news & views with arbitrary spin properties. This is in line with previous findings for hybrid interfaces formed with ferromagnetic surfaces8,9. However, replacing such surfaces with a magnetic skyrmion lattice has an important advantage — the possibility of transporting the spin information stored in a hybrid nano-object, coherently, and potentially over distances comparable to the extent of the skyrmion lattice. To achieve coherent transport of spin information, the researchers used the size of the organic molecules as a control parameter. In an isolated hybrid unit, the total magnetocrystalline anisotropy energy and the energy of the exchange interaction with the surrounding magnetic moments scale with the unit’s area and perimeter, respectively. When the two energy contributions are equal, reversing the magnetization of the hybrid unit will also switch the surrounding magnetic moments, thus allowing the hybrid nano-object to couple with its surroundings by tailoring its size. Compared with the case of the relatively large graphene islands, the use of coronene molecules reduces the number of iron atoms underneath the molecular units by a factor of around 100, while the number of neighbouring atoms drops by only a factor of 10. The anisotropy energy ranges from almost one electronvolt for graphene to millielectronvolts for coronene; the latter is low enough to be comparable to the exchange energy. The switching of the magnetization of a coronene unit that has equal anisotropy and exchange energies has a remarkable effect on
the skyrmion lattice underneath it, which can be traced back to the stable spin texture of the topologically protected skyrmion lattice. The magnetic moments of the iron atoms in a chain follow a right-rotating spiral with a period of about five lattice sides, and an angle between two moments of about 72° (Fig. 1). When an external field is applied, the coronene hybrid couples, as a local magnetic unit, to the field, even though the magnetic skyrmion lattice as a whole does not. When the field is high enough, the magnetization of the coronene hybrid switches towards the direction of the field and two things happen. First, the neighbouring iron atoms flip their spin, at an angle that is set by both the ferromagnetic coupling to the coronene unit and the spin texture of the atomic chain. Second, in order to maintain the stable chiral arrangement of the magnetic moments in the chain, the magnetization profile of the entire chain shifts by half a unit cell. The changes in the spin texture of the chain are therefore non-local, and propagate coherently over the whole chain. When another hybrid is encountered, its magnetization switches to match the modified local spin environment. Such transfer of information via vector spin chirality 10 between hybrids with tunable magnetic anisotropy opens the possibility of transmitting spin information via the skyrmion lattice over long ranges. Crucially, because the hybridization strength allows the magnetocrystalline anisotropy of the hybrid magnetic units to be controlled, which is ultimately responsible for their stability against thermal fluctuations, high operating temperatures can be envisaged.
The work of Brede and co-workers extends the original concept of spinterfaces to the class of spin-textured materials, opening new and exciting routes for controlling spin at the atomic scale. Furthermore, the same degree of control achieved by the team in real space could also be achieved for systems with a spin texture in momentum space, thus allowing control of the spin properties of materials such as Rashba systems and topological insulators. The interplay between exchange interaction, spin–orbit coupling, topology, and hybridization is bound to generate a series of exciting spin phenomena, as has been illustrated recently by results on hybrid interfaces formed with topological insulators11. ❐ Mirko Cinchetti is in the Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Erwin Schroedinger Str. 46, D-67663 Kaiserslautern, Germany. e-mail: [email protected] References
1. Barraud, C. et al. Nature Phys. 6, 615–620 (2010). 2. Sanvito, S. Nature Phys. 6, 562–564 (2010). 3. Dediu, V. A., Hueso, L. E., Bergenti, I. & Taliani, C. Nature Mater. 8, 707–716 (2009). 4. Moodera, J. S., Koopmans, B. & Oppeneer, P. M. Mater. Res. Soc. Bull. 39, 578–581 (2014). 5. Sanvito, S. Chem. Soc. Rev. 40, 3336–3355 (2011). 6. Brede, J. et al. Nature Nanotech. 9, 1018–1023 (2014). 7. Heinze, S. et al. Nature Phys. 7, 713–718 (2011). 8. Callsen, M., Caciuc, V., Kiselev, N., Atodiresei, N. & Blügel, S. Phys. Rev. Lett. 111, 106805 (2013). 9. Atodiresei, N. et al. Phys. Rev. Lett. 105, 066601 (2010). 10. Menzel, M. et al. Phys. Rev. Lett. 108, 197204 (2012). 11. Sessi, P., Bathon, T., Kokh, K., Tereshchenko, O. & Bode, M. Nano Lett. 14, 5092–5096 (2014).
