spin qubit quantum computer

{{Primary sources section|date=January 2021|talk=|small=}}Image:DoubleQuantumDot.jpg. Each electron spin S_L or S_R define one quantum two-level system, or a spin qubit in the Loss-DiVincenzo proposal. A narrow gate between the two dots can modulate the coupling, allowing swap operations.]]

The Loss–DiVicenzo quantum computer proposal tried to fulfill DiVincenzo's criteria for a scalable quantum computer,D. P. DiVincenzo, in Mesoscopic Electron Transport, Vol. 345 of NATO Advanced Study Institute, Series E: Applied Sciences, edited by L. Sohn, L. Kouwenhoven, and G. Schoen (Kluwer, Dordrecht, 1997); [https://arxiv.org/abs/cond-mat/9612126 on arXiv.org in Dec. 1996] namely:

• identification of well-defined qubits;
• reliable state preparation;
• low decoherence;
• accurate quantum gate operations and
• strong quantum measurements.

A candidate for such a quantum computer is a lateral quantum dot system. Earlier work on applications of quantum dots for quantum computing was done by Barenco et al.{{Cite journal|last1=Barenco|first1=Adriano|last2=Deutsch|first2=David|last3=Ekert|first3=Artur|last4=Josza|first4=Richard|date=1995|title=Conditional Quantum Dynamics and Logic Gates|journal=Phys. Rev. Lett.|language=en|volume=74|issue=20|pages=4083–4086|arxiv=quant-ph/9503017|doi=10.1103/PhysRevLett.74.4083|pmid=10058408 |bibcode=1995PhRvL..74.4083B |s2cid=26611140 }}

The Loss–DiVincenzo quantum computer operates, basically, using inter-dot gate voltage for implementing swap operations and local magnetic fields (or any other local spin manipulation) for implementing the controlled NOT gate (CNOT gate).

The swap operation is achieved by applying a pulsed inter-dot gate voltage, so the exchange constant in the Heisenberg Hamiltonian becomes time-dependent:

:$H\_\{\backslash rm\; s\}(t)\; =\; J(t)\backslash mathbf\{S\}\_\{\backslash rm\; L\}\; \backslash cdot\; \backslash mathbf\{S\}\_\{\backslash rm\; R\}\; .$

This description is only valid if:

• the level spacing in the quantum-dot $\backslash Delta\; E$ is much greater than $\backslash ;\; kT$
• the pulse time scale $\backslash tau\_\{\backslash rm\; s\}$ is greater than $\backslash hbar\; /\; \backslash Delta\; E$, so there is no time for transitions to higher orbital levels to happen and
• the decoherence time $\backslash Gamma\; ^\{-1\}$ is longer than $\backslash tau\_\{\backslash rm\; s\}.$

$k$ is the Boltzmann constant and $T$ is the temperature in Kelvin.

From the pulsed Hamiltonian follows the time evolution operator

:$U\_\{\backslash rm\; s\}(t)\; =\; \{\backslash mathcal\{T\}\}\; \backslash exp\backslash left\backslash \{\; -i\backslash int\_0^t\; dt\text{'}\; H\_\{\backslash rm\; s\}(t\text{'})\; \backslash right\backslash \},$

where $\{\backslash mathcal\{T\}\}$ is the time-ordering symbol.

We can choose a specific duration of the pulse such that the integral in time over $J(t)$ gives $J\_0\; \backslash tau\_\{\backslash rm\; s\}\; =\; \backslash pi\; \backslash pmod\{2\backslash pi\},$ and $U\_\{\backslash rm\; s\}$ becomes the swap operator $U\_\{\backslash rm\; s\}\; (J\_0\; \backslash tau\_\{\backslash rm\; s\}\; =\; \backslash pi)\; \backslash equiv\; U\_\{\backslash rm\; sw\}.$

This pulse run for half the time (with $J\_0\; \backslash tau\_\{\backslash rm\; s\}\; =\; \backslash pi\; /2$) results in a square root of swap gate, $U\_\{\backslash rm\; sw\}^\{1/2\}.$

The "XOR" gate may be achieved by combining $U\_\{\backslash rm\; sw\}^\{1/2\}$ operations with individual spin rotation operations:

:$U\_\{\backslash rm\; XOR\}\; =\; e^\{i\backslash frac\{\backslash pi\}\{2\}S\_\{\backslash rm\; L\}^z\}e^\{-i\backslash frac\{\backslash pi\}\{2\}S\_\{\backslash rm\; R\}^z\}U\_\{\backslash rm\; sw\}^\{1/2\}$

e^{i \pi S_{\rm L}^z}U_{\rm sw}^{1/2}.

The $U\_\{\backslash rm\; XOR\}$ operator is a conditional phase shift (controlled-Z) for the state in the basis of $\backslash mathbf\{S\}\_\{\backslash rm\; L\}\; +\; \backslash mathbf\{S\}\_\{\backslash rm\; R\}$.{{r|Loss-DiVincenzo|page=4}} It can be made into a CNOT gate by surrounding the desired target qubit with Hadamard gates.

