Study Of Superconducting Quantum Computation Against Decoherence

Quantum computation focuses on implementing computation, processing information and simulating quantum system. Based on the principle of coherent superposition and quantum entanglement, quantum computation is exponentially faster than conventional computation, and then a quantum computer can solve certain problems that a classical computer cannot do. Unfortunately, the interaction between the quantum system and environment will collapse the quantum state, which is named as decoherence. Decoherence is the most important obstacle to realize quantum computation. In this thesis, we focus on how to deal with decoherence in quantum computation. The main results and the creative points are as follows:We present a theoretical scheme to realize universal quantum computation in a decoherence-free subspace(DFS) for the ?σx-type local collective noise with superconducting charge qubits. In our scheme, a logical qubit consists of two charge qubits coupled by a variable capacitance, and different logical qubits are coupled by a common inductance.A logical qubit provides a DFS immune to the ?σx-type local collective noise. We show how to realize universal quantum computation in the DFS. Finally, we present how to prepare a logical qubit in the DFS. In our scheme, any two logical qubits can be selectively and controllably coupled, which makes it possible that our scheme scales up to a large number of logical qubits. All charge qubits work at their respective degenerate points,which makes it reasonable that we ignore the ?σz-type noises.We propose a theoretical scheme to implement universal quantum computation in a DFS for local collective relaxation with transmon qubits. For the transmon, its dephasing has experimentally been suppressed to an extent that the dephasing time is mainly limited by relaxation process. In the Hilbert space of two transmons, there exists a 2-dimensional subspace immune to the collective relaxation. In this paper, by encoding a logical qubit in this subspace, we demonstrate how to realize universal quantum computation in the decoherence-free subspace. In our scheme, the transmons are coupled through a 1-dimensional superconducting transmission line resonator. By the help of some classical driving fields, two noncommutable single-logical-qubit rotation operators and a controlled-phase gate between two logical qubits are obtained. We always work in the detuning regime, which largely decreases relaxation induced by the Purcell effect.We propose a theoretical scheme to generate flux-qubit clusters using the XY interactions. In our scheme, two neighboring qubits are coupled via a dc superconducting quantum interference device(SQUID). When two coupled qubits are resonant, the XY interaction is obtained in the rotating frame. Furthermore, the XY interaction can be selectively on and off by modulating the bias current applied to the SQUID. Otherwise, when two coupled flux qubits are detuned from each other, the XY interaction can be controlled by the frequency of a microwave pulse applied in the SQUID bias current. The generation of a d-dimension(d = 1, 2, 3) cluster states needs 2d steps. The advantages of our scheme are as follows: All flux qubits are always biased at their optimal points where they have long coherence times; and existing technology allow us to rapidly modulate the bias current and easily control the frequency of the pulse. Thus our scheme is experimentally feasible.We propose a scheme for quantum secret sharing based on quantum error-correcting codes. Quantum secret sharing(QSS) is a procedure of sharing classical information or quantum information by using quantum states. In this paper, we present how to use a[2k- 1, 1, k] quantum error-correcting code(QECC) to implement a quantum(k, 2k- 1)threshold scheme, in which a secret is divided into n shares, and can only be perfectly reconstructed from any k or more shares. We also take advantage of classical enhancement of the [2k- 1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, our schemes can prevent intercept-resend attacks and be implemented on some noisy channels.