Measurement-Based Quantum Computation on Two-Body Interacting Qubits with Adiabatic Evolution

Abstract

A cluster state cannot be a unique ground state of a two-body interacting Hamiltonian. Here, we propose the creation of a cluster state of logical qubits encoded in spin-1/2 particles by adiabatically weakening two-body interactions. The proposal is valid for any spatial dimensional cluster states. Errors induced by thermal fluctuations and adiabatic evolution within finite time can be eliminated ensuring fault-tolerant quantum computing schemes.

Cluster state generation in one-dimensional Kitaev honeycomb model via shortcut to adiabaticity

“…The adiabatic cluster-state scheme [16] is performed by considering a system of N×n spin-1/2 particles under the Hamiltonian (ii) Nonzero interaction strength λ lifts the ground states degeneracy, resulting the system H 0 to a unique ground state with a finite energy gap above it.…”

“…Indeed, whenever we find a physical system that is in the form of (3) and satisfies the two constraints above, we are able to get around [16] the no-go theorem [13] and get cluster states with just two steps. First, we cool the system with a nonzero λ to its ground state.…”

“…Counterdiabatic driving of 1D Kitaev honeycomb model 3.1. The model Let us now put forward everything we have discussed so far within the general framework and apply to a particular model we proposed in [16] as shown in figure 1. We emphasise that our proposal to go beyond adiabatic evolution to attain cluster states, is not limited to the example model we present here.…”

“…One such proposal [7,14,15] involves the creation of cluster states with only nearest-neighbour Ising-type interactions through precise control over the time evolution. In [16], the present authors have also proposed an adiabatic scheme in which one could obtain cluster states without the need to cool a system down to a very low temperature. The essential ingredients of the proposal are as follow.…”

“…These new states could have a much smaller energy gap compared to the initial one present in the system. Thanks to the inherent stabilisers symmetry of the system, the desire ground state can be protected from noise or fluctuations in the parameter space by the finite adiabatic switching rate [16].…”