Entangling Power and Quantum Circuit Complexity

Entangling power of permutation-invariant quantum states

We investigate the von Neumann entanglement entropy as function of the size of a subsystem for permutation invariant ground states in models with finite number of states per site, e.g., in quantum spin models. We demonstrate that the entanglement entropy of n sites in a system of length L generically grows as log2 2 en L−n /L +C, where is the on-site spin and C is a function depending only on m...

Quantum Circuit Complexity

We propose a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomial-size quantum circuit. This result also enables us to construct a universal quantum computer which can simulate, with a polynomial factor slowdown, a broader class of quantum machines ...

Multipartite entanglement, quantum- error-correcting codes, and entangling power of quantum evolutions

On The Complexity of Quantum Circuit Manipulation

The stabilizer class of circuits, introduced by Daniel Gottesman, consists of quantum circuits in which every gate is a controlled-NOT (CNOT), Hadamard or phase gate [5]. These circuits have several interesting properties. For example, they are robust enough to allow for entangled states, yet they are known to be simulable in polynomial time by a classical computer. These circuits also naturall...

On the Quantum Circuit Complexity Equivalence

Nielsen [3] recently asked the following question: ”What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation U , without the use of ancilla qubits?” Nielsen was able to prove that a lower bound on the minimal size circuit is provided by the length of the geodesic between the identity I and U , where the length is defined by a suitable Finsler ...