QIC Abstracts

 Vol.16 No.3&4, March 1, 2016

Research Articles:

Information cost of quantum communication protocols (pp0181-0196)
Iordanis Kerenidis, Mathieu Lauriere, Francois Le Gall, Mathys Rennela
In two-party quantum communication complexity, Alice and Bob receive some classical inputs and wish to compute some function that depends on both these inputs, while minimizing the communication. This model
has found numerous applications in many areas of computer science. One notion that has received a lot of attention recently is the information cost of the protocol, namely how much information the players reveal about their inputs when they run the protocol. In the quantum world, it is not straightforward to define a notion of quantum information cost. We study two different notions and analyze their relation. We also provide new quantum protocols for the Inner Product function and for Private Information Retrieval, and show that protocols for Private Information Retrieval whose classical or quantum information cost for the user is zero can have exponentially different information cost for the server.

Quantum algorithms and circuits for scientific computing (pp0197-0236)
Mihir K. Bhaskar, Stuart Hadfield, Anargyros Papageorgiou, and Iasonas Petras
Quantum algorithms for scientific computing require modules implementing fundamental functions, such as the square root, the logarithm, and others. We require algorithms that have a well-controlled numerical error, that are uniformly scalable and reversible (unitary), and that can be implemented efficiently. We present quantum algorithms and circuits for computing the square root, the natural logarithm, and arbitrary fractional powers. We provide performance guarantees in terms of their worst-case accuracy and cost. We further illustrate their performance by providing tests comparing them to the respective floating point implementations found in widely used numerical software.

On the relation between a graph code and a graph state (pp0237-0250)
Yongsoo Hwang and Jun Heo
A graph state and a graph code respectively are defined based on a mathematical simple graph. In this work, we examine a relation between a graph state and a graph code both obtained from the same graph, and show that a graph state is a superposition of logical qubits of the related graph code. By using the relation, we first discuss that a local complementation which has been used for a graph state can be useful for searching locally equivalent stabilizer codes, and second provide a method to find a stabilizer group of a graph code.

Commuting quantum circuits with few outputs are unlikely to be classically simulatable (pp0251-0270)
Yasuhiro Takahashi, Seiichiro Tani, Takeshi Yamazaki, and Kazuyuki Tanaka
We study the classical simulatability of commuting quantum circuits with $n$ input qubits and $O(\log n)$ output qubits, where a quantum circuit is classically simulatable if its output probability distribution can be sampled up to an exponentially small additive error in classical polynomial time. Our main result is that there exists a commuting quantum circuit that is not classically simulatable unless the polynomial hierarchy collapses to the third level. This is the first formal evidence that a commuting quantum circuit is not classically simulatable even when the number of output qubits is $O(\log n)$. Then, we consider a generalized version of the circuit and clarify the condition under which it is classically simulatable. Lastly, using a proof similar to that of the main result, we provide an evidence that a slightly extended Clifford circuit is not classically simulatable.

Dense quantum communication using single- and two-particle operations on six-particle cluster state (pp0271-0290)
Parminder S. Bhatia
Theory of controlled tripartite quantum dense coding for the transmission of four-binary bits between two distinct locations is presented. The entanglement resource for this transmission is provided by a six-qubit cluster state. Theoretical detail of an encoder that can encode sixteen different operations and a four-bit binary decoder required for this transmission is discussed. We show that in the absence of availability of any four-state analyzer decoding can be reduced to single-particle and two-particle Bell-state measurements (). In our scheme, Bell-state measurements () performed during decoding, result in Bell-pairs, which along with single-particle projections are used to unambiguously discriminate all sixteen encoding operations. Proposed experiment to verify theory of tripartite quantum dense coding scheme, using photonic entanglement, is also briefly discussed. Success probability of the scheme is determined. In addition, long-distance implementation of this tripartite quantum dense coding scheme is discussed. Fault-tolerant quantum repeaters used in this long-distance scheme are based on quantum error-correction, which is achieved with the aid of Calderbank-Shor-Steane () encoding.

Universality of beamsplitters (pp0291-0312)
Adam Sawicki
We consider the problem of building an arbitrary $N\times N$ real orthogonal operator using a finite set, $S$, of elementary quantum optics gates operating on $m\leq N$ modes - the problem of universality of $S$ on $N$ modes. In particular, we focus on the universality problem of an $m$-mode beamsplitter. Using methods of control theory and some properties of rotations in three dimensions, we prove that any nontrivial real 2-mode and `almost' any nontrivial real $3$-mode beamsplitter is universal on $m\geq3$ modes.

Renyi and Tsallis formulations of noise-disturbance trade-off relations (pp0313-0331)
Alexey E. Rastegin
We address an information-theoretic approach to noise and disturbance in quantum measurements. Properties of corresponding probability distributions are characterized by means of both the R\'{e}nyi and
Tsallis entropies. Related information-theoretic measures of noise and disturbance are introduced. These definitions are based on the concept of conditional entropy. To motivate introduced measures, some important properties of the conditional R\'{e}nyi and Tsallis entropies are discussed. There exist several formulations of entropic uncertainty relations for a pair of observables. Trade-off relations for noise and disturbance are derived on the base of known formulations of such a kind.

Squash 2: a hierarchical scalable quantum mapper considering ancilla sharing (pp0332-0356)
Mohammad J. Dousti, Alireza Shafaei, and Massoud Pedram
We present a multi-core reconfigurable quantum processor architecture, called Requp, which supports a hierarchical approach to mapping a quantum algorithm while sharing physical and logical ancilla qubits. Each core is capable of performing any quantum instruction. Moreover, we introduce a scalable quantum mapper, called \textit{Squash~2}, which divides a given quantum circuit into a number of quantum modules---each module is divided into k parts such that each part will run on one of k available cores. Experimental results demonstrate that Squash~2 can handle large-scale quantum algorithms while providing an effective mechanism for sharing ancilla qubits.

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