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

Abstract

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 3n/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.

Constant-cost implementations of Clifford operations and multiply controlled gates using global interactions

“…An implementation with 12n + O(1) GT gates requiring no ancilla was developed in [8], which was superseded by [10] that improved it to 6n + O(1) GT gates, still using no ancilla. Subsequently in [11] the complexity was improved to 6 log(n) + O(1) GT gates, however, with n/2 ancillae. Recently in [3], an ancilla-free, (n, 2n]-GT method was reported.…”

“…In all of these references, the kind of GT gates used were the single-angle, all-pair (drawn from a selectable subset of qubits) type. Indeed, when using a more general GT, the complexity can be improved to O(log(n)) by nesting Toffoli-m, m ≤ n, in a depth-optimal fashion with O(n) ancillae, or 3n/2 GTs with no more than seven ancillae [11]. In our work, we show how to construct a Toffoli-n using O(log * (n)) GT gates with O(log(n)) ancillae or one using 4 GT gates with O(n) ancillae, see Subsection III B.…”

“…GT gates were already used to efficiently compile quantum circuits [6][7][8][9][10][11]. To the best of our knowledge, current state of the art for an n-qubit Clifford operation employs O(log(n)) GT gates [11].…”

“…GT gates were already used to efficiently compile quantum circuits [6][7][8][9][10][11]. To the best of our knowledge, current state of the art for an n-qubit Clifford operation employs O(log(n)) GT gates [11]. While the n-controlled inverter implementation was shown to use O(n) GT gates [8,9,11], we highlight that previous contributions relied on a restricted version of the GT gates where all interactions over a given set of qubits happen simultaneously, whereas in our work, we focus on the gates that can select a subset of interactions that take place.…”

“…To the best of our knowledge, current state of the art for an n-qubit Clifford operation employs O(log(n)) GT gates [11]. While the n-controlled inverter implementation was shown to use O(n) GT gates [8,9,11], we highlight that previous contributions relied on a restricted version of the GT gates where all interactions over a given set of qubits happen simultaneously, whereas in our work, we focus on the gates that can select a subset of interactions that take place. This means that an implementation with O(log(n)) GT gates was implicitly known, based on the well-known logarithmic-depth implementation using single-and two-qubit gates.…”