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.
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