Spin qubit quantum computer

<h2 id="lossdivicenzo-proposal">Loss–DiVicenzo proposal</h2>

The Loss–DiVicenzo quantum computer proposal tried to fulfill <a href="/facts/DiVincenzo%27s_criteria/k2Vmf9ga">DiVincenzo's criteria</a> for a scalable quantum computer,<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a> namely:

<ul><li>identification of well-defined qubits;</li>
<li>reliable state preparation;</li>
<li>low decoherence;</li>
<li>accurate quantum gate operations and</li>
<li>strong quantum measurements.</li></ul>
A candidate for such a quantum computer is a <a href="/facts/Lateral_quantum_dot/46DvCnXg">lateral quantum dot</a> system. Earlier work on applications of quantum dots for quantum computing was done by Barenco et al.<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a>

<h3>Implementation of the two-qubit gate</h3>
The Loss–DiVincenzo quantum computer operates, basically, using inter-dot gate voltage for implementing <a href="/facts/Swap_(computer_science)/lMfoMXCq">swap</a> operations and local magnetic fields (or any other local spin manipulation) for implementing the <a href="/facts/Controlled_NOT_gate/hP1y4K6d">controlled NOT gate</a> (CNOT gate).
The swap operation is achieved by applying a pulsed inter-dot gate voltage, so the exchange constant in the <a href="/facts/Heisenberg_model_(quantum)/8RPu8n5n">Heisenberg Hamiltonian</a> becomes time-dependent:

H
          
            
              s
            
          
        
        (
        t
        )
        =
        J
        (
        t
        )
        
          
            S
          
          
            
              L
            
          
        
        ⋅
        
          
            S
          
          
            
              R
            
          
        
        .
      
    
    {\displaystyle H_{\rm {s}}(t)=J(t)\mathbf {S} _{\rm {L}}\cdot \mathbf {S} _{\rm {R}}.}

This description is only valid if:

<ul><li>the <a href="/facts/Energy_level/66x51Khc">level spacing</a> in the quantum-dot 
 
 
 
 Δ
 E
 
 
 {\displaystyle \Delta E}
 
 is much greater than 
 
 
 
 
 k
 T
 
 
 {\displaystyle \;kT}
 
</li>
<li>the pulse time scale 
 
 
 
 
 τ
 
 
 s
 
 
 
 
 
 {\displaystyle \tau _{\rm {s}}}
 
 is greater than 
 
 
 
 ℏ
 
 /
 
 Δ
 E
 
 
 {\displaystyle \hbar /\Delta E}
 
, so there is no time for transitions to higher orbital levels to happen and</li>
<li>the <a href="/facts/Quantum_decoherence/mngM3rxy">decoherence</a> time 
 
 
 
 
 Γ
 
 −
 1
 
 
 
 
 {\displaystyle \Gamma ^{-1}}
 
 is longer than 
 
 
 
 
 τ
 
 
 s
 
 
 
 .
 
 
 {\displaystyle \tau _{\rm {s}}.}
 
</li></ul>

 
 
 
 k
 
 
 {\displaystyle k}
 
 is the <a href="/facts/Boltzmann_constant/5DIejyR3">Boltzmann constant</a> and 
 
 
 
 T
 
 
 {\displaystyle T}
 
 is the temperature in <a href="/facts/Kelvin/E3trzC4C">Kelvin</a>.
From the pulsed Hamiltonian follows the <a href="/facts/Time_evolution_operator/8XxTc0fN">time evolution operator</a>

U
          
            
              s
            
          
        
        (
        t
        )
        =
        
          
            T
          
        
        exp
        ⁡
        
          {
          
            −
            i
            
              ∫
              
                0
              
              
                t
              
            
            d
            
              t
              ′
            
            
              H
              
                
                  s
                
              
            
            (
            
              t
              ′
            
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          }
        
        ,
      
    
    {\displaystyle U_{\rm {s}}(t)={\mathcal {T}}\exp \left\{-i\int _{0}^{t}dt'H_{\rm {s}}(t')\right\},}

where 
 
 
 
 
 
 T
 
 
 
 
 {\displaystyle {\mathcal {T}}}
 
 is the <a href="/facts/Time-ordering/j37d7a37">time-ordering</a> symbol.
We can choose a specific duration of the pulse such that the integral in time over 
 
 
 
 J
 (
 t
 )
 
 
 {\displaystyle J(t)}
 
 gives 
 
 
 
 
 J
 
 0
 
 
 
 τ
 
 
 s
 
 
 
 =
 π
 
 
 (
 mod
 
 2
 π
 )
 
 ,
 
 
 {\displaystyle J_{0}\tau _{\rm {s}}=\pi {\pmod {2\pi }},}
 
 and 
 
 
 
 
 U
 
 
 s
 
 
 
 
 
 {\displaystyle U_{\rm {s}}}
 
 becomes the swap operator 
 
 
 
 
 U
 
 
 s
 
 
 
 (
 
 J
 
 0
 
 
 
 τ
 
 
 s
 
 
 
 =
 π
 )
 ≡
 
 U
 
 
 s
 w
 
 
 
 .
 
 
 {\displaystyle U_{\rm {s}}(J_{0}\tau _{\rm {s}}=\pi )\equiv U_{\rm {sw}}.}

This pulse run for half the time (with 
 
 
 
 
 J
 
 0
 
 
 
 τ
 
 
 s
 
 
 
 =
 π
 
 /
 
 2
 
 
 {\displaystyle J_{0}\tau _{\rm {s}}=\pi /2}
 
) results in a <a href="/facts/List_of_quantum_logic_gates/mw2S6tFn">square root of swap</a> gate, 
 
 
 
 
 U
 
 
 s
 w
 
 
 
 1
 
 /
 
 2
 
 
 .
 
