Three-qubit entangling gates with simultaneous exchange controls in spin qubit systems

TL;DR

This work tackles the overhead of entangling spin qubits using pairwise exchange gates by introducing a multi-qubit entangling gate that simultaneously modulates multiple exchange couplings. It derives an exact three-qubit time-evolution unitary, U3, for three spins in linear or triangular geometries and shows how to compose it with single-qubit rotations to realize GHZ and W states as well as the Toffoli gate with considerably fewer operations. The approach reduces circuit depth and operation counts compared with conventional two-qubit gate decompositions, offering a scalable path toward more coherent spin-qubit processors. The authors also discuss extending the method to more qubits and other qubit platforms, highlighting broad potential impact for efficient quantum circuit synthesis.

Abstract

Pairwise exchange couplings have long been the standard mechanism for entangling spin qubits in semiconductor systems. However, implementing quantum circuits based on pairwise exchange gates often requires a lengthy sequence of elementary gate operations. In this work, we present an alternative approach: multi-qubit entangling gate operations that simultaneously drive the exchange couplings between multiple pairs of spin qubits. We explore three spin qubit systems in linear or triangular configurations. We derive analytical expressions for these multi-exchange entangling operations and demonstrate how to use the resulting three-qubit gates to construct quantum circuits capable of generating standard entangled states such as GHZ and W states, and the Toffoli gate, by optimizing control parameters. Our results show that this multi-qubit strategy significantly reduces the number of required operations, offering a pathway to more efficient, shallower, and more coherent circuits for spin-qubit processors.

Figures (4)

• Figure 1: Two geometries of three spin qubit systems, (a) linear geometry and (b) triangular geometry. Each neighboring pair of spins are coupled by an exchange interaction.
• Figure 2: A quantum circuit utilizing the three-qubit entangling gate. The three-qubit gate is sandwiched by layers of single-qubit gates, and it is repeated as many times as necessary. All single-qubit gates and three-qubit gates will be individually optimized for the circuit to perform a given task.
• Figure 3: Standard quantum circuits for generating entangled three-qubit states. (a) A circuit for the three-qubit GHZ state, $|GHZ\rangle_3 = \left( |000\rangle + |111\rangle \right) / \sqrt{2}$. (b) A circuit for the three-qubit W state, $|W\rangle_3 = \left( |001\rangle + |010\rangle + |100\rangle \right) / \sqrt{3}$. $\phi_3=2\cos^{-1}({1/\sqrt{3}})$. (c) A circuit that encodes a three-qubit bit-flip error correction code.
• Figure 4: A quantum circuit that implements the Toffoli gate using single-qubit gates and two-qubit CNOT gates Nielsen_ChuangToffoli_circuit.