner product between two quantum states or the distance between two vectors of classical data. To date, SWAP test have been only implemented between two quantum states at a time. We study how to extend the SWAP test to an arbitrary number n of quantum states. We first design a genetic algorithm that constructs circuits for an arbitrary but small number of quantum states (n=5 to 15) using combination of single-control CSWAP and Hadamard gates. However, when expanded to an arbitrary large number n of quantum gates, these circuits would require a number of copies of quantum states that is exponential in n. Our approach based on single-control CSWAP gates would be outperformed by a naive approach that treats each pair of quantum states separately and requires only a polynomial number of copies of the quantum states. This observation motivates the use and optimization of multi-control CSWAP gates that would allow to execute the SWAP test for each of the n(n-1)/2 pairs with a linear number of copies of the quantum states.

**Meeting Information**

Join Zoom Meeting ID:934 6880 2063

https://gmu.zoom.us/j/93468802063