Chris Pollett > Students > Yunxuan

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    [First Proposal]

    [Final Step of Shor's and Grover's Algorithms]

    [jQuantum QFT]

    [My Quantum Circuits]

    [Three Models]

    [Threshold of Error Correction]

    [jQuantum Manual]

    [Quantum State and LH]

    [QHC Scientists]

    [LH and Tensor Networks]

    [k-LH is QMA-complete]

    [Deutch Josza Algorithm]

    [Semester Report]

    [Second Proposal]

    [SolveQ Algorithm: 2-SAT]

    [Random-kSAT-Generator: Version 1]

    [Freezing Point Experiment]

    [Random-kQSAT-Generator: Version 2]

    [Random-kQSAT-Generator: Version 3]

    [Antiferromagnetic Heisenberg Model]

    [Ising Model]

    [Random-kQSAT-Generator: Version 4]

    [Random-kQSAT-Generator: Version 5]

    [Random-kQSAT-Generator: Version 6]

    [SolveQ Algorithm: 2-QSAT]


Recent Discoveries in Quantum Hamiltonian Complexity

  • Kitaev proved that k-LH is in QMA for k>=1 and QMA-hard for k>=5.
  • Oliveira and Terhal showed that LH with Hamiltonians restricted to nearest neighbor interaction on a 2D grid is still QMA-complete.
  • Aharonov, Gottesman, Irani and Kempe showed that 2-LH with nearest neighbor interactions on the line is also QMA complete if the local system have dimension of at least 12.
  • Cubitt and Montanaro established a quantum variant of Schaefers Dichotomy Theorem.
  • Bravyi defined Quantum k-SAT in which all local constraints are positive semidefinite, and the question is whether the ground state energy is zero.
  • Aharonov and Eldar proved that approximating the ground state energy of commuting local Hamiltonians on good locally-expanding graphs is in NP.
  • Gharibian, Landau, Shin and Wang showed that the commuting variant of the Stoquastic k-SAT problem is in NP for logarithmic k and any constant d.
  • Yan and Bacon showed that LH with all commuting terms are products of Pauli operators is in P.
  • Schuch and Verstraete showed that Hubbard Model has QMA hardness.
  • Bravyi has given a Fully Polynomial Randomized Approximation Scheme for approximating the partition function of the transverse field Ising model.
  • Baharonas works showed that finding a ground state and computing the magnetic partition function of an Ising spin glass in a nonuniform magnetic field are NP hard tasks.
  • Whites discovered his celebrated Density Matrix Renormalization Group.
  • Verstraete and Cirac Projected entangled pair states
  • Schuch, Wolf, Verstraete and Cirac found that MPS and MERA networks can be efficiently contracted.
  • Arad, Kitaev, Landau, Vazirani showed that MPS with sublinear bond dimension suffices to approximate the ground state.
  • A combinatorial proof improving on Hastings result for the frustration-free case was later given by Aharonov, Arad, Landau and Vazarani.
  • Cubitt, Perez, Garcia, Wolf showed that determining whether a translational-invariant, nearest-neighbor Hamiltonian on a 2D square lattice is gapped is undecidable.
  • Gosset, Terhal, and Vershynina showed how to perform universal adiabatic quantum computation using space-time circuit-to-Hamiltonian construction.
  • Fitzsimons and Vidick gave a multiprover interactive proof system for the Local Hamiltonian problem involving a constant number of entangled provers.
  • Chubb and Flamia extended the works of Landau, Vazirani and Vidick and Huang to give a polynomial time algorithm for approximating ground space projectors of gapped 1D Hamiltonians with degenerate groun spaces.
  • Gharibian and Sikora showed that given a local Hamiltonian and two ground states, is there a sequence of local unitaries mapping between the two states.
  • Ge and Eisert showed that in two and higher dimensions, it is not general true that an area law for the Renyi entanglement entropy implies the ability to faithfully describe a quantum many-body state by an efficient tensor network.
  • Aharonov showed that a generalized version of the area law fails to hold.
  • Movassah and Shor showed that a generalization of Bravyis spin-1 model to integer spin-s chains yields a power law violation of the area law.
  • Brandao and Cramer showed that the exponential decay in the specific heat capacity at low temperatures yields an area law for low-energy states
  • Marien proved that the stability of the area law for entanglement entropy in quantum spin systems in the setting of adiabatic and quasi-adiabatic evolutions.