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Quantum Circuits For Two-Dimensional Isometric Tensor Networks
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The variational quantum eigensolver (VQE) combines classical and quantum resources in order simulate classically intractable quantum states. Amongst other variables, successful VQE depends on the choice of variational ansatz for a problem Hamiltonian. We give a detailed description of a quantum circuit version of the 2D isometric tensor network (isoTNS) ansatz which we call qisoTNS. We benchmark the performance of qisoTNS on two different 2D spin 1/2 Hamiltonians. We find that the ansatz has several advantages. It is qubit efficient with the number of qubits allowing for access to some exponentially large bond-dimension tensors at polynomial quantum cost. In addition, the ansatz is robust to the barren plateau problem due emergent layerwise training. We further explore the effect of noise on the efficacy of the ansatz. Overall, we find that qisoTNS is a suitable variational ansatz for 2D Hamiltonians with local interactions.
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Cited by 1 Pith paper
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Diagonal Isometric Form for Tensor Network States in Two Dimensions
A new isometric form for 2D tensor network states uses auxiliary tensors on a 45-degree rotated lattice, enabling a local Yang-Baxter move and a TEBD algorithm that captures area-law ground states and short-time dynamics.
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