Abstract
In this paper we study the ways to use a global entangling operator to efficiently implement circuitry common to a selection of important quantum algorithms. In particular, we focus on the circuits composed with global Ising entangling gates and arbitrary addressable single-qubit gates. We show that under various circumstances the use of global operations can substantially improve the entangling gate count.
Highlights
Trapped atomic ions [1] and superconducting circuits [2] are two examples of quantum information processing (QIP) approaches that have delivered small yet already universal and fully programmable machines
We focus on minimizing the number of times an XX gate is called—be it addressable local or global, thereby targeting the most expensive resource in quantum computations using trapped ions QIP
We broke down the set of operations that benefit from global Molmer-Sorensen (GMS) gates into three subsets—those suitable for near-term demonstration, those targeted for next-generation machines, and those applying to arbitrary n
Summary
Trapped atomic ions [1] and superconducting circuits [2] are two examples of quantum information processing (QIP) approaches that have delivered small yet already universal and fully programmable machines. References [7, 17] study the ways to implement quantum algorithms efficiently on a trapped ion quantum computer with the two-qubit gates enabled by the global entangling operator, concentrating on the case featuring anywhere between two to four qubits. Computational universality of the control given by selectable two-qubit couplings and arbitrary single-qubit gates was the subject of an early foundational study establishing the upper bound of O(n34n) and the lower bound of Ω(4n) on the number of the CNOT gates required to implement an arbitrary unitary [19]. It is known how to implement the 3-qubit Toffoli gate with only three size-3 GMS gates [7, 8], whereas the best known implementation over two-qubit local addressable control requires five entangling gates [22] Motivated by this example, we look into what other important unitary transformations benefit from the control by global gates
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