Quantum codes for quantum simulation of fermions on a square lattice of qubits

Mark Steudtner, Stephanie Wehner

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)
138 Downloads (Pure)


Quantum simulation of fermionic systems is a promising application of quantum computers, but to program them, we need to map fermionic states and operators to qubit states and quantum gates. While quantum processors may be built as two-dimensional qubit networks with couplings between nearest neighbors, standard fermion-To-qubit mappings do not account for that kind of connectivity. In this work we concatenate the (one-dimensional) Jordan-Wigner transform with specific quantum codes defined under the addition of a certain number of auxiliary qubits. This yields a class of mappings with which any fermionic system can be embedded in a two-dimensional qubit setup, fostering scalable quantum simulation. Our technique is demonstrated on the two-dimensional Fermi-Hubbard model, which we transform into a local Hamiltonian. What is more, we adapt the Verstraete-Cirac transform and Bravyi-Kitaev superfast simulation to the square lattice connectivity and compare them to our mappings. An advantage of our approach in this comparison is that it allows us to encode and decode a logical state with a simple unitary quantum circuit.

Original languageEnglish
Article number022308
Number of pages32
JournalPhysical Review A
Issue number2
Publication statusPublished - 2019


  • Quantum algorithms
  • Quantum computation
  • Quantum simulation
  • Quantum Information

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