Related papers: Simplifying quantum double Hamiltonians using pert…
Perturbative gadgets are used to construct a quantum Hamiltonian whose low-energy subspace approximates a given quantum $k$-body Hamiltonian up to an absolute error $\epsilon$. Typically, gadget constructions involve terms with large…
Adiabatic quantum algorithms are often most easily formulated using many-body interactions. However, experimentally available interactions are generally two-body. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by which…
Perturbative gadgets are a tool to encode part of a Hamiltonian, usually the low-energy subspace, into a different Hamiltonian with favorable properties, for instance, reduced locality. Many constructions of perturbative gadgets have been…
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain…
Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental…
Many-body entangled systems, in particular topologically ordered spin systems proposed as resources for quantum information processing tasks, often involve highly non-local interaction terms. While one may approximate such systems through…
Continuous-time quantum hardware implementations generally lack the native capability to implement high-order terms that would facilitate efficient compilation of quantum algorithms. This limitation has, in part, motivated the development…
We present a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on…
Simple families of quantum Hamiltonians can simulate general many-body systems at arbitrary precision through the use of perturbative gadgets, however this generally requires interaction strengths spanning many orders of magnitude which…
We develop a resource efficient method by which the ground-state of an arbitrary k-local, optimization Hamiltonian can be encoded as the ground-state of a (k-1)-local optimization Hamiltonian. This result is important because adiabatic…
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-local qubit Hamiltonians with a small set of physically…
In certain scenarios, quantum annealing can be made more efficient by additional $XX$ interactions. It has been shown that the additional interactions can reduce the scaling of perturbative crossings. In traditional annealing devices these…
We construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS). Making use of perturbation gadget techniques, we define a perturbative Hamiltonian acting on the virtual…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
Perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. An effective Hamiltonian that is accurate to second order in the inverse heavy mass is derived. It contains a new…
Quantum simulations of lattice gauge theories for the foreseeable future will be hampered by limited resources. The historical success of improved lattice actions in classical simulations strongly suggests that Hamiltonians with improved…
Kitaev model has both Abelian and non-Abelian anyonic excitations. It can act as a starting point for topological quantum computation. However, this model Hamiltonian is difficult to implement in natural condensed matter systems. Here we…
NISQ era devices suffer from a number of challenges like limited qubit connectivity, short coherence times and sizable gate error rates. Thus, quantum algorithms are desired that require shallow circuit depths and low qubit counts to take…
Classical hardness-of-sampling results are largely established for random quantum circuits, whereas analog simulators natively realize time evolutions under geometrically local Hamiltonians. Does a typical such Hamiltonian already yield…
We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles…