Universal Simulation of Hamiltonians Using a Finite Set of Control Operations

Abstract

Any quantum system with a non-trivial Hamiltonian is able to simulate any other Hamiltonian evolution provided that a sufficiently large group of unitary control operations is available. We show that there exist finite groups with this property and present a sufficient condition in terms of group characters. We give examples of such groups in dimension 2 and 3. Furthermore, we show that it is possible to simulate an arbitrary bipartite interaction by a given one using such groups acting locally on the subsystems.

18 pages, LaTeX2e

References in corpus (5)

• Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries
• Optimal simulation of two-qubit Hamiltonians using general local operations
• Quantum control without access to the controlling interaction
• Quantum message authentication codes
• Simulating Arbitrary Pair-Interactions by a Given Hamiltonian: Graph-Theoretical Bounds on the Time Complexity

Cited by in corpus (3)

• Optimal Entanglement Generation from Quantum Operations
• Simulating Hamiltonians in Quantum Networks: Efficient Schemes and Complexity Bounds
• Quantum information science and complex quantum systems