QUANTUM COMPUTATION
Silicon comes back
The extraordinary long coherence times and high-fidelity manipulation of electron spins trapped in isotopically purified silicon could be an essential step towards the realization of a solid-state quantum computer.
Lars R. Schreiber and Hendrik Bluhm
Q
uantum computing promises to solve certain problems that are practically unsolvable on classical computers because of their long run time. Bringing this vision into practice will require many millions of quantum bits (qubits), which are the base units of a quantum computer. Countless papers begin with a statement that electron spins in semiconductors are promising qubits because they can build on microelectronics technology and because they exhibit a weak interaction with the 966
solid-state host material. However, most pioneering works so far are difficult to scale up or use materials in which the interaction between electron and nuclear spins is still strong enough to heavily disturb the phase of the electron spins, thus destroying the information stored in the qubit very quickly. Now, three experiments from different groups published in Nature Nanotechnology 1–3 confirm the expectation that individual electron spins in silicon are indeed highly decoupled from their environment and can
be controlled coherently with high accuracy. The demonstrated accuracy of single-qubit control is at the minimum threshold for scalable quantum computing. Each of the three groups defines a single electron spin as one qubit, but each follows its own approach to confine this single electron in some nanoscale device. Computer chips used today are based on silicon, but so far silicon has played a minor role in quantum computation research. Major breakthroughs were
NATURE NANOTECHNOLOGY | VOL 9 | DECEMBER 2014 | www.nature.com/naturenanotechnology
© 2014 Macmillan Publishers Limited. All rights reserved
news & views
Micromagnet Co Metallic gates
Co Quantum dot
Al2O3
b
c Microwave antenna
Microwave antenna
−
SET
Strained Si Si0.7Ge0.3
Metallic gates
Metallic gates
Si0.7Ge0.3 Quantum dot
SiO2
−
SET
Isotopically purified 28Si
25 nm
43 nm
a
SiO2
SET
+ 31
−
P donor
Isotopically purified 28Si
Figure 1 | Schematics of the Si-based spin-qubit devices used by the three groups. a, In the work of Vandersypen and colleagues, a single electron is trapped in a quantum dot, which is formed by the Si/SiGe quantum well and by the electrostatic potential of metallic top-gates. A global positively charged gate, which induces electrons in the quantum well, is not shown. b, Veldhorst and colleagues confine the single electron at the Si/SiO2 interface by means of metallic top-gates (crossing gates, yellow and orange, are isolated by Al2O3). c, In the work by Muhonen and colleagues, the electron is bound to a single phosphorus dopant. The spin of the phosphorus nucleus can be used as long-lasting qubit memory. Devices in b,c are fabricated on isotopically purified 28Si. Read-out of the charge state of the quantum dot is done by a single electron transistor (SET) formed by top-gates in the Si/SiGe quantum well (a) and at the oxide interface (b,c). Electrons were manipulated either by ESR pulses (b,c) emitted from a microwave antenna or by EDSR pulses (a), which require an inhomogeneous magnetic field generated by a micromagnet. (The actual gate patterns in a,b are more complicated and allow trapping of two qubits in a tunnel-coupled double dot.)
