Efficient quantum programming using EASE gates on a trapped-ion quantum computer

Nikodem Grzesiak1, Andrii Maksymov1, Pradeep Niroula2,3, and Yunseong Nam1,4

1IonQ, College Park, MD 20740, USA
2Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD 20742, USA
3Joint Quantum Institute, University of Maryland, College Park, MD 20742, USA
4Department of Physics, University of Maryland, College Park, MD 20742, USA

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Parallel operations in conventional computing have proven to be an essential tool for efficient and practical computation, and the story is not different for quantum computing. Indeed, there exists a large body of works that study advantages of parallel implementations of quantum gates for efficient quantum circuit implementations. Here, we focus on the recently invented efficient, arbitrary, simultaneously entangling (EASE) gates, available on a trapped-ion quantum computer. Leveraging its flexibility in selecting arbitrary pairs of qubits to be coupled with any degrees of entanglement, all in parallel, we show an $n$-qubit Clifford circuit can be implemented using 6log($n$) EASE gates, an $n$-qubit multiply-controlled NOT gate can be implemented using 3$n$/2 EASE gates, and an $n$-qubit permutation can be implemented using six EASE gates. We discuss their implications to near-term quantum chemistry simulations and the state of the art pattern matching algorithm. Given Clifford + multiply-controlled NOT gates form a universal gate set for quantum computing, our results imply efficient quantum computation by EASE gates, in general.

Trapped-ion quantum computers are capable of exotic operations which entangle several qubits at once. One such powerful operation is the Efficient, Arbitrary, Simultaneously Entangling (EASE) gate. We show that EASE gates make it drastically easier to implement circuit elements for universal quantum computation: An n-qubit Clifford circuit can be applied in only 6log(n) EASE gates, an n-qubit multiply-controlled NOT gate in 3n/2 EASE gates, and an n-qubit permutation in only six EASE gates.

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