Fast Universal Quantum Computation with Railroad-switch Local Hamiltonians
arXiv:0908.4219 · doi:10.1063/1.3384661
Abstract
We present two universal models of quantum computation with a time-independent, frustration-free Hamiltonian. The first construction uses 3-local (qubit) projectors, and the second one requires only 2-local qubit-qutrit projectors. We build on Feynman's Hamiltonian computer idea and use a railroad-switch type clock register. The resources required to simulate a quantum circuit with L gates in this model are O(L) small-dimensional quantum systems (qubits or qutrits), a time-independent Hamiltonian composed of O(L) local, constant norm, projector terms, the possibility to prepare computational basis product states, a running time O(L log^2 L), and the possibility to measure a few qubits in the computational basis. Our models also give a simplified proof of the universality of 3-local Adiabatic Quantum Computation.
Added references to work by de Falco et al., and realized that Feynman's '85 paper already contained the idea of a switch in it
References in corpus (10)
- Universal computation by quantum walk
- Simple proof of equivalence between adiabatic quantum computation and the circuit model
- Realizable Hamiltonians for Universal Adiabatic Quantum Computers
- Towards Fault Tolerant Adiabatic Quantum Computation
- A new construction for a QMA complete 3-local Hamiltonian
- Quantum simulators, continuous-time automata, and translationally invariant systems
- Hamiltonian Quantum Cellular Automata in 1D
- Speed and entropy of an interacting continuous time quantum walk
- Grover's algorithm on a Feynman computer
- Entropy generation in a model of reversible computation
Cited by in corpus (20)
- Quantum many-body systems out of equilibrium
- Adiabatic Quantum Simulation of Quantum Chemistry
- Quantum algorithm for simulating real time evolution of lattice Hamiltonians
- Exploiting locality in quantum computation for quantum chemistry
- Direct certification of a class of quantum simulations
- Space-Time Circuit-to-Hamiltonian Construction and Its Applications
- Universal 2-local Hamiltonian Quantum Computing
- Adiabatic and Hamiltonian computing on a 2D lattice with simple 2-qubit interactions
- Noise-assisted quantum transport and computation
- Native three-body interaction in superconducting circuits
- A comparative study of universal quantum computing models: towards a physical unification
- Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians
- Quantum 3-SAT is QMA1-complete
- Hamiltonian quantum computing with superconducting qubits
- Universal resources for quantum computing
- Quantum walk on a chimera graph
- Circuit-to-Hamiltonian from tensor networks and fault tolerance
- Real Time Simulations of Quantum Spin Chains: Density-of-States and Reweighting approaches
- Time-dependent density functional theory for open spin chains
- Dissipative dynamics of a spin system with three-body interaction