Minimal physical resources for the realisation of measurement-based quantum computation

In measurement-based quantum computation (MBQC), a special highly-entangled state (called a resource state) allows for universal quantum computation driven by single-qubit measurements and post-measurement corrections. Physical realisations of this model have been achieved in various physical systems for low numbers of qubits. The large number of qubits necessary to construct the resource state constitutes one of the main down sides to MBQC. However, in some instances it is possible to extend the resource state on the fly, meaning that not every qubit must be realised in the devices simultaneously. We consider the question of the minimal number of physical qubits that must be present in a system to directly implement a given measurement pattern. For measurement patterns with n inputs, n outputs and m total qubits which have flow, we show that only min(n + 1, m) qubits are required, while the number of required qubits can be as high as m-2 for measurement patterns with only gflow. We discuss the implications of removing the Clifford part of a measurement pattern, using well-established transformation rules for Pauli measurements, for the presence of flow versus gflow, and hence the effect on the minimum number of physical qubits required to directly realise the measurement pattern.Comment: 6 pages, 2 figure

Composable secure multi-client delegated quantum computation

The engineering challenges involved in building large scale quantum computers, and the associated infrastructure requirements, mean that when such devices become available it is likely that this will be in limited numbers and in limited geographic locations. It is likely that many users will need to rely on remote access to delegate their computation to the available hardware. In such a scenario, the privacy and reliability of the delegated computations are important concerns. On the other hand, the distributed nature of modern computations has led to a widespread class of applications in which a group of parties attempt to perform a joint task over their inputs, e.g., in cloud computing. In this paper, we study the multi-client delegated quantum computation problem where we consider the global computation be made up of local computations that are individually decided by the clients. Each client part is kept secret from the server and the other clients. We construct a composable secure multi-client delegated quantum computation scheme from any composable secure single-client delegated quantum computation protocol and quantum authentication codes.Comment: 24 pages, 7 figures. Comments welcom

Bidirectional quantum teleportation and secure direct communication via entanglement swapping

In this paper, a bidirectional quantum teleportation protocol based on Einstein-Podolsky-Rosen (EPR) pairs and entanglement swapping is proposed. In this scheme, two users can simultaneously transmit an unknown single-qubit state to each other. The implementation of the proposed scheme is easier in experiment as compared to previous work. By utilizing this bidirectional quantum teleportation protocol, a bidirectional quantum secure direct communication scheme without carrying secret message is presented. Therefore, in the case of using perfect quantum channel, the protocol is completely secure. Finally, security analyses are investigated

Eco-Routing of Plug-In Hybrid Electric Vehicles in Transportation Networks

We study the problem of eco-routing Plug-In Hybrid Electric Vehicles (PHEVs) to minimize the overall energy consumption costs. Unlike the traditional Charge Depleting First (CDF) approaches in the literature where the power-train control strategy is fixed, we propose a Combined Routing and Power-train Control (CRPTC) algorithm which can simultaneously calculate the optimal energy route as well as the optimal power-train control strategy. To validate our method, we apply our eco-routing algorithm to a subnetwork of the Eastern Massachusetts (EMA) transportation network using actual traffic data provided by the Boston Region Metropolitan Planning Organization. As an alternative benchmark, we also simulate the traffic behavior of the network using the extracted flow data from the aforementioned traffic dataset. We show that the CRPTC approach outperforms the traditional CDF approach and we quantify the trade-off between saving energy and time in using eco-routing algorithms

Minimal memory requirements for pearl-necklace encoders of quantum convolutional codes

One of the major goals in quantum information processing is to reduce the overhead associated with the practical implementation of quantum protocols, and often, routines for quantum error correction account for most of this overhead. A particular technique for quantum error correction that may be useful for protecting a stream of quantum information is quantum convolutional coding. The encoder for a quantum convolutional code has a representation as a convolutional encoder or as a "pearl-necklace" encoder. In the pearl-necklace representation, it has not been particularly clear in the research literature how much quantum memory such an encoder would require for implementation. Here, we offer an algorithm that answers this question. The algorithm first constructs a weighted, directed acyclic graph where each vertex of the graph corresponds to a gate string in the pearl-necklace encoder, and each path through the graph represents a path through non-commuting gates in the encoder. We show that the weight of the longest path through the graph is equal to the minimal amount of memory needed to implement the encoder. A dynamic programming search through this graph determines the longest path. The running time for the construction of the graph and search through it is quadratic in the number of gate strings in the pearl-necklace encoder.Comment: 30 pages, 9 figures, Accepted for publication in the IEEE Transactions on Computer

The Penetration Rate Effect of Connected and Automated Vehicles in Mixed Traffic Routing

We study the problem of routing Connected and Automated Vehicles (CAVs) in the presence of mixed traffic (coexistence of regular vehicles and CAVs). In this setting, we assume that all CAVs belong to the same fleet, and can be routed using a centralized controller. The routing objective is to minimize a given overall fleet traveling cost (travel time or energy consumption). We assume that regular vehicles (non-CAVs) choose their routing decisions selfishly to minimize their traveling time. We propose an algorithm that deals with the routing interaction between CAVs and regular uncontrolled vehicles. We investigate the effect of assigning system-centric routes under different penetration rates (fractions) of CAVs. To validate our method, we apply the proposed routing algorithms to the Braess Network and to a sub-network of the Eastern Massachusetts (EMA) transportation network using actual traffic data provided by the Boston Region Metropolitan Planning Organization. The results suggest that collaborative routing decisions of CAVs improve not only the cost of CAVs, but also that of the non-CAVs. Furthermore, even a small CAV penetration rate can ease congestion for the entire network

