Entanglement in a solid-state spin ensemble

Abstract

Entanglement is the quintessential quantum phenomenon. It is a necessary ingredient in most emerging quantum technologies, including quantum repeaters, quantum information processing and the strongest forms of quantum cryptography. Spin ensembles, such as those used in liquid-state nuclear magnetic resonance, have been important for the development of quantum control methods. However, these demonstrations contain no entanglement and ultimately constitute classical simulations of quantum algorithms. Here we report the on-demand generation of entanglement between an ensemble of electron and nuclear spins in isotopically engineered, phosphorus-doped silicon. We combined high-field (3.4 T), low-temperature (2.9 K) electron spin resonance with hyperpolarization of the (31)P nuclear spin to obtain an initial state of sufficient purity to create a non-classical, inseparable state. The state was verified using density matrix tomography based on geometric phase gates, and had a fidelity of 98% relative to the ideal state at this field and temperature. The entanglement operation was performed simultaneously, with high fidelity, on 10(10) spin pairs; this fulfils one of the essential requirements for a silicon-based quantum information processor.

Isotope engineering of silicon and diamond for quantum computing and sensing applications

“…[69] Confirmation of long-enough coherence times in various electron and nuclear spins in silicon encouraged researchers to develop qubit initialization schemes. Although initialization of the electron spins can be achieved by reducing the sample temperature and increasing the externally applied magnetic field to make the thermal energy much smaller than the Zeeman split electronic levels, [38,70] initialization of the nuclear spins is not straightforward. This is because of the extremely small gyromagnetic ratios of the nuclear spins that do not allow a large-enough Zeeman energy separation with respect to the thermal energy, even with an externally applied magnetic field~10 T at a temperature of~1 K. Therefore, it was necessary to develop a method to polarize the nuclear spins in silicon using reasonable experimental conditions.…”

Electrically detected spin echoes of donor nuclei in silicon

“…Whilst this could be achieved in a number of ways 23,24 , we make use of the fact that the donor electrons are nearly entirely polarized by implementing a simple swap pulse sequence (π(f e 2 ) -π(f n 1 )) (Ref. 31), similar to the sequence used in recent related work 11,25,26 ,which results in an excess of nuclear spin up.…”

Maximizing the purity of a qubit evolving in an anisotropic environment

“…(11). In this case, the parameters λ µ (t) are the real eigenvalues of the superoperator L(t) and the unit vectorsê µ (t) determine the associated eigenoperators through…”

“…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.…”

“…This topic has become especially interesting in the context of spin-bath dynamics. [17][18][19][20] For slowly-evolving nuclear-spin baths, it is indeed possible to approach pure-state initial conditions through algorithmic cooling [9][10][11] or direct measurement of the bath state, 13,[21][22][23][24][25] so studying the purity for these systems is especially important from both a practical and a fundamental point of view.…”