Routing of Quantum States in 2D Lattices

Running quantum algorithms in a quantum machine may solve some complex problems that are intractable for even the most powerful classical computers. Quantum algorithms can be described by quantum circuits consisting of a set of qubits and a sequence of gates operating on those qubits when the quantum circuit model of computation is adopted. This circuit description on an algorithm usually assumes that any kind of interaction between qubits is possible. However, in real experiments, qubits are placed on a specific physical qubit layout, which constraints the possible interactions between qubits due to its limited connectivity. One possible layout for arranging qubits is a 2D array with 4 neighbours per qubit, which corresponds with the topology of surface code, one of the most promising quantum correction codes. In such 2D nearest-neighbour (NN) arrangement of qubits not all pairs of qubits that have to interact during computation can be directly connected (be neighbours). This means that non-adjacent qubits or qubit states need to be moved or routed (by e.g. SWAP operations) and be placed close to each other when required. In this thesis, we applied different routing algorithms used in Network on Chip (NoC) for defining the routing paths when quantum states are moved. After investigating 7 different NoC routing algorithms, we redesign and adapt them to the quantum scenario. We use the quantum plane simulation platform for comparing the routing overhead and the success rate of such routing algorithms when running 4 different quantum algorithms. We conclude that the routing algorithm which has the best overall routing performance is the one called Hot Potato. It is deadlock and livelock free in perfect qubit lattices, and shows the best fault-tolerance when faulty qubits are considered.

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2017-04-26

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master thesis

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