achieved in superconducting systems or in other semiconductor systems, for example (Al,Ga)As heterostructures4, which can be fabricated with high crystal quality and confine electrons to two dimensions. However, in (Al,Ga)As the spin–orbit coupling, which makes the spins sensitive to fluctuating electric fields usually present in solid-state systems, is relatively strong. Moreover, the coupling of the electrons to nuclear spins turned out to be an even bigger concern for electron spin qubits in (Al,Ga)As and all other III–V semiconductors. This interaction of a trapped electron with typically 106 randomly fluctuating nuclei leads to a loss of the phase information stored in the qubit on the timescale of T* 2 ≈ 10 ns. The spin–orbit interaction in silicon is very weak, and, more importantly, this material can be made nuclear-spin-free by isotopic purification5. Thus, the electron spin couples weakly to its environment and long coherence times have been predicted6. Hence, surprisingly at first sight, what makes silicon ideal for spin-based quantum computation is not much related to the properties that favour its use for conventional transistors. Nevertheless, the advanced semiconductor technology available will certainly be advantageous for implementing a silicon-based quantum computer. The three papers presented here are important steps towards this goal, and, as mentioned, employ different approaches to confine a single electron. In the work by Lieven Vandersypen and colleagues from the Technical University of Delft, the University of Wisconsin-Madison and the University of Basel1, a single electron is trapped in a Si/SiGe quantum well by means of band discontinuities and electrical topgates forming the quantum dot potential
(Fig. 1a). In this case, the silicon contains a natural abundance of 5% 29Si with non-zero nuclear spin. In contrast, Menno Veldhorst and colleagues from The University of New South Wales, the University of Twente and Keio University 2 used isotopically purified 28Si with only 800 ppm of residual 29 Si and formed a gate-defined quantum dot in the silicon inversion layer at the Si/SiO2 interface (Fig. 1b). Finally, Juha Muhonen and colleagues from the University of New South Wales, Keio University and the University of Melbourne3 used a single electron spin bound to a phosphorus dopant also in isotopically purified 28Si (Fig. 1c). For SiGe quantum dots, such isotopic purification has also been previously demonstrated7. All groups observed an electron spin dephasing time T*2 that is orders of magnitude larger than in (Al,Ga)As (Table 1). In accordance with the higher fraction of spinless 28Si nuclei Veldhorst and colleagues and Muhonen and colleagues found even longer T*2 of 120 μs and 270 μs, respectively. It is interesting to compare the details of the qubit coherence and control. The stronger the coupling to an external control signal, the faster the manipulation can be and the more computational operations can be performed within the coherence time of the qubit. Veldhorst and colleagues and Muhonen and colleagues employed a control technique called electron spin resonance (ESR). They applied a microwave magnetic field via an on-chip antenna to the qubit. Vandersypen and colleagues employed a related method called electron dipole spin resonance (ESDR). Here, an on-chip micromagnet generates an inhomogeneous magnetic field across the quantum dot. Applying a microwave signal to one of the metal gates displaces the electron and thus
NATURE NANOTECHNOLOGY | VOL 9 | DECEMBER 2014 | www.nature.com/naturenanotechnology
© 2014 Macmillan Publishers Limited. All rights reserved
generates an oscillating magnetic field in the electron’s rest frame. Both ESR and EDSR pulses enable universal qubit control, meaning that all possible single-qubit operations can be generated. The three groups all achieved manipulation rates in or just below the MHz regime (Table 1). The fidelity of these quantum gates is an even more fundamental (but closely related) figure of merit than the coherence time. Roughly speaking, it specifies the success probability of a single gate operation. The measurements or estimates (based on methods with different degrees of reliability) of all three papers yield values around 99% (Table 1). These results are close to the level required for quantum error correction, a technique that eliminates unavoidable gate errors provided they occur rarely enough and lies at the heart of scalable quantum computing. In the isotopically purified systems, much higher values would be expected based on the coherence time, and it will be interesting to see what actually limits the reported values. This qubit control allows all three groups to apply spin-echo techniques well known from NMR to extend the qubit coherence even further by cancelling out any dephasing due to fluctuations that are slow compared with the electron spin dynamics. One preeminent source of such slow magnetic noise is the remaining nuclear-spin bath. After eliminating slow noise with a sequence of multiple EDSR pulses, Vandersypen and colleagues found a longer coherence time of T2 = 44 μs (Table 1). Their data indicate an additional fast noise source, which the authors attribute to switching between different valleys of the silicon band structure. Hence, one may expect that increasing the valley splitting can ameliorate 967
