Efficient quantum algorithms for GHZ and W states, and implementation on the IBM quantum computer

We propose efficient algorithms with logarithmic step complexities for the generation of entangled GHZ and W states (see Fig. 1), and we demonstrate an implementation on the IBM quantum computer. These algorithms are of high... [ view full abstract ]

We propose efficient algorithms with logarithmic step complexities for the generation of entangled GHZ and W states (see Fig. 1), and we demonstrate an implementation on the IBM quantum computer. These algorithms are of high relevance for quantum networks since they are potential working horses to create deterministically by local extension a shared GHZ or W state, this without any prior entanglement, and even if the number of parties is arbitrary. This has many promising applications in distributed quantum information processing. We generate and characterize these entangled states with up to N=16 superconducting qubits on the IBM quantum computer, twice the number of qubits previously achieved. Different characterization methods are discussed: full quantum tomography for low-N GHZ and W states, parity oscillations (see Fig. 2) and histogram distance for large N GHZ and W states (Fig. 3) respectively. They prove the efficiency and robustness of our algorithms, and reveal the current limitations of the IBM Q platform in terms of decoherence. Quantum error correction on the generated GHZ states is attempted and prove to be limited by the current level of decoherence. The observed linear increase in decoherence rate with number of qubits is promising given the latest improvement in experimental quantum computing. New processors will offer superior coherence properties and higher connectivity. They should allow to further demonstrate the superior performance of the logarithmic algorithms presented here. Overall we show that the Open Source Quantum Information Science Kit (QISKit) enables the deployment of large experiments on currently available quantum computers.