Quantum error correction in a solid-state hybrid spin register

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Abstract

Hybrid quantum systems seek to combine the strength of its constituents to master the fundamental conflicting requirements of quantum technology: fast and accurate systems control together with perfect shielding from the environment, including the measurements apparatus, to achieve long quantum coherence. Excellent examples for hybrid quantum systems are heterogeneous spin systems where electron spins are used for readout and control while nuclear spins are used as long-lived quantum bits. Here we show that joint initialization, projective readout and fast local and non-local gate operations are no longer conflicting requirements in those systems, even under ambient conditions. We demonstrate high-fidelity initialization of a whole spin register (99 %) and single-shot readout of multiple individual nuclear spins by using the ancillary electron spin of a nitrogen-vacancy defect in diamond. Implementation of a novel non-local gate generic to our hybrid electron-nuclear quantum register allows to prepare entangled states of three nuclear spins, with fidelities exceeding 85 %. An important tool for scalable quantum computation is quantum error correction. Combining, for the first time, optimal-control based error avoidance with error correction, we realize a three-qubit phase-flip error correction algorithm. Utilizing optimal control, all of the above algorithms achieve fidelities approaching fault tolerant quantum operation, thus paving the way to large scale integrations. Our techniques can be used to improve scaling of quantum networks relying on diamond spins, phosphorous in silicon or other spin systems like quantum dots, silicon carbide or rare earth ions in solids.

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High-fidelity projective readout of a solid-state spin quantum register

Paul Alkemade, Lilian Childress, Ronald Hanson … (2013)

Initialization and readout of coupled quantum systems are essential ingredients for the implementation of quantum algorithms. If the state of a multi-qubit register can be read out in a single shot, this enables further key resources such as quantum error correction and deterministic quantum teleportation, as well as direct investigation of quantum correlations (entanglement). While spins in solids are attractive candidates for scalable quantum information processing, thus far single-shot detection has only been achieved for isolated qubits. Here, we demonstrate preparation and measurement of a multi-spin quantum register by implementing resonant optical excitation techniques originally developed in atomic physics. We achieve high-fidelity readout of the electronic spin associated with a single nitrogen-vacancy (NV) centre in diamond at low temperature, and exploit this readout to project up to three nearby nuclear spin qubits onto a well-defined state. Conversely, we can distinguish the state of the nuclear spins in a single shot by mapping it onto and subsequently measuring the electronic spin. Finally, we show compatibility with qubit control by demonstrating initialization, coherent manipulation, and single-shot readout in a single experiment on a two-qubit register, using techniques suitable for extension to larger registers. These results pave the way for the first test of Bell's inequalities on solid-state spins and the implementation of measurement-based quantum information protocols.

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High-fidelity readout and control of a nuclear spin qubit in silicon

Floris Zwanenburg, Andrew S. Dzurak, Andrea Morello … (2013)

A single nuclear spin holds the promise of being a long-lived quantum bit or quantum memory, with the high fidelities required for fault-tolerant quantum computing. We show here that such promise could be fulfilled by a single phosphorus (31P) nuclear spin in a silicon nanostructure. By integrating single-shot readout of the electron spin with on-chip electron spin resonance, we demonstrate the quantum non-demolition, electrical single-shot readout of the nuclear spin, with readout fidelity better than 99.8% - the highest for any solid-state qubit. The single nuclear spin is then operated as a qubit by applying coherent radiofrequency (RF) pulses. For an ionized 31P donor we find a nuclear spin coherence time of 60 ms and a 1-qubit gate control fidelity exceeding 98%. These results demonstrate that the dominant technology of modern electronics can be adapted to host a complete electrical measurement and control platform for nuclear spin-based quantum information processing.

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Solid state quantum memory using the 31P nuclear spin

Shyam Shankar, Arzhang Ardavan, Joel W. Ager … (2008)

The transfer of information between different physical forms is a central theme in communication and computation, for example between processing entities and memory. Nowhere is this more crucial than in quantum computation, where great effort must be taken to protect the integrity of a fragile quantum bit. Nuclear spins are known to benefit from long coherence times compared to electron spins, but are slow to manipulate and suffer from weak thermal polarisation. A powerful model for quantum computation is thus one in which electron spins are used for processing and readout while nuclear spins are used for storage. Here we demonstrate the coherent transfer of a superposition state in an electron spin 'processing' qubit to a nuclear spin 'memory' qubit, using a combination of microwave and radiofrequency pulses applied to 31P donors in an isotopically pure 28Si crystal. The electron spin state can be stored in the nuclear spin on a timescale that is long compared with the electron decoherence time and then coherently transferred back to the electron spin, thus demonstrating the 31P nuclear spin as a solid-state quantum memory. The overall store/readout fidelity is about 90%, attributed to systematic imperfections in radiofrequency pulses which can be improved through the use of composite pulses. We apply dynamic decoupling to protect the nuclear spin quantum memory element from sources of decoherence. The coherence lifetime of the quantum memory element is found to exceed one second at 5.5K.