Universal Quantum Computation with Spin-$1/2$ Pairs and Heisenberg Exchange

An efficient and intuitive framework for universal quantum computation is presented that uses pairs of spin-1/2 particles to form logical qubits and a single physical interaction, Heisenberg exchange, to produce all gate operations. Only two Heisenberg gate operations are required to produce a controlled $\pi$-phase shift, compared to nineteen for exchange-only proposals employing three spins. Evolved from well-studied decoherence-free subspaces, this architecture inherits immunity from collective decoherence mechanisms. The simplicity and adaptability of this approach should make it attractive for spin-based quantum computing architectures.

Figure 1

(a) Logical qubit $Q$ formed from the $S_z=0$ subspace of two spin-1/2 physical qubits with different Landé $g$ factors $g_1$ (gray) and $g_2$ (white). Heisenberg coupling within the logical qubit is represented by a solid black line. (b) Two logical qubits coupled via Heisenberg exchange, represented by a solid gray line.

Figure 2

Scalable qubit geometries in $d=1,2$ dimensions. (a) Longitudinal $d=1$ layout. (b) Vertical $d=1$ layout. (c) Horizontal $d=2$ layout. (d) Vertical $d=2$ layout.