**
***
*Research Articles:

**Optimal ancilla-free Clifford+$T$ approximation of
z-rotations** (pp0901-0953)

Neil J. Ross and
Peter Selinger

We consider the problem of approximating arbitrarysingle-qubit
$z$-rotations by ancilla-free Clifford+$T$ circuits, up to given
epsilon. We present a fast new probabilistic algorithm for solving this
problem optimally, i.e., for finding the shortest possible circuit
whatsoever for the given problem instance. The algorithm requires a
factoring oracle (such as a quantum computer). Even in the absence of a
factoring oracle, the algorithm is still near-optimal under a mild
number-theoretic hypothesis. In this case, the algorithm finds a
solution of $T$-count $m + O(\log(\log(1/\epsilon)))$, where $m$ is the
$T$-count of the

second-to-optimal solution. In the typical case, this yields circuit
approximations of $T$-count $3\log_2(1/\epsilon) +
O(\log(\log(1/\epsilon)))$. Our algorithm is efficient in practice, and
provably efficient under the above-mentioned number-theoretic
hypothesis, in the sense that its expected runtime is
$O(\polylog(1/\epsilon))$.

**Coherent modification of entanglement: benefits
due to extended Hilbert space** (pp0954-0968)

Dmitry Solenov

A quantum computing system is typically represented by a set of
non-interacting (local) two-state systems---qubits. Many physical
systems can naturally have more accessible states, both local and
non-local. We show that the resulting non-local network of states
connecting qubits can be efficiently addressed via continuous time
quantum random walks, leading to substantial speed-up of multiqubit
entanglement manipulations. We discuss a three-qubit Toffoli gate and a
system of superconducting qubits as an illustration.

**The entangling power of a glocal dissipative map** (pp0969-0981)

Alireza
Nourmandipour, M.K. Tavassoly, and Stefano Mancini

We consider a model of two qubits dissipating into both local and global
environments (generally at non-zero temperatures), with the possibility
of interpolating between purely local dissipation and purely global one.
The corresponding dissipative dynamical map is characterized in terms of
its Kraus operators focusing on the stationary regime. We then determine
conditions under which entanglement can be induced by the action of such
a map. It results (rather counterintuitively) that in order to have
entanglement in the presence of local environment, this latter must be
at nonzero temperature.

**Environment-assisted entanglement purification** (pp0982-0990)

Liang Qiu, Zhi
Liu, and Xin Wang

Two qubits in a pure entangled state passing through and interacting
with amplitude damping noises will cause the decay of entanglement.
Entanglement swapping combined with environment measurement is proposed
to purify entanglement of the two-qubit state. Some initial states can
be purified into the maximally entangled ones by just using the protocol
for one time, in contrast to iteratively using the protocol given in
Phys. Rev. A 89, 014303 (2014).

**Optimal universal quantum cloning: asymmetries and
fidelity measures** (pp0991-1028)

Alastair Kay

We study the problem of universal quantum cloning -- taking several
identical copies of a pure but unknown quantum state and producing
further copies. While it is well known that it is impossible to
perfectly reproduce the state, how well the copies can be cloned can be
quantified using the fidelity. We examine how individual fidelities can
be traded against each other, and how different fidelity measures can be
incorporated. The broadly applicable formalism into which we transform
the cloning problem is described as a series of quadratic constraints
which are amenable to mathematical and computational scrutiny. As such,
we reproduce all known results on optimal universal cloning, and push
the recent results on asymmetric cloning much further, giving new
trade-off relations between fidelities for broad classes of optimal
cloning machines. We also provide substantial evidence that motivates
why other parameter ranges (number of input copies) have not, and will
not, yield to similar analysis.

**Solving constrained quadratic binary problems via
quantum adiabatic evolution** (pp1029-1047)

Pooya Ronagh, Brad
Woods, and Ehsan Iranmanesh

Quantum adiabatic evolution is perceived as useful for binary quadratic
programming problems that are a priori unconstrained. For constrained
problems, it is a common practice to relax linear equality constraints
as penalty terms in the objective function. However, there has not yet
been proposed a method for efficiently dealing with inequality
constraints using the quantum adiabatic approach. In this paper, we give
a method for solving the Lagrangian dual of a binary quadratic
programming (BQP) problem in the presence of inequality constraints and
employ this procedure within a branch-and-bound framework for
constrained BQP (CBQP) problems.

**An adaptive attack on Wiesner's quantum money**
(pp1048-1070)

Daniel Nagaj, Or
Sattath, Aharon Brodutch, and Dominique Unruh

Unlike classical money, which is hard to forge for practical reasons
(e.g. producing paper with a certain property), quantum money is
attractive because its security might be based on the no-cloning
theorem. The first quantum money scheme was introduced by Wiesner circa
1970. Although more sophisticated quantum money schemes were proposed,
Wiesner's scheme remained appealing because it is both conceptually
clean as well as relatively easy to implement. We show efficient
adaptive attacks on Wiesner's quantum money scheme (and its variant by
Bennett et al.), when valid money is accepted and passed on, while
invalid money is destroyed. We propose two attacks, the first is
inspired by the Elitzur-Vaidman bomb testing problem, while the second
is based on the idea of {\it protective measurements}. It allows us to
break Wiesner's scheme with 4 possible states per qubit, and
generalizations which use more than 4 states per qubit. The attack shows
that Wiesner's scheme can only be safe if the bank replaces valid notes
after validation.