news & views
Table 1 | Electron spin coherence times and control fidelity, and the main figures of merit of the three silicon systems. Vandersypen1 (Fig. 1a)
Veldhorst2 (Fig. 1b)
Muhonen3 (Fig. 1c)
Fraction of non-zero nuclear spins
Natural abundance (5% 29Si)
Isotopically purified 28Si (with 800 ppm 29Si)
Isotopically purified 28Si (with 800 ppm 29Si)
Qubit dephasing time T *2 (μs)
0.9
120
270
Maximum qubit manipulation rate (MHz)
5
the skyrmion lattice underneath it, which can be traced back to the stable spin texture of the topologically protected skyrmion lattice. The magnetic moments of the iron atoms in a chain follow a right-rotating spiral with a period of about five lattice sides, and an angle between two moments of about 72° (Fig. 1). When an external field is applied, the coronene hybrid couples, as a local magnetic unit, to the field, even though the magnetic skyrmion lattice as a whole does not. When the field is high enough, the magnetization of the coronene hybrid switches towards the direction of the field and two things happen. First, the neighbouring iron atoms flip their spin, at an angle that is set by both the ferromagnetic coupling to the coronene unit and the spin texture of the atomic chain. Second, in order to maintain the stable chiral arrangement of the magnetic moments in the chain, the magnetization profile of the entire chain shifts by half a unit cell. The changes in the spin texture of the chain are therefore non-local, and propagate coherently over the whole chain. When another hybrid is encountered, its magnetization switches to match the modified local spin environment. Such transfer of information via vector spin chirality 10 between hybrids with tunable magnetic anisotropy opens the possibility of transmitting spin information via the skyrmion lattice over long ranges. Crucially, because the hybridization strength allows the magnetocrystalline anisotropy of the hybrid magnetic units to be controlled, which is ultimately responsible for their stability against thermal fluctuations, high operating temperatures can be envisaged.
The work of Brede and co-workers extends the original concept of spinterfaces to the class of spin-textured materials, opening new and exciting routes for controlling spin at the atomic scale. Furthermore, the same degree of control achieved by the team in real space could also be achieved for systems with a spin texture in momentum space, thus allowing control of the spin properties of materials such as Rashba systems and topological insulators. The interplay between exchange interaction, spin–orbit coupling, topology, and hybridization is bound to generate a series of exciting spin phenomena, as has been illustrated recently by results on hybrid interfaces formed with topological insulators11. ❐ Mirko Cinchetti is in the Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Erwin Schroedinger Str. 46, D-67663 Kaiserslautern, Germany. e-mail: [email protected] References
1. Barraud, C. et al. Nature Phys. 6, 615–620 (2010). 2. Sanvito, S. Nature Phys. 6, 562–564 (2010). 3. Dediu, V. A., Hueso, L. E., Bergenti, I. & Taliani, C. Nature Mater. 8, 707–716 (2009). 4. Moodera, J. S., Koopmans, B. & Oppeneer, P. M. Mater. Res. Soc. Bull. 39, 578–581 (2014). 5. Sanvito, S. Chem. Soc. Rev. 40, 3336–3355 (2011). 6. Brede, J. et al. Nature Nanotech. 9, 1018–1023 (2014). 7. Heinze, S. et al. Nature Phys. 7, 713–718 (2011). 8. Callsen, M., Caciuc, V., Kiselev, N., Atodiresei, N. & Blügel, S. Phys. Rev. Lett. 111, 106805 (2013). 9. Atodiresei, N. et al. Phys. Rev. Lett. 105, 066601 (2010). 10. Menzel, M. et al. Phys. Rev. Lett. 108, 197204 (2012). 11. Sessi, P., Bathon, T., Kokh, K., Tereshchenko, O. & Bode, M. Nano Lett. 14, 5092–5096 (2014).
QUANTUM COMPUTATION
Silicon comes back
The extraordinary long coherence times and high-fidelity manipulation of electron spins trapped in isotopically purified silicon could be an essential step towards the realization of a solid-state quantum computer.