 
 {\displaystyle U_{\rm {sw}}^{1/2}.}

The "XOR" gate may be achieved by combining 
 
 
 
 
 U
 
 
 s
 w
 
 
 
 1
 
 /
 
 2
 
 
 
 
 {\displaystyle U_{\rm {sw}}^{1/2}}
 
 operations with individual <a href="/facts/List_of_quantum_logic_gates/mw2S6tFn">spin rotation</a> operations:

U
          
            
              X
              O
              R
            
          
        
        =
        
          e
          
            i
            
              
                π
                2
              
            
            
              S
              
                
                  L
                
              
              
                z
              
            
          
        
        
          e
          
            −
            i
            
              
                π
                2
              
            
            
              S
              
                
                  R
                
              
              
                z
              
            
          
        
        
          U
          
            
              s
              w
            
          
          
            1
            
              /
            
            2
          
        
        
          e
          
            i
            π
            
              S
              
                
                  L
                
              
              
                z
              
            
          
        
        
          U
          
            
              s
              w
            
          
          
            1
            
              /
            
            2
          
        
        .
      
    
    {\displaystyle U_{\rm {XOR}}=e^{i{\frac {\pi }{2}}S_{\rm {L}}^{z}}e^{-i{\frac {\pi }{2}}S_{\rm {R}}^{z}}U_{\rm {sw}}^{1/2}e^{i\pi S_{\rm {L}}^{z}}U_{\rm {sw}}^{1/2}.}

The 
 
 
 
 
 U
 
 
 X
 O
 R
 
 
 
 
 
 {\displaystyle U_{\rm {XOR}}}
 
 operator is a <a href="/facts/Quantum_logic_gate/EFV5sPCU">conditional phase shift</a> (controlled-Z) for the state in the basis of 
 
 
 
 
 
 S
 
 
 
 L
 
 
 
 +
 
 
 S
 
 
 
 R
 
 
 
 
 
 {\displaystyle \mathbf {S} _{\rm {L}}+\mathbf {S} _{\rm {R}}}
 
.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a>: 4  It can be made into a <a href="/facts/CNOT/hP1y4K6d">CNOT</a> gate by surrounding the desired target qubit with <a href="/facts/Quantum_logic_gate/EFV5sPCU">Hadamard gates</a>.

<h2 id="experimental-realizations">Experimental realizations</h2>
Spin qubits mostly have been implemented by locally depleting <a href="/facts/Two-dimensional_electron_gas/tkGhkJxG">two-dimensional electron gases</a> in semiconductors such a <a href="/facts/Gallium_arsenide/BakLFjpp">gallium arsenide</a>,<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a><a class="footnote-ref" id="fnref:8" href="#fn:8">8</a> and <a href="/facts/Germanium/wtoALHGs">germanium</a>.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> Spin qubits have also been implemented in other material systems such as <a href="/facts/Graphene/QDGUBaPt">graphene</a>.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> A more recent development is using silicon spin qubits, an approach that is e.g. pursued by <a href="/facts/Intel/SMF0gJJX">Intel</a>.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a><a class="footnote-ref" id="fnref:12" href="#fn:12">12</a> The advantage of the <a href="/facts/Silicon/cgWx0hdr">silicon</a> platform is that it allows using modern <a href="/facts/Semiconductor_device_fabrication/Jd23Mu1z">semiconductor device fabrication</a> for making the qubits. Some of these devices have a comparably high operation temperature of a few <a href="/facts/Kelvin/E3trzC4C">kelvins</a> (hot qubits) which is advantageous for scaling the number of qubits in a quantum processor.<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a><a class="footnote-ref" id="fnref:14" href="#fn:14">14</a>

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Kane_quantum_computer/LEGEubjz">Kane quantum computer</a></li>
<li><a href="/facts/Quantum_dot_cellular_automaton/4fLjbAwL">Quantum dot cellular automaton</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="https://www.quantum-inspire.com/contact">QuantumInspire</a> online platform from <a href="/facts/Delft_University_of_Technology/wtPV7UmG">Delft University of Technology</a>, allows building and running quantum algorithms on "Spin-2" a 2 silicon spin qubits processor.</li></ul>

<h2 id="references">References</h2>

<ol>
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<li id="fn:9">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. 9 (1): 3902. arXiv:1802.00395. Bibcode:2018NatCo...9.3902W. doi:10.1038/s41467-018-06418-4. ISSN 2041-1723. PMC 6156604. PMID 30254225. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6156604" target="_blank">https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6156604</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
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<li id="fn:12">"What Intel is Planning for the Future of Quantum Computing: Hot Qubits, Cold Control Chips, and Rapid Testing - IEEE Spectrum". <a href="https://spectrum.ieee.org/intels-quantum-computing-plans-hot-qubits-cold-control-chips-and-rapid-testing" target="_blank">https://spectrum.ieee.org/intels-quantum-computing-plans-hot-qubits-cold-control-chips-and-rapid-testing</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
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<li id="fn:14">Camenzind, Leon C.; Geyer, Simon; Fuhrer, Andreas; Warburton, Richard J.; Zumbühl, Dominik M.; Kuhlmann, Andreas V. (2022-03-03). "A hole spin qubit in a fin field-effect transistor above 4 kelvin". Nature Electronics. 5 (3): 178–183. arXiv:2103.07369. doi:10.1038/s41928-022-00722-0. ISSN 2520-1131. <a href="https://doi.org/10.1038%2Fs41928-022-00722-0" target="_blank">https://doi.org/10.1038%2Fs41928-022-00722-0</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
</ol>

Spin qubit quantum computer open-in-new

Spin qubit quantum computer