Simulating the Open System Dynamics of Multiple Exchange-Only Qubits using Subspace Monte Carlo

We propose a Monte Carlo based method for simulating the open system dynamics of multiple exchange-only (EO) qubits. In the EO encoding, the total z magnetization of the three constituent spins remains unchanged under ideal qubit operations, in contrast to the open system (or multi-qubit miscalibration) setting where coherent and incoherent mixing of magnetization subspaces occurs. In our approach, we choose to measure the magnetization of each EO qubit after every quantum operation, which decoheres coherent mixtures of the subspaces. Independent simulations thus give different trajectories of the system in the subspaces, so we refer to this method as the Subspace Monte Carlo method. With each EO qubit restricted to one subspace, the density matrix of n qubits can be represented by a vector of dimension 3²ⁿ instead of 8²ⁿ. We can expect this method to be inaccurate when the coherences between different subspaces affects the dynamics, and we give an example of such a case with a circuit involving two EO qubits. We show that by introducing randomized compiling into the circuit, which effectively turns coherent errors into stochastic errors, the accuracy of the method is restored. In order to highlight the scalability of the approach, we give additional examples with up to six EO qubits.