Spin-1/2 particles moving on a 2D lattice with nearest-neighbor interactions can realize an autonomous quantum computer

Abstract

What is the simplest Hamiltonian which can implement quantum computation without requiring any control operations during the computation process? In a previous paper we have constructed a 10-local finite-range interaction among qubits on a 2D lattice having this property. Here we show that pair-interactions among qutrits on a 2D lattice are sufficient, too, and can also implement an ergodic computer where the result can be read out from the time average state after some post-selection with high success probability. Two of the 3 qutrit states are given by the two levels of a spin-1/2 particle located at a specific lattice site, the third state is its absence. Usual hopping terms together with an attractive force among adjacent particles induce a coupled quantum walk where the particle spins are subjected to spatially inhomogeneous interactions implementing holonomic quantum computing. The holonomic method ensures that the implemented circuit does not depend on the time needed for the walk. Even though the implementation of the required type of spin-spin interactions is currently unclear, the model shows that quite simple Hamiltonians are powerful enough to allow for universal quantum computing in a closed physical system.

More detailed explanations including description of a programmable version. 44 pages, 12 figures, latex. To appear in PRA

References in corpus (10)

• The cold atom Hubbard toolbox
• Exponential algorithmic speedup by quantum walk
• Long-range quantum entanglement in noisy cluster states
• Reversible quantum cellular automata
• Computation by measurements: a unifying picture
• A quantum cellular automaton for universal quantum computation
• A universally programmable Quantum Cellular Automaton
• A Random Matrix Model of Adiabatic Quantum Computing
• Quantum Register Physics
• Exact solutions for a universal set of quantum gates on a family of iso-spectral spin chains

Cited by in corpus (18)

• Adiabatic Quantum Computing
• Universal computation by quantum walk
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Hamiltonian Quantum Cellular Automata in 1D
• Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction
• Adiabatic and Hamiltonian computing on a 2D lattice with simple 2-qubit interactions
• Time Independent Universal Computing with Spin Chains: Quantum Plinko Machine
• Local Hamiltonians in Quantum Computation
• A comparative study of universal quantum computing models: towards a physical unification
• Universal quantum walks and adiabatic algorithms by 1D Hamiltonians
• Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference
• A single-shot measurement of the energy of product states in a translation invariant spin chain can replace any quantum computation
• Hamiltonian quantum computing with superconducting qubits
• Universal resources for quantum computing
• Time independent quantum circuits with local interactions
• Is there a physically universal cellular automaton or Hamiltonian?
• Does universal controllability of physical systems prohibit thermodynamic cycles?
• A PromiseBQP-complete String Rewriting Problem