Robustness of Charge-qubit Cluster States to Double Quantum Point Contact Measurement

One-way quantum computing [1, 2] is an important approach for quantum computation based on a series of one-qubit measurements starting from a cluster state of a qubit array. Cluster states are highly-entangled states involving all qubits and are typically generated from an Ising-like Hamiltonian, starting from an initial product state |Ψ0〉 ≡ |Ψ(t = 0)〉 = Πi=1|+〉i , where |±〉i = (|0〉i±|1〉i)/ √ 2. Here, |0〉i and |1〉i are the two states of the i-th qubit in an N -qubit system. In ref. [3], we showed that cluster states in charge qubits[4–17] can be created by applying a single gate bias pulse, right after preparing the initial product state (one-step generation method), and are more robust against nonuniformities among qubits than decoherence-free (DF) states [18, 19] under a noise environment generated by a quantum point contact (QPC) detector, which is a sensitive detector of electric charge distribution[20, 21]. However, trap sites are often unavoidable in solid-state qubits owing to their small fabrication size and several experiments show that trap states significantly affect electric transport properties of nanoscale devices[22–25]. Here, we model the trap site as the island (discrete energy state) between double QPCs (DQPC) and investigate robustness of cluster states in charge qubits measured by the DQPC detector (Fig. 1). The charge qubits are based on quantum dots (QD), in which the position of the excess charge in a qubit affects the QPC current electrically, resulting in detection of charged state. Owing to this additional external degrees of freedom, this setup is considered to be a harsher and more realistic condition for qubits than that of ref .[3]. Here, we calculate a time-dependent fidelity of four charge qubits with DQPC by solving density matrix (DM) equations.