Synthesis of and compilation with time-optimal multi-qubit gates

TL;DR

This paper presents a method to synthesize and compile time-optimal multi-qubit entangling gates for quantum computers with fixed Ising interactions, enabling efficient implementation of complex quantum algorithms.

Contribution

The authors develop a time-optimal synthesis method for multi-qubit gates in fixed-interaction quantum systems and demonstrate its application to various quantum algorithms.

Findings

Gate time scales approximately linearly with the number of qubits.

Any Clifford circuit on n qubits can be implemented with at most 2n multi-qubit gates.

Efficient compilation of quantum Fourier transform and molecular dynamics simulation.

Abstract

We develop a method to synthesize a class of entangling multi-qubit gates for a quantum computing platform with fixed Ising-type interaction with all-to-all connectivity. The only requirement on the flexibility of the interaction is that it can be switched on and off for individual qubits. Our method yields a time-optimal implementation of the multi-qubit gates. We numerically demonstrate that the total multi-qubit gate time scales approximately linear in the number of qubits. Using this gate synthesis as a subroutine, we provide compilation strategies for important use cases: (i) we show that any Clifford circuit on $n$ qubits can be implemented using at most $2n$ multi-qubit gates without requiring ancilla qubits, (ii) we decompose the quantum Fourier transform in a similar fashion, (iii) we compile a simulation of molecular dynamics, and (iv) we propose a method for the compilation of diagonal unitaries with time-optimal multi-qubit gates, as a step towards general unitaries. As motivation, we provide a detailed discussion on a microwave controlled ion trap architecture with magnetic gradient induced coupling (MAGIC) for the generation of the Ising-type interactions.