Quantum computers have shown promise in simulating quantum many-body physics, even under the constraints that arise due to limitations in the number of qubits involved. Considering the effects of tunneling, backscattering and the accumulation of a geometric phase, we see the possibility of simulating weak anti-localization (WAL), in addition to the weak localization in a multi-path system. We show how a quantum simulator works through the construction of multiple scattering centers in closed paths and tunnel barriers yielding a large return probability (Pr) for electrons. A combination of inter- and intra-layer tunneling in a double-path circuit creates a phase reversal and subsequently the WAL effect. Incorporation of such arrangements of tunnel barriers can add a geometric phase and demonstrate Aharonov–Bohm-type Φ0 and Φ0/2 oscillations in a ring and a tube, respectively. Finally, the angle dependence of Pr shows a phase reversal in the two-path circuit caused by the inter-path resonance.

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The holonomic approach to controlling (nitrogen-vacancy) NV-center qubits provides an elegant way of theoretically devising universal quantum gates that operate on qubits via calculable microwave pulses. There is, however, a lack of simulated results from the theory of holonomic control of quantum registers with more than two qubits describing the transition between the dark states. Considering this, we have been experimenting with the IBM Quantum Experience technology to determine the capabilities of simulating holonomic control of NV-centers for three qubits describing an eight-level system that produces a non-Abelian geometric phase. The tunability of the geometric phase via the detuning frequency is demonstrated through the high fidelity (~85%) of three-qubit off-resonant holonomic gates over the on-resonant ones. The transition between the dark states shows the alignment of the gate’s dark state with the qubit’s initial state hence decoherence of the multi-qubit system is well-controlled through a π/3 rotation.