Realization of quantum error correction

Abstract

Scalable quantum computation and communication require error control to protect quantum information against unavoidable noise. Quantum error correction protects information stored in two-level quantum systems (qubits) by rectifying errors with operations conditioned on the measurement outcomes. Error-correction protocols have been implemented in nuclear magnetic resonance experiments, but the inherent limitations of this technique prevent its application to quantum information processing. Here we experimentally demonstrate quantum error correction using three beryllium atomic-ion qubits confined to a linear, multi-zone trap. An encoded one-qubit state is protected against spin-flip errors by means of a three-qubit quantum error-correcting code. A primary ion qubit is prepared in an initial state, which is then encoded into an entangled state of three physical qubits (the primary and two ancilla qubits). Errors are induced simultaneously in all qubits at various rates. The encoded state is decoded back to the primary ion one-qubit state, making error information available on the ancilla ions, which are separated from the primary ion and measured. Finally, the primary qubit state is corrected on the basis of the ancillae measurement outcome. We verify error correction by comparing the corrected final state to the uncorrected state and to the initial state. In principle, the approach enables a quantum state to be maintained by means of repeated error correction, an important step towards scalable fault-tolerant quantum computation using trapped ions.

Optimization of segmented linear Paul traps and transport of stored particles

“…The required radial frequencies should be achieved with moderate voltages on the electrodes of several hundreds volts. Therefore, the RF trap drive may not exceed the break-through voltage -a limitation which plays a significant role in the case of very small traps [20,21].…”

“…The same techniques may be applied for the optimization of planar ion traps [21,22,23,24]. In the second section we optimize the transport of a single ion between two regions and illustrate the application of optimal control theory [25].…”

Transport Dynamics of Single Ions in Segmented Microstructured Paul Trap Arrays

“…as used in recent experiments [5,14,15,16,22,23], consists typically of two alumina wafers with gold coated electrode surfaces of a few micrometer thickness. The slotted wafers provide electrical RF and DC fields for 3D confinement of ions.…”

“…In the last few years methods were developed that enable quantum state engineering with high precision and long coherence times [7,8,9,10,11]. The necessary criteria [12] for large-scale quantum computation have been demonstrated in the past years, and small algorithms have been implemented successfully [13,14,15,16,17]. However, as in other approaches aiming towards quantum computation, scaling to many qubits is challenging.…”

Maximizing the purity of a qubit evolving in an anisotropic environment

“…Pure ancillas are required to introduce redundancy into quantum errorcorrecting codes, [1][2][3][4][5][6] for the preparation of GreenbergerHorne-Zeilinger (GHZ) states for quantum-enhanced precision measurements, 7,8 as a low-entropy resource for algorithmic cooling, [9][10][11] and to perform high-fidelity qubit readout. [12][13][14][15] Despite the importance of having high-quality ancillas, it is often taken for granted that high-purity ancillas can be prepared by allowing a physical qubit system to fall into its non-interacting ground state in contact with a thermal bath at low temperature.…”