We relax one of the requirements for topological quantum computation with Majorana fermions. Topological quantum computation was discussed so far as manipulation of the wave function within degenerate many-body ground state. The simplest particles providing degenerate ground state, Majorana fermions, often coexist with extremely low-energy excitations so keeping the system in the ground state may be hard. We show that the topological protection extends to the excited states, as long as the Majorana fermions do not interact neither directly nor via the excited states. This protection relies on the fermion parity conservation and so it is generic to any implementation of Majorana fermions.We relax one of the requirements for topological quantum computation with Majorana fermions. Topological quantum computation was discussed so far as manipulation of the wave function within degenerate many-body ground state. The simplest particles providing degenerate ground state, Majorana fermions, often coexist with extremely low-energy excitations so keeping the system in the ground state may be hard. We show that the topological protection extends to the excited states, as long as the Majorana fermions do not interact neither directly nor via the excited states. This protection relies on the fermion parity conservation and so it is generic to any implementation of Majorana fermions.

arXiv:1004.5533Physical Review BJul 20, 2010106 citations

Simulating strongly interacting fermionic systems in a quantum computer

Alexandre Choquette, Panagiotis Kl. Barkoutsos, Agustín Di Paolo +4 more

Bulletin of the American Physical SocietyMar 5, 20190 citations

Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states

Philippe Corboz, Román Orús, Bela Bauer +1 more

We explain how to implement, in the context of projected entangled-pair states (PEPSs), the general procedure of fermionization of a tensor network introduced in P. Corboz and G. Vidal, Phys. Rev. B 80, 165129 (2009). The resulting fermionic PEPS, similar to previous proposals, can be used to study the ground state of interacting fermions on a two-dimensional lattice. As in the bosonic case, the cost of simulations depends on the amount of entanglement in the ground state and not directly on the strength of interactions. The present formulation of fermionic PEPS leads to a straightforward numerical implementation that allowed us to recycle much of the code for bosonic PEPS. We demonstrate that fermionic PEPS are a useful variational ansatz for interacting fermion systems by computing approximations to the ground state of several models on an infinite lattice. For a model of interacting spinless fermions, ground state energies lower than Hartree-Fock results are obtained, shifting the boundary between the metal and charge-density wave phases. For the $t\text{\ensuremath{-}}J$ model, energies comparable with those of a specialized Gutzwiller-projected ansatz are also obtained.We explain how to implement, in the context of projected entangled-pair states (PEPSs), the general procedure of fermionization of a tensor network introduced in P. Corboz and G. Vidal, Phys. Rev. B 80, 165129 (2009). The resulting fermionic PEPS, similar to previous proposals, can be used to study the ground state of interacting fermions on a two-dimensional lattice. As in the bosonic case, the cost of simulations depends on the amount of entanglement in the ground state and not directly on the strength of interactions. The present formulation of fermionic PEPS leads to a straightforward numerical implementation that allowed us to recycle much of the code for bosonic PEPS. We demonstrate that fermionic PEPS are a useful variational ansatz for interacting fermion systems by computing approximations to the ground state of several models on an infinite lattice. For a model of interacting spinless fermions, ground state energies lower than Hartree-Fock results are obtained, shifting the boundary between the metal and charge-density wave phases. For the $t\text{\ensuremath{-}}J$ model, energies comparable with those of a specialized Gutzwiller-projected ansatz are also obtained.

arXiv:0912.0646Physical Review BApr 8, 2010323 citations

Ground-state energy of the polarized dilute gas of interacting spin- 12 fermions

Piotr H. Chankowski, Jacek Wojtkiewicz

The effective field theory approach simplifies the perturbative computation of the ground-state energy of the diluted gas of repulsively interacting fermions allowing in the case of the unpolarized system to easily rederive the classic results up to the ${({k}_{\mathrm{F}}{a}_{0})}^{2}$ order (where ${k}_{\mathrm{F}}$ is the system's Fermi momentum and ${a}_{0}$ the $s$ -wave scattering length) and (with more labor) to extend it up to the order ${({k}_{\mathrm{F}}{a}_{0})}^{4}$ . The analogous expansion of the ground-state energy of the polarized gas of spin $1/2$ fermions is known only up to the ${k}_{\mathrm{F}}{a}_{0}$ order (where ${k}_{\mathrm{F}}$ stands for ${k}_{\mathrm{F}\ensuremath{\uparrow}}$ or ${k}_{\mathrm{F}\ensuremath{\downarrow}}$); the order ${({k}_{\mathrm{F}}{a}_{0})}^{2}$ contribution has been computed (analytically) only using a specific (hard-core type) interaction potential. Here we show that the effective field theory method also allows to easily obtain the order ${({k}_{\mathrm{F}}{a}_{0})}^{2}$ correction to the ground state of the polarized gas in a way applicable to all repulsive interactions.The effective field theory approach simplifies the perturbative computation of the ground-state energy of the diluted gas of repulsively interacting fermions allowing in the case of the unpolarized system to easily rederive the classic results up to the ${({k}_{\mathrm{F}}{a}_{0})}^{2}$ order (where ${k}_{\mathrm{F}}$ is the system's Fermi momentum and ${a}_{0}$ the $s$-wave scattering length) and (with more labor) to extend it up to the order ${({k}_{\mathrm{F}}{a}_{0})}^{4}$. The analogous expansion of the ground-state energy of the polarized gas of spin $1/2$ fermions is known only up to the ${k}_{\mathrm{F}}{a}_{0}$ order (where ${k}_{\mathrm{F}}$ stands for ${k}_{\mathrm{F}\ensuremath{\uparrow}}$ or ${k}_{\mathrm{F}\ensuremath{\downarrow}}$); the order ${({k}_{\mathrm{F}}{a}_{0})}^{2}$ contribution has been computed (analytically) only using a specific (hard-core type) interaction potential. Here we show that the effective field theory method also allows to easily obtain the order ${({k}_{\mathrm{F}}{a}_{0})}^{2}$ correction to the ground state of the polarized gas in a way applicable to all repulsive interactions.

arXiv:2108.00793Physical review. B./Physical review. BOct 27, 20219 citations

Fermionic One-Way Quantum Computation

曹信, 尚云

Chinese Physics LettersJan 1, 20140 citations

{({k}_{\mathrm{F}}{a}_{0})}^{2}

order (where

{k}_{\mathrm{F}}

is the system's Fermi momentum and

{a}_{0}

the

s

-wave scattering length) and (with more labor) to extend it up to the order

{({k}_{\mathrm{F}}{a}_{0})}^{4}

. The analogous expansion of the ground-state energy of the polarized gas of spin

1/2

fermions is known only up to the

{k}_{\mathrm{F}}{a}_{0}

order (where

{k}_{\mathrm{F}}

stands for ${k}_{\mathrm{F}\ensuremath{\uparrow}}$ or ${k}_{\mathrm{F}\ensuremath{\downarrow}}$); the order

{({k}_{\mathrm{F}}{a}_{0})}^{2}

contribution has been computed (analytically) only using a specific (hard-core type) interaction potential. Here we show that the effective field theory method also allows to easily obtain the order

{({k}_{\mathrm{F}}{a}_{0})}^{2}

correction to the ground state of the polarized gas in a way applicable to all repulsive interactions.