Abstract
Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated, also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundaries. We show how maintaining particle-hole symmetry when sampling through the Brillouin zone is critical to obtaining high accuracy. This work illustrates how topological protection intrinsic to a quantum model can be employed to perform robust calculations on NISQ hardware, when one measures the appropriate protected quantum properties. It opens the door for further simulation of topological quantum models on quantum hardware available today.
Highlights
Kitaev-inspired models and exact solvabilityBased on the seminal work by Kitaev [15], significant effort was made to generalize the exact solution procedures to other strongly correlated spin models [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]
Quantum computers are fragile and susceptible to rapid decoherence [1], and the use of topological protection has been proposed as a potential remedy
By using a particlehole symmetry-preserving methodology that includes high-symmetry points in the Brillouin zone, the simulation identifies the quantum phase diagram of both the Kitaev spin chain and the original Kitaev honeycomb model for systems larger than are otherwise possible on NISQ hardware
Summary
Based on the seminal work by Kitaev [15], significant effort was made to generalize the exact solution procedures to other strongly correlated spin models [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41]. As long as we are interested in ground states of the model, the z-component coupling terms can be treated as if they are only quadratic (in terms of γ Majorana fermions) and the quadratic in the η fermions can be replaced by the constant gauge field value. In the Appendix D, one additional example of applying our approach to the 1D BCSHubbard model is provided
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