QIC Abstracts

 Vol.17 No.5&6, May 1, 2017

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

back to QIC online Front page