Spin qubit quantum computer explained

The spin qubit quantum computer is a quantum computer based on controlling the spin of charge carriers (electrons and electron holes) in semiconductor devices.[1] The first spin qubit quantum computer was first proposed by Daniel Loss and David P. DiVincenzo in 1997,[2] . The proposal was to use the intrinsic spin-1/2 degree of freedom of individual electrons confined in quantum dots as qubits. This should not be confused with other proposals that use the nuclear spin as qubit, like the Kane quantum computer or the nuclear magnetic resonance quantum computer.

Loss–DiVicenzo proposal

The Loss–DiVicenzo quantum computer proposal tried to fulfill DiVincenzo's criteria for a scalable quantum computer,[3] namely:

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.[4]

Implementation of the two-qubit gate

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\rm(t)=J(t)S\rm ⋅ S\rm.

This description is only valid if:

\DeltaE

is much greater than

 kT

\tau\rm

is greater than

\hbar/\DeltaE

, so there is no time for transitions to higher orbital levels to happen and

\Gamma-1

is longer than

\tau\rm.

k

is the Boltzmann constant and

T

is the temperature in Kelvin.

From the pulsed Hamiltonian follows the time evolution operator

U\rm(t)={l{T}}\exp\left\{

t
-i\int
0

dt'H\rm(t')\right\},

where

{l{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

J0\tau\rm=\pi\pmod{2\pi},

and

U\rm

becomes the swap operator

U\rm(J0\tau\rm=\pi)\equivU\rm.

This pulse run for half the time (with

J0\tau\rm=\pi/2

) results in a square root of swap gate,
1/2
U
\rmsw

.

The "XOR" gate may be achieved by combining

1/2
U
\rmsw
operations with individual spin rotation operations:

U\rm=

i\pi
z
S
\rmL
2
e
-i\pi
z
S
\rmR
2
e
1/2
U
\rmsw
i\pi
z
S
\rmL
e
1/2
U
\rmsw

.

The

U\rm

operator is a conditional phase shift (controlled-Z) for the state in the basis of

S\rm+S\rm

. It can be made into a CNOT gate by surrounding the desired target qubit with Hadamard gates.

Experimental realizations

Spin qubits mostly have been implemented by locally depleting two-dimensional electron gases in semiconductors such a gallium arsenide,[5] [6] and germanium.[7] Spin qubits have also been implemented in other material systems such as graphene.[8] A more recent development is using silicon spin qubits, an approach that is e.g. pursued by Intel.[9] [10] 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.[11] [12]

See also

External links

Notes and References

  1. Vandersypen. Lieven M. K.. Eriksson. Mark A.. 2019-08-01. Quantum computing with semiconductor spins. Physics Today. en. 72. 8. 38. 10.1063/PT.3.4270. 2019PhT....72h..38V . 201305644 . 0031-9228.
  2. Loss . Daniel . DiVincenzo . David P. . Quantum computation with quantum dots . Physical Review A . 57 . 1 . 1998-01-01 . 1050-2947 . 10.1103/physreva.57.120 . 120–126. free. cond-mat/9701055. 1998PhRvA..57..120L .
  3. 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); on arXiv.org in Dec. 1996
  4. Barenco. Adriano. Deutsch. David. Ekert. Artur. Josza. Richard. 1995. Conditional Quantum Dynamics and Logic Gates. Phys. Rev. Lett.. en. 74. 20. 4083–4086. quant-ph/9503017. 10.1103/PhysRevLett.74.4083. 10058408 . 1995PhRvL..74.4083B . 26611140 .
  5. Petta. J. R.. 2005. Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots. Science. 309. 5744. 2180–2184. 10.1126/science.1116955. 16141370 . 2005Sci...309.2180P . 9107033 . 0036-8075.
  6. Bluhm. Hendrik. Foletti. Sandra. Neder. Izhar. Rudner. Mark. Mahalu. Diana. Umansky. Vladimir. Yacoby. Amir. 2010. Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs. Nature Physics. 7. 2. 109–113. 10.1038/nphys1856. 1745-2473. free.
  7. Watzinger. Hannes. Kukučka. Josip. Vukušić. Lada. Gao. Fei. Wang. Ting. Schäffler. Friedrich. Zhang. Jian-Jun. Katsaros. Georgios. 2018-09-25. A germanium hole spin qubit. Nature Communications. en. 9. 1. 3902. 10.1038/s41467-018-06418-4. 30254225 . 6156604 . 1802.00395 . 2018NatCo...9.3902W . 2041-1723. free.
  8. Trauzettel. Björn. Bulaev. Denis V.. Loss. Daniel. Burkard. Guido. 2007. Spin qubits in graphene quantum dots. Nature Physics. 3. 3. 192–196. cond-mat/0611252. 10.1038/nphys544. 2007NatPh...3..192T . 119431314 . 1745-2473.
  9. Xue . Xiao . Patra . Bishnu . van Dijk . Jeroen P. G. . Samkharadze . Nodar . Subramanian . Sushil . Corna . Andrea . Paquelet Wuetz . Brian . Jeon . Charles . Sheikh . Farhana . Juarez-Hernandez . Esdras . Esparza . Brando Perez . Rampurawala . Huzaifa . Carlton . Brent . Ravikumar . Surej . Nieva . Carlos . Kim . Sungwon . Lee . Hyung-Jin . Sammak . Amir . Scappucci . Giordano . Veldhorst . Menno . Sebastiano . Fabio . Babaie . Masoud . Pellerano . Stefano . Charbon . Edoardo . Vandersypen . Lieven M. K. . CMOS-based cryogenic control of silicon quantum circuits . Nature . 593 . 7858 . 2021-05-13 . 0028-0836 . 10.1038/s41586-021-03469-4 . free . 205–210.
  10. Web site: What Intel is Planning for the Future of Quantum Computing: Hot Qubits, Cold Control Chips, and Rapid Testing - IEEE Spectrum .
  11. Yang . C. H. . Leon . R. C. C. . Hwang . J. C. C. . Saraiva . A. . Tanttu . T. . Huang . W. . Camirand Lemyre . J. . Chan . K. W. . Tan . K. Y. . Hudson . F. E. . Itoh . K. M. . Morello . A. . Pioro-Ladrière . M. . Laucht . A. . Dzurak . A. S. . Operation of a silicon quantum processor unit cell above one kelvin . Nature . 580 . 7803 . 2020-04-16 . 0028-0836 . 10.1038/s41586-020-2171-6 . free . 350–354.
  12. Camenzind . Leon C. . Geyer . Simon . Fuhrer . Andreas . Warburton . Richard J. . Zumbühl . Dominik M. . Kuhlmann . Andreas V. . A hole spin qubit in a fin field-effect transistor above 4 kelvin . Nature Electronics . 5 . 3 . 2022-03-03 . 2520-1131 . 10.1038/s41928-022-00722-0 . free . 178–183.

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