Implementation of the three-qubit phase-flip error correction code with superconducting qubits

Abstract

We investigate the performance of a three qubit error correcting code in the framework of superconducting qubit implementations. Such a code can recover a quantum state perfectly in the case of dephasing errors but only in situations where the dephasing rate is low. Numerical studies in previous work have however shown that the code does increase the fidelity of the encoded state even in the presence of high error probability, during both storage and processing. In this work we give analytical expressions for the fidelity of such a code. We consider two specific schemes for qubit-qubit interaction realizable in superconducting systems; one ${\sigma }_z{\sigma }_z$-coupling and one cavity mediated coupling. With these realizations in mind, and considering errors during storing as well as processing, we calculate the maximum operation time allowed in order to still benefit from the code. We show that this limit can be reached with current technology.

10 pages, 8 figures

References in corpus (20)

• Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box
• Charge insensitive qubit design derived from the Cooper pair box
• Quantum state engineering with Josephson-junction devices
• Manipulating the Quantum State of an Electrical Circuit
• Coupling Superconducting Qubits via a Cavity Bus
• Multiple Particle Interference and Quantum Error Correction
• Reliable Quantum Computers
• Quantum oscillations in two coupled charge qubits
• Coherent quantum state storage and transfer between two phase qubits via a resonant cavity
• Experimental Quantum Error Correction
• Quantum Manipulations of Small Josephson Junctions
• Continuous quantum error correction via quantum feedback control
• Implementation of the Five Qubit Error Correction Benchmark
• Tunable resonators for quantum circuits
• Selective coupling of superconducting qubits via tunable stripline cavity
• Experimental Implementation of a Concatenated Quantum Error-Correcting Code
• Josephson junction qubit network with current-controlled interaction
• Cavity QED in superconducting circuits: susceptibility at elevated temperatures
• Effects of noise on quantum error correction algorithms
• Active suppression of dephasing in Josephson-junction qubits

Cited by in corpus (6)

• Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
• Entanglement Metrology Using a Joint Readout of Superconducting Qubits
• Circuit QED and engineering charge based superconducting qubits
• Simple quantum error detection and correction for superconducting qubits
• Simplify proposal for realizing multiqubit tunable phase gate in circuit QED
• Two- and three-mode squeezing in a three-qubit entangled system