Three- and Four-Body Interactions in Spin-Based Quantum Computers

In the effort to design and to construct a quantum computer, several leading proposals make use of spin-based qubits. These designs generally assume that spins undergo pairwise interactions. We point out that, when several spins are engaged mutually in pairwise interactions, the quantitative strengths of the interactions can change and qualitatively new terms can arise in the Hamiltonian, including four-body interactions. In parameter regimes of experimental interest, these coherent effects are large enough to interfere with computation and may require new error correction or avoidance techniques.

Figure 1

Plot of the exchange constant as a function of tunneling barrier and Coulomb energy in the case of three mutually interacting electrons (dimensionless units).

Figure 2

Plot of the change in the exchange constant due to three-electron-swap matrix elements. Horizontal axes as in Fig. 1 (with their directions flipped for clarity).

Figure 3

Plot of the exchange constant in the case of four mutually interacting electrons. Horizontal axes as in Fig. 1.

Figure 4

Plot of the four-body exchange constant in the case of four mutually interacting electrons. Horizontal axes as in Fig. 1.