Solid-state quantum memory using the 31P nuclear spin

Abstract

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 [1], where great effort must be taken to protect the integrity of a fragile quantum bit (qubit) [2]. However, transfer of quantum information is particularly challenging, as the process must remain coherent at all times to preserve the quantum nature of the information [3]. 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 31 P donors in an isotopically pure 28 Si crystal [4,5]. The state is left 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 31 P nuclear spin as a solid-state quantum memory. The overall store/readout fidelity is about 90%, attributed to imperfect rotations which can be improved through the use of composite pulses [6]. The coherence lifetime of the quantum memory element at 5.5 K exceeds one second.Classically, transfer of information can include a copying step, facilitating the identification and correction of errors. However, the no-cloning theorem limits the ability to faithfully copy quantum states across different degrees of freedom [7]; thus error correction becomes more challenging than for classical information and the transfer of information must take place directly. Experimental demonstrations of such transfer include moving a trapped ion qubit in and out of a decoherence-free subspace for storage purposes [8] and optical measurements of NV centres in diamond [9].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. The storage element can be a single, well-defined nuclear spin, or perhaps a bath of nearby nuclear spins [10]. 31 P donors in silicon provide an ideal combination of long-lived spin-1/2 electron [11] and nuclear spins [12], with the additional advantage of integration with existing technologies [4] and the possibility of single spin detection by electrical measurement [13,14,15]. Direct measurement of the 31 P nuclear spin by NMR has only been possible at very high doping levels (e.g. near the metal insulator transition [16]). Instead, electron-nuclear double resonance (ENDOR) can be used to excite both the electron and nuclear spin associated with the donor site, and measure the nuclear spin via the electron [17]. This was recently used to measure the nuclear spin-lattice relaxation time T 1n , which was found to follow the electron relaxation time T 1e over the range 6 to 12 K with the relationship T 1n ≈ 250T 1e [5,...

Electrically detected spin echoes of donor nuclei in silicon

“…We note that, whilst long, the T n 2 we measure is nonetheless shorter than has been previously measured for donors in silicon using conventional means 7 . A number of processes exist which limit T n 2 in those measurements, but the fundamental limit seems to be the lifetime of the hyperfine coupled donor electron 7,24 : T n 2 ≤ 2T e 1 .…”

“…A number of processes exist which limit T n 2 in those measurements, but the fundamental limit seems to be the lifetime of the hyperfine coupled donor electron 7,24 : T n 2 ≤ 2T e 1 . In the experiments reported here, the nuclear coherence time measured is indeed very close to twice the spin lifetime of the coupled donor electron, T n 2 = 2.8 ± 0.4 ms ≈ 2T e 1 = 3.72 ± 0.04 ms [dashed line, Fig.…”

“…Here, we utilize a spin echo technique to show that electrical readout of donor nuclear spins is compatible with phase coherence times T n 2 exceeding 2 ms, nearly two orders of magnitude longer than that previously seen 12 . We also determine that the artificially shortened donor electron lifetime T e 1 limits T n 2 via hyperfine coupling to the nuclei 7 , and discuss ways to overcome this limitation. To access the nuclear spin state of phosphorus donors in silicon, we exploit the precise hyperfine coupling between the donor nucleus and electron.…”

“…Whilst electron spins are an obvious choice for manipulating information, nuclear spins provide a robust system in which to store spin information for long periods of time 7 . However, whilst a number of optical 8,9 and quantum Hall based techniques 10 exist for reading the state of small ensembles of nuclear spins, until recently there has been no technique for doing so which is compatible with conventional electronic devices, particularly those in silicon.…”

Coherent feedback control of a single qubit in diamond

“…These limits could be overcome by re-initialising the ancilla or, if additional ancillas (such as nearby 13 C spins) are available, by repeating the algorithm with fresh ancillas, or by concatenating layers of protections against multi-axis noise (see Methods). Moreover, our scheme is more flexible than other protection schemes, including coherent transfer to the ancilla qubit [24], as it still allows applying some gate operations on the qubit [16]. For example, in our implementation the qubit was still evolving under the action of the hyperfine coupling, as indicated by the coherent oscillations of the fidelity (these oscillations could be removed e.g.…”