Lars R. Schreiber and Hendrik Bluhm
Q
uantum computing promises to solve certain problems that are practically unsolvable on classical computers because of their long run time. Bringing this vision into practice will require many millions of quantum bits (qubits), which are the base units of a quantum computer. Countless papers begin with a statement that electron spins in semiconductors are promising qubits because they can build on microelectronics technology and because they exhibit a weak interaction with the 966
solid-state host material. However, most pioneering works so far are difficult to scale up or use materials in which the interaction between electron and nuclear spins is still strong enough to heavily disturb the phase of the electron spins, thus destroying the information stored in the qubit very quickly. Now, three experiments from different groups published in Nature Nanotechnology 1–3 confirm the expectation that individual electron spins in silicon are indeed highly decoupled from their environment and can
be controlled coherently with high accuracy. The demonstrated accuracy of single-qubit control is at the minimum threshold for scalable quantum computing. Each of the three groups defines a single electron spin as one qubit, but each follows its own approach to confine this single electron in some nanoscale device. Computer chips used today are based on silicon, but so far silicon has played a minor role in quantum computation research. Major breakthroughs were
NATURE NANOTECHNOLOGY | VOL 9 | DECEMBER 2014 | www.nature.com/naturenanotechnology
© 2014 Macmillan Publishers Limited. All rights reserved
news & views
Micromagnet Co Metallic gates
Co Quantum dot
Al2O3
b
c Microwave antenna
Microwave antenna
−
SET
Strained Si Si0.7Ge0.3
Metallic gates
Metallic gates
Si0.7Ge0.3 Quantum dot
SiO2
−
SET
Isotopically purified 28Si
25 nm
43 nm
a
SiO2
SET
+ 31
−
P donor
Isotopically purified 28Si
Figure 1 | Schematics of the Si-based spin-qubit devices used by the three groups. a, In the work of Vandersypen and colleagues, a single electron is trapped in a quantum dot, which is formed by the Si/SiGe quantum well and by the electrostatic potential of metallic top-gates. A global positively charged gate, which induces electrons in the quantum well, is not shown. b, Veldhorst and colleagues confine the single electron at the Si/SiO2 interface by means of metallic top-gates (crossing gates, yellow and orange, are isolated by Al2O3). c, In the work by Muhonen and colleagues, the electron is bound to a single phosphorus dopant. The spin of the phosphorus nucleus can be used as long-lasting qubit memory. Devices in b,c are fabricated on isotopically purified 28Si. Read-out of the charge state of the quantum dot is done by a single electron transistor (SET) formed by top-gates in the Si/SiGe quantum well (a) and at the oxide interface (b,c). Electrons were manipulated either by ESR pulses (b,c) emitted from a microwave antenna or by EDSR pulses (a), which require an inhomogeneous magnetic field generated by a micromagnet. (The actual gate patterns in a,b are more complicated and allow trapping of two qubits in a tunnel-coupled double dot.)
