Research Articles:
CV-MDI quantum key distribution via satellite
(pp0361-0379)
Nedasadat Hosseinidehaj and Robert Malaney
In this work we analyze a
measurement-device-independent (MDI)
protocol to establish continuous-variable (CV) quantum key distribution
(QKD)
between two ground stations. We assume communication occurs between the
ground stations via satellite over two independent atmospheric-fading
channels influenced by turbulence-induced beam wandering. In this
MDI
protocol the measurement device is the satellite itself, and the
security of the protocol is analyzed through an equivalent
entanglement-based swapping scheme. We quantify the positive impact the
fading channels can have on the final quantum key rates, demonstrating
how the protocol is able to generate a positive key rate even over
high-loss atmospheric channels provided that the maximum transmission
coefficient of the channel is sufficiently large. This is somewhat
counter-intuitive given that the same outcome is only possible in the
low-loss regime for a measurement device centrally positioned in a
fiber-optic channel. Our results show that useful space-based quantum
key generation rates between two ground stations are possible even when
the relay satellite is held by an adversary. The cost in key rate
incurred by altering the status of the satellite from trustworthy to
untrustworthy is presented.
On the one-shot zero-error
classical capacity of classical-quantum channels assisted by quantum
non-signalling correlations
(pp0380-0398)
Ching-Yi Lai and Runyao Duan
Duan
and Winter studied the one-shot zero-error classical capacity of a
quantum channel assisted by quantum non-signalling
correlations, and formulated this problem as a
semidefinite
program depending only on the
Kraus
operator space of the channel. For the class of classical-quantum
channels, they showed that the \emph{asymptotic}
zero-error classical capacity assisted by quantum non-signalling
correlations, minimized over all classical-quantum channels with a
confusability graph
$G$,
is exactly $\log \vartheta(G)$,
where $\vartheta(G)$
is the celebrated
Lov\'{a}sz
theta function. In this paper, we show that the
\emph{one-shot}
capacity for a classical-quantum channel, induced from a
\emph{circulant
graph} $G$
defined by \emph{equal-sized
cyclotomic
cosets},
is $\log \lfloor \vartheta(G) \rfloor$,
which further implies that its
\emph{asymptotic}
capacity is $\log \vartheta(G)$.
This type of graphs include the cycle graphs of odd length, the Paley
graphs of prime
vertices,
and the cubit residue graphs of prime
vertices.
Examples of other graphs are also
discussed. This gives
Lov\'{a}sz
$\vartheta$
function another operational meaning in zero-error
classical-quantum communication.
Spreading
behavior of quantum walks induced by random walks
(pp0399-0414)
Yusuke
Higuchi and Etsuo Segawa
In this paper, we consider the quantum
walk on $\mathbb{Z}$
with attachment of one-length path periodically. This small modification
to $\mathbb{Z}$
provides localization of the quantum walk. The
eigenspace
causing this localization is generated by finite length round trip
paths. We find that the localization is due to the eigenvalues of
an underlying random walk. Moreover we find that the transience of the
underlying random walk provides a slow down of the pseudo velocity of
the induced quantum walk and a different limit distribution from the
Konno
distribution.
Quantum
gates via continuous time quantum walks in multiqubit systems with
non-local auxiliary states
(pp0415-0455)
Dmitry Solenov
Non-local higher-energy auxiliary
states have been successfully used to entangle pairs of
qubits
in different quantum computing systems. Typically a longer-span
non-local state or sequential application of few-qubit
entangling gates are needed to produce a non-trivial
multiqubit
gate. In many cases a single non-local state that span over the entire
system is difficult to use due to spectral crowding or impossible to
have. At the same time, many
multiqubit
systems can naturally develop a network of multiple non-local
higher-energy states that span over few
qubits
each. We show that continuous time quantum walks can be used to address
this problem by involving multiple such states to perform local and
entangling operations concurrently on many
qubits.