Spin qubits mostly have been implemented by locally depleting two-dimensional electron gases in semiconductors such a gallium arsenide,{{cite journal|last1=Petta|first1=J. R.|year=2005|title=Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots|journal=Science|volume=309|issue=5744|pages=2180–2184|doi=10.1126/science.1116955|pmid=16141370 |bibcode=2005Sci...309.2180P |s2cid=9107033 |issn=0036-8075}}{{cite journal|last1=Bluhm|first1=Hendrik|last2=Foletti|first2=Sandra|last3=Neder|first3=Izhar|last4=Rudner|first4=Mark|last5=Mahalu|first5=Diana|last6=Umansky|first6=Vladimir|last7=Yacoby|first7=Amir|year=2010|title=Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs|journal=Nature Physics|volume=7|issue=2|pages=109–113|doi=10.1038/nphys1856|issn=1745-2473|doi-access=free}} and germanium.{{Cite journal|last1=Watzinger|first1=Hannes|last2=Kukučka|first2=Josip|last3=Vukušić|first3=Lada|last4=Gao|first4=Fei|last5=Wang|first5=Ting|last6=Schäffler|first6=Friedrich|last7=Zhang|first7=Jian-Jun|last8=Katsaros|first8=Georgios|date=2018-09-25|title=A germanium hole spin qubit|journal=Nature Communications|language=en|volume=9|issue=1|pages=3902|doi=10.1038/s41467-018-06418-4|pmid=30254225 |pmc=6156604 |arxiv=1802.00395 |bibcode=2018NatCo...9.3902W |issn=2041-1723|doi-access=free}} Spin qubits have also been implemented in other material systems such as graphene.{{cite journal|last1=Trauzettel|first1=Björn|last2=Bulaev|first2=Denis V.|last3=Loss|first3=Daniel|last4=Burkard|first4=Guido|year=2007|title=Spin qubits in graphene quantum dots|journal=Nature Physics|volume=3|issue=3|pages=192–196|arxiv=cond-mat/0611252|doi=10.1038/nphys544|bibcode=2007NatPh...3..192T |s2cid=119431314 |issn=1745-2473}} A more recent development is using silicon spin qubits, an approach that is e.g. pursued by Intel.{{cite journal | last1=Xue | first1=Xiao | last2=Patra | first2=Bishnu | last3=van Dijk | first3=Jeroen P. G. | last4=Samkharadze | first4=Nodar | last5=Subramanian | first5=Sushil | last6=Corna | first6=Andrea | last7=Paquelet Wuetz | first7=Brian | last8=Jeon | first8=Charles | last9=Sheikh | first9=Farhana | last10=Juarez-Hernandez | first10=Esdras | last11=Esparza | first11=Brando Perez | last12=Rampurawala | first12=Huzaifa | last13=Carlton | first13=Brent | last14=Ravikumar | first14=Surej | last15=Nieva | first15=Carlos | last16=Kim | first16=Sungwon | last17=Lee | first17=Hyung-Jin | last18=Sammak | first18=Amir | last19=Scappucci | first19=Giordano | last20=Veldhorst | first20=Menno | last21=Sebastiano | first21=Fabio | last22=Babaie | first22=Masoud | last23=Pellerano | first23=Stefano | last24=Charbon | first24=Edoardo | last25=Vandersypen | first25=Lieven M. K. | title=CMOS-based cryogenic control of silicon quantum circuits | journal=Nature | volume=593 | issue=7858 | date=2021-05-13 | issn=0028-0836 | doi=10.1038/s41586-021-03469-4 | doi-access=free | pages=205–210| pmid=33981049 | arxiv=2009.14185 }}{{cite web | url=https://spectrum.ieee.org/intels-quantum-computing-plans-hot-qubits-cold-control-chips-and-rapid-testing | title=What Intel is Planning for the Future of Quantum Computing: Hot Qubits, Cold Control Chips, and Rapid Testing - IEEE Spectrum }} The advantage of the silicon platform is that it allows using modern semiconductor device fabrication for making the qubits. Some of these devices have a comparably high operation temperature of a few kelvins (hot qubits) which is advantageous for scaling the number of qubits in a quantum processor.{{cite journal | last1=Yang | first1=C. H. | last2=Leon | first2=R. C. C. | last3=Hwang | first3=J. C. C. | last4=Saraiva | first4=A. | last5=Tanttu | first5=T. | last6=Huang | first6=W. | last7=Camirand Lemyre | first7=J. | last8=Chan | first8=K. W. | last9=Tan | first9=K. Y. | last10=Hudson | first10=F. E. | last11=Itoh | first11=K. M. | last12=Morello | first12=A. | last13=Pioro-Ladrière | first13=M. | last14=Laucht | first14=A. | last15=Dzurak | first15=A. S. | title=Operation of a silicon quantum processor unit cell above one kelvin | journal=Nature | volume=580 | issue=7803 | date=2020-04-16 | issn=0028-0836 | doi=10.1038/s41586-020-2171-6 | doi-access=free | pages=350–354| pmid=32296190 | arxiv=1902.09126 }}{{cite journal | last1=Camenzind | first1=Leon C. | last2=Geyer | first2=Simon | last3=Fuhrer | first3=Andreas | last4=Warburton | first4=Richard J. | last5=Zumbühl | first5=Dominik M. | last6=Kuhlmann | first6=Andreas V. | title=A hole spin qubit in a fin field-effect transistor above 4 kelvin | journal=Nature Electronics | volume=5 | issue=3 | date=2022-03-03 | issn=2520-1131 | doi=10.1038/s41928-022-00722-0 | doi-access=free | pages=178–183| arxiv=2103.07369 }}

• Kane quantum computer
• Quantum dot cellular automaton

{{reflist}}

• [https://www.quantum-inspire.com/contact QuantumInspire] online platform from Delft University of Technology, allows building and running quantum algorithms on "Spin-2" a 2 silicon spin qubits processor.

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