achieved in superconducting systems or in other semiconductor systems, for example (Al,Ga)As heterostructures4, which can be fabricated with high crystal quality and confine electrons to two dimensions. However, in (Al,Ga)As the spin–orbit coupling, which makes the spins sensitive to fluctuating electric fields usually present in solid-state systems, is relatively strong. Moreover, the coupling of the electrons to nuclear spins turned out to be an even bigger concern for electron spin qubits in (Al,Ga)As and all other III–V semiconductors. This interaction of a trapped electron with typically 106 randomly fluctuating nuclei leads to a loss of the phase information stored in the qubit on the timescale of T* 2 ≈ 10 ns. The spin–orbit interaction in silicon is very weak, and, more importantly, this material can be made nuclear-spin-free by isotopic purification5. Thus, the electron spin couples weakly to its environment and long coherence times have been predicted6. Hence, surprisingly at first sight, what makes silicon ideal for spin-based quantum computation is not much related to the properties that favour its use for conventional transistors. Nevertheless, the advanced semiconductor technology available will certainly be advantageous for implementing a silicon-based quantum computer. The three papers presented here are important steps towards this goal, and, as mentioned, employ different approaches to confine a single electron. In the work by Lieven Vandersypen and colleagues from the Technical University of Delft, the University of Wisconsin-Madison and the University of Basel1, a single electron is trapped in a Si/SiGe quantum well by means of band discontinuities and electrical topgates forming the quantum dot potential
(Fig. 1a). In this case, the silicon contains a natural abundance of 5% 29Si with non-zero nuclear spin. In contrast, Menno Veldhorst and colleagues from The University of New South Wales, the University of Twente and Keio University 2 used isotopically purified 28Si with only 800 ppm of residual 29 Si and formed a gate-defined quantum dot in the silicon inversion layer at the Si/SiO2 interface (Fig. 1b). Finally, Juha Muhonen and colleagues from the University of New South Wales, Keio University and the University of Melbourne3 used a single electron spin bound to a phosphorus dopant also in isotopically purified 28Si (Fig. 1c). For SiGe quantum dots, such isotopic purification has also been previously demonstrated7. All groups observed an electron spin dephasing time T*2 that is orders of magnitude larger than in (Al,Ga)As (Table 1). In accordance with the higher fraction of spinless 28Si nuclei Veldhorst and colleagues and Muhonen and colleagues found even longer T*2 of 120 μs and 270 μs, respectively. It is interesting to compare the details of the qubit coherence and control. The stronger the coupling to an external control signal, the faster the manipulation can be and the more computational operations can be performed within the coherence time of the qubit. Veldhorst and colleagues and Muhonen and colleagues employed a control technique called electron spin resonance (ESR). They applied a microwave magnetic field via an on-chip antenna to the qubit. Vandersypen and colleagues employed a related method called electron dipole spin resonance (ESDR). Here, an on-chip micromagnet generates an inhomogeneous magnetic field across the quantum dot. Applying a microwave signal to one of the metal gates displaces the electron and thus
NATURE NANOTECHNOLOGY | VOL 9 | DECEMBER 2014 | www.nature.com/naturenanotechnology
© 2014 Macmillan Publishers Limited. All rights reserved
generates an oscillating magnetic field in the electron’s rest frame. Both ESR and EDSR pulses enable universal qubit control, meaning that all possible single-qubit operations can be generated. The three groups all achieved manipulation rates in or just below the MHz regime (Table 1). The fidelity of these quantum gates is an even more fundamental (but closely related) figure of merit than the coherence time. Roughly speaking, it specifies the success probability of a single gate operation. The measurements or estimates (based on methods with different degrees of reliability) of all three papers yield values around 99% (Table 1). These results are close to the level required for quantum error correction, a technique that eliminates unavoidable gate errors provided they occur rarely enough and lies at the heart of scalable quantum computing. In the isotopically purified systems, much higher values would be expected based on the coherence time, and it will be interesting to see what actually limits the reported values. This qubit control allows all three groups to apply spin-echo techniques well known from NMR to extend the qubit coherence even further by cancelling out any dephasing due to fluctuations that are slow compared with the electron spin dynamics. One preeminent source of such slow magnetic noise is the remaining nuclear-spin bath. After eliminating slow noise with a sequence of multiple EDSR pulses, Vandersypen and colleagues found a longer coherence time of T2 = 44 μs (Table 1). Their data indicate an additional fast noise source, which the authors attribute to switching between different valleys of the silicon band structure. Hence, one may expect that increasing the valley splitting can ameliorate 967
news & views
Table 1 | Electron spin coherence times and control fidelity, and the main figures of merit of the three silicon systems. Vandersypen1 (Fig. 1a)
Veldhorst2 (Fig. 1b)
Muhonen3 (Fig. 1c)
Fraction of non-zero nuclear spins
Natural abundance (5% 29Si)
Isotopically purified 28Si (with 800 ppm 29Si)
Isotopically purified 28Si (with 800 ppm 29Si)
Qubit dephasing time T *2 (μs)
0.9
120
270
Maximum qubit manipulation rate (MHz)
5
