No-go theorem for one-way quantum computing on naturally occurring two-level systems
- Department of Computer Science and Technology, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing (China)
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts (United States)
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario (Canada)
- Institute for Quantum Computing and Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario (Canada)
The ground states of some many-body quantum systems can serve as resource states for the one-way quantum computing model, achieving the full power of quantum computation. Such resource states are found, for example, in spin-(5/2) and spin-(3/2) systems. It is, of course, desirable to have a natural resource state in a spin-(1/2), that is, qubit system. Here, we give a negative answer to this question for frustration-free systems with two-body interactions. In fact, it is shown to be impossible for any genuinely entangled qubit state to be a nondegenerate ground state of any two-body frustration-free Hamiltonian. What is more, we also prove that every spin-(1/2) frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states. In other words, there cannot be any interesting entanglement features in the ground state of such a qubit Hamiltonian.
- OSTI ID:
- 21546672
- Journal Information:
- Physical Review. A, Vol. 83, Issue 5; Other Information: DOI: 10.1103/PhysRevA.83.050301; (c) 2011 American Institute of Physics; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in the Variational Quantum Eigensolver