Quantum simulation of interacting fermion lattice models in trapped ions.

We propose a method of simulating efficiently many-body interacting fermion lattice models in trapped ions, including highly nonlinear interactions in arbitrary spatial dimensions and for arbitrarily distant couplings. We map products of fermionic operators onto nonlocal spin operators and decompose the resulting dynamics in efficient steps with Trotter methods, yielding an overall protocol that employs only polynomial resources. The proposed scheme can be relevant in a variety of fields such as condensed-matter or high-energy physics, where quantum simulations may solve problems intractable for classical computers.

[1]  L. Lamata,et al.  Relativistic quantum mechanics with trapped ions , 2011, 1106.6222.

[2]  T. Schaetz,et al.  Simulating a quantum magnet with trapped ions , 2008 .

[3]  J. J. Sakurai,et al.  Advanced Quantum Mechanics , 1969 .

[4]  E. Wigner,et al.  About the Pauli exclusion principle , 1928 .

[5]  R. Cleve,et al.  Efficient Quantum Algorithms for Simulating Sparse Hamiltonians , 2005, quant-ph/0508139.

[6]  T. Monz,et al.  An open-system quantum simulator with trapped ions , 2011, Nature.

[7]  R. Albers,et al.  Hubbard-U band-structure methods , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[8]  B. Lanyon,et al.  Quantum simulation of the Klein paradox with trapped ions. , 2010, Physical review letters.

[9]  Matthias Troyer,et al.  Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations , 2004, Physical review letters.

[10]  C. Monroe,et al.  Quantum dynamics of single trapped ions , 2003 .

[11]  M. Berciu,et al.  Optical conductivity of the Holstein polaron. , 2011, Physical review letters.

[12]  F. Schmidt-Kaler,et al.  Designing spin-spin interactions with one and two dimensional ion crystals in planar micro traps , 2011, 1102.3645.

[13]  D. Abrams,et al.  Simulation of Many-Body Fermi Systems on a Universal Quantum Computer , 1997, quant-ph/9703054.

[14]  C. F. Roos,et al.  Simulating open quantum systems: from many-body interactions to stabilizer pumping , 2011, 1104.2507.

[15]  R. Blatt,et al.  Quantum simulation of the Dirac equation , 2009, Nature.

[16]  B. Lanyon,et al.  Universal Digital Quantum Simulation with Trapped Ions , 2011, Science.

[17]  E. Solano,et al.  Klein tunneling and Dirac potentials in trapped ions , 2010, 1004.5400.

[18]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[19]  G. Mahan.  Many-particle physics , 1981 .

[20]  E Solano,et al.  Dirac equation and quantum relativistic effects in a single trapped ion. , 2007, Physical review letters.

[21]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[22]  E. Wigner,et al.  Über das Paulische Äquivalenzverbot , 1928 .

[23]  J. Ignacio Cirac,et al.  Simulation of quantum dynamics with quantum optical systems , 2003, Quantum Inf. Comput..

[24]  J. Kondo.  Resistance Minimum in Dilute Magnetic Alloys , 1964 .

[25]  T. Hänsch,et al.  Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms , 2002, Nature.

[26]  47 , 2014, Fetch the Devil.

[27]  R. Feynman.  Simulating physics with computers , 1999 .

[28]  J. Cirac,et al.  Effective quantum spin systems with trapped ions. , 2004, Physical Review Letters.

[29]  Lu-Ming Duan,et al.  Quantum simulation of frustrated Ising spins with trapped ions , 2010, Nature.

[30]  B. Lanyon,et al.  Towards quantum chemistry on a quantum computer. , 2009, Nature chemistry.

[31]  J Casanova,et al.  Quantum simulation of quantum field theories in trapped ions. , 2011, Physical review letters.

[32]  M. Johanning,et al.  Quantum simulations with cold trapped ions , 2009, 0905.0118.

[33]  White,et al.  Sign problem in the numerical simulation of many-electron systems. , 1990, Physical review. B, Condensed matter.

[34]  P. Zoller,et al.  A Rydberg quantum simulator , 2009, 0907.1657.

[35]  F. Verstraete,et al.  Mapping local Hamiltonians of fermions to local Hamiltonians of spins , 2005, cond-mat/0508353.