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Bulletin of the American Physical Society

Universal Matchgate Quantum Computing With Cold Polar Molecules

Felipe Herrera

Published Mar 5, 2015• 0 citations
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Implementing a scalable quantum information processor using polar molecules in optical lattices requires precise control over the long-range dipole-dipole interaction between molecules in selected lattice sites.We present here a scheme using trapped open-shell Σ 2 polar molecules that allows dipolar exchange processes between nearest and next-nearest neighbors to be controlled in order to construct a generalized transverse Ising spin Hamiltonian with tunable XX, YY and XY couplings in the rotating frame of the driving lasers.The scheme requires a moderately strong bias magnetic field together with near-infrared light to provide local tuning of the qubit energy gap, and mid-infrared pulses to perform rotational state transfer via stimulated Raman adiabatic passage.No interaction between qubits occurs in the absence of the infrared driving.We analyze the fidelity of the resulting two-qubit matchgate, and demonstrate its robustness as a function of the driving parameters.We discuss a realistic application of the system for universal matchgate quantum computing in optical lattices.

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Extending matchgates to universal quantum computation via the Hubbard model

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Quantum circuits solely comprising matchgates can perform nontrivial (but nonuniversal) quantum algorithms. Because matchgates can be mapped to noninteracting fermions, these circuits can be efficiently simulated on a classical computer. Universal quantum computation is attainable by adding any nonmatchgate parity-preserving gate, from which one may infer that interacting fermions are natural candidates for universal quantum computation. We consider the quantum computational power of fermions hopping on a one-dimensional double-well lattice within the context of matchgates. In particular, we show that universal quantum computation can be implemented using spinless (spin-polarized) fermions and nearest-neighbor interactions, as well as with spin-half fermions with on-site interactions (i.e., the Hubbard model). We suggest that these schemes are currently within reach in the context of ultracold atomic gases.

Physical Review A•Nov 19, 2019•3 citations
Implementing a scalable quantum information processor using polar molecules in optical lattices requires precise control over the long-range dipole-dipole interaction between molecules in selected lattice sites.We present here a scheme using trapped open-shell Σ 2 polar molecules that allows dipolar exchange processes between nearest and next-nearest neighbors to be controlled in order to construct a generalized transverse Ising spin Hamiltonian with tunable XX, YY and XY couplings in the rotating frame of the driving lasers.The scheme requires a moderately strong bias magnetic field together with near-infrared light to provide local tuning of the qubit energy gap, and mid-infrared pulses to perform rotational state transfer via stimulated Raman adiabatic passage.No interaction between qubits occurs in the absence of the infrared driving.We analyze the fidelity of the resulting two-qubit matchgate, and demonstrate its robustness as a function of the driving parameters.We discuss a realistic application of the system for universal matchgate quantum computing in optical lattices.
Quantum circuits solely comprising matchgates can perform nontrivial (but nonuniversal) quantum algorithms. Because matchgates can be mapped to noninteracting fermions, these circuits can be efficiently simulated on a classical computer. Universal quantum computation is attainable by adding any nonmatchgate parity-preserving gate, from which one may infer that interacting fermions are natural candidates for universal quantum computation. We consider the quantum computational power of fermions hopping on a one-dimensional double-well lattice within the context of matchgates. In particular, we show that universal quantum computation can be implemented using spinless (spin-polarized) fermions and nearest-neighbor interactions, as well as with spin-half fermions with on-site interactions (i.e., the Hubbard model). We suggest that these schemes are currently within reach in the context of ultracold atomic gases.