Local spin operators for fermion simulations

  title={Local spin operators for fermion simulations},
  author={James Daniel Whitfield and Vojtvech Havl'ivcek and Matthias Troyer},
  journal={Physical Review A},
Digital quantum simulation of fermionic systems is important in the context of chemistry and physics. Simulating fermionic models on general purpose quantum computers requires imposing a fermionic algebra on qubits. The previously studied Jordan-Wigner and Bravyi-Kitaev transformations are two techniques for accomplishing this task. Here, we reexamine an auxiliary fermion construction which maps fermionic operators to local operators on qubits. The local simulation is performed by relaxing the… 

Figures from this paper

Quantum codes for quantum simulation of fermions on a square lattice of qubits
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
Lowering qubit requirements for quantum simulations of fermionic systems.
The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the
Optimal fermion-qubit mappings
Simulating fermionic systems on a quantum computer requires a high-performing mapping of fermionic states to qubits. The key characteristic of an efficient mapping is its ability to translate local
Fermion-to-qubit mappings with varying resource requirements for quantum simulation
The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the
Variational solutions to fermion-to-qubit mappings in two spatial dimensions
Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional
Quantum algorithms to simulate many-body physics of correlated fermions.
Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum
Hardware-efficient fermionic simulation with a cavity–QED system
This work shows how one can use a cavity–QED system to perform digital quantum simulation of fermionic models with qubits, and shows that highly nonlocal Jordan–Wigner or Bravyi–Kitaev transformations can be efficiently implemented through a hardware approach.
Majorana-Based Fermionic Quantum Computation.
The scheme has a lower overhead for implementing both unitary coupled cluster variational quantum eigensolver and quantum phase estimation algorithms, allowing for simulation of the Trotterized Hubbard Hamiltonian in O(1) time per unitary step.
Low Weight Fermionic Encodings for Lattice Models
We present two fermion to qubit encodings tailored to square and hexagonal lattices that preserve the locality of even fermionic operators. These encodings use fewer than 1.5 qubits per fermionic
Exponentially more precise quantum simulation of fermions in the configuration interaction representation
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As


Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed
  • 137, 224109
  • 2012
International Journal of Quantum Chemistry 115
  • 14311441
  • 2015
  • Rev. A 89, 012302
  • 2014
New J
  • Phys. 18, 033032
  • 2016
Quantum Info
  • Comput. 15, 1
  • 2015
Science 309
  • 1704
  • 2005
  • Mod. Phys. 86, 153
  • 2014
New J
  • Phys. 14, 115023
  • 2012
  • 109, 735
  • 2011