A multi-objective synthesis methodology for majority/minority logic networks

New technologies such as Quantum-dot Cellular Automata (QCA), Single Electron Tunneling (SET), Tunneling Phase Logic (TPL) and all-spin logic (ASL) devices have been widely advocated in nanotechnology as a response to the physical limits associated with complementary metal oxide semiconductor (CMOS) technology in atomic scales. Some of their peculiar features are their smaller size, higher speed, higher switching frequency, lower power consumption, and higher scale integration. In these technologies, the majority (or minority) and inverter gates are employed for the production of the functions as this set of gates makes a universal set of Boolean primitives in these technologies. An important step in the generation of Boolean functions using the majority gate is reducing the number of involved gates. In this paper, a multi-objective synthesis methodology (with the objective priority of gate counts, gate levels and the number of inverter gates) is presented for finding the minimal number of possible majority gates in the synthesis of Boolean functions using the proposed Majority Specification Matrix (MSM) concept. Moreover, based on MSM, a synthesis flow is proposed for the synthesis of multi-output Boolean functions. To reveal the efficiency of the proposed method, it is compared with a meta-heuristic method, multi-objective Genetic Programing (GP). Besides, it is applied to synthesize MCNC benchmark circuits. The results are indicative of the outperformance of the proposed method in comparison to multi-objective GP method. Also, for the MCNC benchmark circuits, there is an average reduction of 10.5% in the number of levels as well as 16.8% and 33.5% in the number of majority and inverter gates, as compared to the best available method respectively.Comment: Accepted in Journal of Computational Electronic

Geometry-Based Optimization of One-Way Quantum Computation Measurement Patterns

In one-way quantum computation (1WQC) model, an initial highly entangled state called a graph state is used to perform universal quantum computations by a sequence of adaptive single-qubit measurements and post-measurement Pauli-X and Pauli-Z corrections. The needed computations are organized as measurement patterns, or simply patterns, in the 1WQC model. The entanglement operations in a pattern can be shown by a graph which together with the set of its input and output qubits is called the geometry of the pattern. Since a one-way quantum computation pattern is based on quantum measurements, which are fundamentally nondeterministic evolutions, there must be conditions over geometries to guarantee determinism. Causal flow is a sufficient and generalized flow (gflow) is a necessary and sufficient condition over geometries to identify a dependency structure for the measurement sequences in order to achieve determinism. Previously, three optimization methods have been proposed to simplify 1WQC patterns which are called standardization, signal shifting and Pauli simplification. These optimizations can be performed using measurement calculus formalism by rewriting rules. However, maintaining and searching these rules in the library can be complicated with respect to implementation. Moreover, serial execution of these rules is time consuming due to executing many ineffective commutation rules. To overcome this problem, in this paper, a new scheme is proposed to perform optimization techniques on patterns with flow or gflow only based on their geometries instead of using rewriting rules. Furthermore, the proposed scheme obtains the maximally delayed gflow order for geometries with flow. It is shown that the time complexity of the proposed approach is improved over the previous ones

Decomposition of Diagonal Hermitian Quantum Gates Using Multiple-Controlled Pauli Z Gates

Quantum logic decomposition refers to decomposing a given quantum gate to a set of physically implementable gates. An approach has been presented to decompose arbitrary diagonal quantum gates to a set of multiplexed-rotation gates around z axis. In this paper, a special class of diagonal quantum gates, namely diagonal Hermitian quantum gates, is considered and a new perspective to the decomposition problem with respect to decomposing these gates is presented. It is first shown that these gates can be decomposed to a set that solely consists of multiple-controlled Z gates. Then a binary representation for the diagonal Hermitian gates is introduced. It is shown that the binary representations of multiple-controlled Z gates form a basis for the vector space that is produced by the binary representations of all diagonal Hermitian quantum gates. Moreover, the problem of decomposing a given diagonal Hermitian gate is mapped to the problem of writing its binary representation in the specific basis mentioned above. Moreover, CZ gate is suggested to be the two-qubit gate in the decomposition library, instead of previously used CNOT gate. Experimental results show that the proposed approach can lead to circuits with lower costs in comparison with the previous ones.Comment: To Appear in ACM Journal on Emerging Technologies in Computing System

Quantum-Logic Synthesis of Hermitian Gates

In this paper, the problem of synthesizing a general Hermitian quantum gate into a set of primary quantum gates is addressed. To this end, an extended version of the Jacobi approach for calculating the eigenvalues of Hermitian matrices in linear algebra is considered as the basis of the proposed synthesis method. The quantum circuit synthesis method derived from the Jacobi approach and its optimization challenges are described. It is shown that the proposed method results in multiple-control rotation gates around the y axis, multiple-control phase shift gates, multiple-control NOT gates and a middle diagonal Hermitian matrix, which can be synthesized to multiple-control Pauli Z gates. Using the proposed approach, it is shown how multiple-control U gates, where U is a single-qubit Hermitian quantum gate, can be implemented using a linear number of elementary gates in terms of circuit lines with the aid of one auxiliary qubit in an arbitrary state.Comment: 14 page