Implementation of standard quantum error correction codes for solid-state qubits

Abstract

In quantum error-correcting code (QECC), many quantum operations and measurements are necessary to correct errors in logical qubits. In the stabilizer formalism, which is widely used in QECC, generators $G_i(i=1,2,..)$ consist of multiples of Pauli matrices and perform encoding, decoding and measurement. In order to maintain encoding states, the stabilizer Hamiltonian $H_{\mathrm{stab}}=-{\sum }_i{G}_i$ is suitable because its ground state corresponds to the code space. On the other hand, Hamiltonians of most solid-state qubits have two-body interactions and show their own dynamics. In addition solid-state qubits are fixed on substrate and qubit-qubit operation is restricted in their neighborhood. The main purpose of this paper is to show how to directly generate the stabilizer Hamiltonian $H_{\mathrm{stab}}$ from conventional two-body Hamiltonians with Ising interaction and XY interaction by applying a pulse control method such as an NMR technique. We show that generation times of $H_{\mathrm{stab}}$ for nine-qubit code, five-qubit code and Steane code are estimated to be less than 300 ns when typical experimental data of superconducting qubits are used, and sufficient pulse control is assumed. We also show how to prepare encoded states from an initial state $|0....0>$. In addition, we discuss an appropriate arrangement of two- or three-dimensional arrayed qubits.

14 pages, 4 figures

References in corpus (13)

• Surface codes: Towards practical large-scale quantum computation
• An Open-System Quantum Simulator with Trapped Ions
• Superconducting Circuits and Quantum Information
• Fault-tolerant quantum computation with high threshold in two dimensions
• Generating Single Microwave Photons in a Circuit
• Controllable coupling of superconducting flux qubits
• Switchable resonant coupling of flux qubits
• Robust CNOT gates from almost any interaction
• Topologically decoherence-protected qubits with trapped ions
• Generalized switchable coupling for superconducting qubits using double resonance
• Spectroscopy of three strongly coupled flux qubits
• Dynamic Generation of Topologically Protected Self-Correcting Quantum Memory
• Strategy for implementing stabilizer-based codes on solid-state qubits

Cited by in corpus (6)

• Dicke-state preparation through global transverse control of Ising-coupled qubits
• Interconversion of $W$ and Greenberger-Horne-Zeilinger states for Ising-coupled qubits with transverse global control
• Feasibility of single-shot realizations of conditional three-qubit gates in exchange-coupled qubit arrays with local control
• Dynamical topological quantum computation using spin pulse control in the Heisenberg model
• Generation of all-to-all connections in a two-dimensional qubit array with two-body interactions
• Generation of chiral spin state by quantum simulation