Measure of decoherence in quantum error correction for solid-state quantum computing

Abstract

We considered the interaction of semiconductor quantum register with noisy environment leading to various types of qubit errors. We analysed both phase and amplitude decays during the process of electron-phonon interaction. The performance of quantum error correction codes (QECC) which will be inevitably used in full scale quantum information processors was studied in realistic conditions in semiconductor nanostructures. As a hardware basis for quantum bit we chose the quantum spatial states of single electron in semiconductor coupled double quantum dot system. The modified 5-and 9-qubit quantum error correction (QEC) algorithms by Shor and DiVincenzo without error syndrome extraction were applied to quantum register. 5-qubit error correction procedures were implemented for Si charge double dot qubits in the presence of acoustic phonon environment. χ-matrix, Choi-Jamio lkowski state and measure of decoherence techniques were used to quantify qubit fault-tolerance. Our results showed that the introduction of above quantum error correction techniques at small phonon noise levels provided quadratic improvement of output error rates. The efficiency of 5-qubits quantum error correction algorithm in semiconductor quantum information processors was demonstrated.

Hitting time for quantum walks of identical particles

“…The described physical implementation of quantum walks has several advantages for quantum computing. One of them is that semiconductor charge qubits can be protected from computational errors 28,29 with the help of standard quantum error correction algorithms, 30,31 and by using a decoherence-free subspace qubit encoding. 32 In a single electron regime of the described quantum system, the electron spreads coherently which corresponds to a quantum walk dynamics of a single particle, 33 as in Fig.…”

Quantum walks of interacting fermions on a cycle graph

“…( 17) leads to errors in quantum information stored in the system of electrons. In order to quantify this error we use the measure of decoherence [22,54]…”

“…Quantum dots in semiconductors can be used as building blocks for a construction of a quantum computer, where quantum dots positions provide a spatial degree of freedom of a quantum particle [17][18][19][20]. It was shown that a spatial location of an electron in one of two semiconductor quantum dots can serve for encoding a qubit [17,18] and errors that occur mostly because of the interaction * melnikov@phystech.edu † leonid@phystech.edu with acoustic phonons can be corrected [21,22]. In this paper we study quantum dots arranged in a circle, where each quantum dot can be populated by no more than one electron.…”