Quantum computations on a topologically encoded qubit

By Daniel Nigg, Markus P. Müller, E. Martinez, Philipp Schindler, M. Hennrich, Thomas Monz, Miguel Angel Martin-Delgado, Rainer Blatt. Science, 2014

396 citations recorded by the source corpus.

Fault-tolerant quantum computing Quantum states can be delicate. Attempts to process and manipulate quantum states can destroy the encoded information. Nigg et al. encoded the quantum state of a single qubit (in this case, a trapped ion) over the global properties of a series of trapped ions. These so-called stabilizers protected the information against noise sources that can degrade the single qubit. The protocol provides a route to fault-tolerant quantum computing. Science, this issue p. 302 A protocol is implemented that allows for fault-tolerant quantum computing. The construction of a quantum computer remains a fundamental scientific and technological challenge because of the influence of unavoidable noise. Quantum states and operations can be protected from errors through the use of protocols for quantum computing with faulty components. We present a quantum error-correcting code in which one qubit is encoded in entangled states distributed over seven trapped-ion qubits. The code can detect one bit flip error, one phase flip error, or a combined error of both, regardless on which of the qubits they occur. We applied sequences of gate operations on the encoded qubit to explore its computational capabilities. This seven-qubit code represents a fully functional instance of a topologically encoded qubit, or color code, and opens a route toward fault-tolerant quantum computing.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/bef5f88c24033573afe4069738f74722784be9d3

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

New class of quantum error-correcting codes for a bosonic mode (2016, background): “Rudimentary QEC protocols have been successfully carried out in ion traps [45,47,48], with nuclear magnetic resonance [51–53], nitrogen-vacancy centers in diamond [54,55], Rydberg atoms [33], and superconducting qubits [56–59].”
Quantum memories at finite temperature (2014, background): “…protocols present an uphill technical challenge for both engineering complex entangled error-correcting codes, and for reducing incident laboratory noise below a threshold value when compared with current experimental achievements (Barends et al., 2014; Nigg et al., 2014; Reed et al., 2012).”
Quantum error mitigation (2022, background): “…correcting errors is required for scalability (Shor, 1996), quantum error detection of artificially-added symmetries has been widely recognised as an important mile-stone towards this end goal (C´orcoles et al. , 2015; Gottes-man, 2016; Kelly et al. , 2015; Linke et al. , 2017; Nigg et al. , 2014).”
Realizing repeated quantum error correction in a distance-three surface code (2021, methodology): “requires the measurement of only 2 = 512 terms [20, 47].”
Demonstration of fault-tolerant universal quantum gate operations (2021, neutral): “ρ = |Φ ⟩⟨Φ | 1 2 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 (23) Φ + + L + ”
A quantum processor based on coherent transport of entangled atom arrays (2021, positive): “We use this architecture to realize programmable generation of entangled graph states such as cluster states and a 7-qubit Steane code state [6, 7].”
Quantum error correction for quantum memories (2013, positive): “tical beams (Aoki et al., 2009). In (Bell et al., 2014) the authors did an implementation of the [[4,1,2]] code in an all-optical set-up using a ve-qubit polarization-based optical cluster state. In (Nigg et al., 2014) seven trapped-ion qubits were used to represent, using Steane’s 7-qubit code (see”