This introduces an alternative approach to
multiqubit
gate compression based on available physical resources. We formulate
general requirements for such walks and discuss configurations of
non-local auxiliary states that can emerge in quantum computing
architectures based on self-assembled quantum dots, defects in diamond,
and superconducting
qubits,
as examples. Specifically, we discuss a
scalable
multiqubit quantum register
constructed as a single chain with nearest-neighbor interactions. We
illustrate how quantum walks can be configured to perform single-, two-
and three-qubit
gates, including
Hadamard,
Control-NOT, and
Toffoli
gates. Continuous time quantum walks on graphs involved in these gates
are investigated.
Analytical
evidence of ultrafast generation of spin-motion entanglement
(pp0456-0468)
Kuo Hai, Yunrong Luo, Guishu Chong, Hao Chen, and Wenhua Hai
We investigate
ultrafast
generation of spin-motion entanglement of a trapped and
Gaussian-pulse-kicked two-level ion in the Lamb-Dicke
limit and high field regime. A set of exact
motional
states and the probabilities occupying different
pseudospin
states are derived and the visible differences between the results with
those of the delta-kick case are shown during a kick moment, which
analytically evidence the
ultrafast
generation of an exact spin-motion entangled state regardless of initial
state. Our results can be justified with the current experimental
capability and provide an
analytical
method for further study of the
ultrafast
entanglement in atomic qubits.
Learning
quantum annealing
(pp0469-0487)
E.C. Behrman, J.E. Steck, and M.A. Moustafa
We propose and develop a new
procedure, whereby a quantum system can learn to anneal to a desired
ground state. We demonstrate successful learning to produce an entangled
state for a two-qubit
system, then demonstrate
generalizability to larger systems.
The amount of additional learning necessary decreases as the size of the
system increases. Because current technologies limit measurement of the
states of quantum annealing machines to determination of the average
spin at each site, we then construct a ``broken pathway'' between the
initial and desired states, at each step of which the average spins are
nonzero, and show successful learning of that pathway. Using this
technique we show we can direct annealing to
multiqubit
GHZ and W states, and verify that we have done so. Because quantum
neural networks are robust to noise and
decoherence
we expect our method to be readily implemented experimentally; we show
some preliminary results which support this.
Turning gate
synthesis errors into incoherent errors
(pp0488-0494)
Matthew B. Hastings
Using error correcting codes and fault
tolerant techniques, it is possible, at least in theory, to produce
logical
qubits
with significantly lower error rates than
the underlying physical
qubits.
Suppose, however, that the gates that act on these logical
qubits
are only approximation of the desired gate. This can arise, for
example, in synthesizing a single
qubit
unitary from a set of Clifford and
$T$ gates; for a generic such
unitary, any finite sequence of gates only approximates the desired
target.In this case, errors in the gate can add coherently so that,
roughly, the error $\epsilon$
in the unitary of each gate must scale as
$\epsilon \stackrel{<}{\sim} 1/N$,
where $N$
is the number of gates. If, however,
one has the option of synthesizing one of several
unitaries
near the desired target, and if an average of these options is closer to
the target, we give some elementary bounds showing cases in which the
errors can be made to add incoherently by averaging over random choices,
so that, roughly, one needs
$\epsilon \stackrel{<}{\sim} 1/\sqrt{N}$.
We remark on one particular application to distilling magic states where
this effect happens automatically in the usual circuits.
Perfect state transfer is poly-time (pp0495-0502)
Gabriel Coutinho and Chris Godsil
We show that deciding whether a graph
admits perfect state transfer can be done in polynomial time on a
classical computer with respect to the size of the graph.
Erratum:
Erratum to
Coherence measures and optimal conversion for coherent states
(Quantum Information and Computation, Vol. 15 (2015), 1307-1316)
(pp0503-0505)
Shuanping Du, Zhaofang Bai, and Xiaofei Qi