A switching approach for perfect state transfer over a scalable and routing enabled network architecture with superconducting qubits

We propose a hypercube switching architecture for the perfect state transfer (PST) where we prove that it is always possible to find an induced hypercube in any given hypercube of any dimension such that PST can be performed between any two given vertices of the original hypercube. We then generalise this switching scheme over arbitrary number of qubits where also this routing feature of PST between any two vertices is possible. It is shown that this is optimal and scalable architecture for quantum computing with the feature of routing. This allows for a scalable and growing network of qubits. We demonstrate this switching scheme to be experimentally realizable using superconducting transmon qubits with tunable couplings. We also propose a PST assisted quantum computing model where we show the computational advantage of using PST against the conventional resource expensive quantum swap gates. In addition, we present the numerical study of signed graphs under Corona product of graphs and show few examples where PST is established, in contrast to pre-existing results in the literature for disproof of PST under Corona product. We also report an error in pre-existing research for qudit state transfer over Bosonic Hamiltonian where unitarity is violated.