Experimental Quantum Computations on a Topologically Encoded Qubit

Abstract

The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant quantum computing (FTQC). Here we present a step towards this by implementing a quantum error correcting code, encoding one qubit in entangled states distributed over 7 trapped-ion qubits. We demonstrate the capability of the code to detect one bit flip, phase flip or a combined error of both, regardless on which of the qubits they occur. Furthermore, we apply combinations of the entire set of logical single-qubit Clifford gates on the encoded qubit to explore its computational capabilities. The implemented 7-qubit code is the first realization of a complete Calderbank-Shor-Steane (CSS) code and constitutes a central building block for FTQC schemes based on concatenated elementary quantum codes. It also represents the smallest fully functional instance of the color code, opening a route towards topological FTQC.

7 pages, 4 figures and appendix

References in corpus (8)

• Quantum Computing
• An Open-System Quantum Simulator with Trapped Ions
• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• Towards fault-tolerant quantum computing with trapped ions
• Experimental demonstration of topological error correction
• Topological Computation without Braiding
• Error Threshold for Color Codes and Random 3-Body Ising Models

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• Evidence against a mean field description of short-range spin glasses revealed through thermal boundary conditions
• Precision measurement of branching fractions of ${}^{138}$Ba${}^{+}$: Testing many body theories below one percent level
• Ground-state cooling of a trapped ion using long-wavelength radiation
• Generalized Color Codes Supporting Non-Abelian Anyons
• Parafermion stabilizer codes
• Optimized Quantum Error Correction Codes for Experiments
• Determination of stabilizer states