Biomedical subjects

Tobias J Osborne

Publications and source records attributed to Tobias J Osborne.

5 recordsLinked to original sources

PubMed2006

General entanglement scaling laws from time evolution.

We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.

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PubMed2006

Efficient approximation of the dynamics of one-dimensional quantum spin systems.

In this Letter we show that an arbitrarily good approximation to the propagator e(itH) for a 1D lattice of n quantum spins with Hamiltonian H may be obtained with polynomial computational resources in n and the error epsilon and exponential resources in |t|. Our proof makes use of the finitely correlated state or matrix product state formalism exploited by numerical renormalization group algorithms like the density matrix renormalization group. There are two immediate consequences of this result. The first is that Vidal's time-dependent density matrix renormalization group will require only polynomial resources to simulate 1D quantum spin systems for logarithmic |t|. The second consequence is that continuous-time 1D quantum circuits with logarithmic |t| can be simulated efficiently on a classical computer, despite the fact that, after discretization, such circuits are of polynomial depth.

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PubMed2006

General monogamy inequality for bipartite qubit entanglement.

We consider multipartite states of qubits and prove that their bipartite quantum entanglement, as quantified by the concurrence, satisfies a monogamy inequality conjectured by Coffman, Kundu, and Wootters. We relate this monogamy inequality to the concept of frustration of correlations in quantum spin systems.

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PubMed2003

Quantum states far from the energy eigenstates of any local Hamiltonian.

What quantum states are possible energy eigenstates of a many-body Hamiltonian? Suppose the Hamiltonian is nontrivial, i.e., not a multiple of the identity, and L local, in the sense of containing interaction terms involving at most L bodies, for some fixed L. We construct quantum states psi which are "far away" from all the eigenstates E of any nontrivial L-local Hamiltonian, in the sense that ||psi-E|| is greater than some constant lower bound, independent of the form of the Hamiltonian.

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PubMed2002

Practical scheme for quantum computation with any two-qubit entangling gate.

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not, are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. We present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this result for systems of arbitrary finite dimension has been provided by Brylinski and Brylinski; however, their proof relies on a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical.

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