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arXiv:1005.1103 · Japanese Journal of Applied Physics

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

Tetsufumi Tanamoto

Published Apr 1, 2010• 3 citations
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Abstract

We theoretically investigate the robustness of cluster states in charge qubit system based on quantum dot (QD) and double quantum point contact (DQPC). Trap state is modeled by an island structure in DQPC and represents a dynamical fluctuation. We found that the dynamical fluctuations affect the cluster states more than static fluctuation caused by QD size fluctuation.

DOI
10.1143/jjap.49.04dj08

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We theoretically investigate the robustness of cluster states in charge qubit system based on quantum dot (QD) and double quantum point contact (DQPC). Trap state is modeled by an island structure in DQPC and represents a dynamical fluctuation. We found that the dynamical fluctuations affect the cluster states more than static fluctuation caused by QD size fluctuation.
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.
We performed real-time observation of charge states in a double quantum dot (QD) by monitoring the current passing through an adjacent quantum point contact (QPC). The position of the QPC was chosen in such a way that the Coulomb coupling of the QPC to one QD is made stronger than to the other QD, so that the QPC current can clearly resolve the charge states of the double QD. With a response time of ∼200 µs, we also investigated the energy relaxation time T 1 of the double QD by applying rectangular voltage pulses to the double QD. We confirmed that T 1 can be made sufficiently longer than the response time of the QPC.
Quantum measurement always disturbs the quantum system being measured, which is known as measurement-induced backaction. We consider a specific model, a double quantum dot charge qubit measured by a nearby quantum point contact. We explore the evolution by deriving a master equation. The advantages of this master equation are (i) it has the Lindblad form and the non-Markovian effects are embodied in the time-dependent coefficients, (ii) the tunnelling and decay effect can be clearly understood in the master equation, and (iii) it can be further easily controlled by manipulate the Hamiltonian.
We consider evolution of a double quantum dot (DQD) two-electron spin qubit which is continuously weakly measured with a linear charge detector (quantum point contact). Since the interaction between the spins of two electrons depends on their charge state, the charge measurement affects the state of two spins, and induces non-trivial spin dynamics. We consider the regimes of strong and weak coupling to the detector, and investigate the measurement-induced spin dynamics both analytically and numerically. We observe emergence of the negative-result evolution and the system stabilization due to an analog of quantum Zeno effect. Moreover, unitary evolution between the triplet and a singlet state is induced by the negative-result measurement. We demonstrate that these effects exist for both strong and weak coupling between the detector and the DQD system.
We study theoretically transitions of a double quantum-dot qubit caused by nonequilibrium charge fluctuations in a nearby quantum point contact (QPC) used as a detector. We show that these transitions are related to the fundamental Heisenberg backaction associated with the measurement, and use the uncertainty principle to derive a lower bound on the transition rates. We also derive simple expressions for the transition rates for the usual model of a QPC as a mesoscopic conductor, with screening treated at the RPA level. Finally, numerical results are presented which demonstrate that the charge noise and shot noise backaction mechanisms can be distinguished in QPCs having nonadiabatic potentials. The enhanced sensitivity of the charge noise to the QPC potential is explained in terms of interference contributions similar to those which cause Friedel oscillations.
We solve the master equations of two charge qubits measured by two serially coupled quantum point contacts (QPCs). We describe two-qubit dynamics by comparing entangled states with product states, and show that the QPC current can be used for reading out results of quantum calculations and providing evidences of two-qubit entanglement. We also calculate the concurrence of the two qubits as a function of dephasing rate that originates from the measurement. We conclude that coupled charge qubits can be effectively detected by a QPC-based detector.