量子门电路(量子门电路)

作者:cmwxj@126.com
发布时间: 2019-12-28 09:23:40 (4年前)
关键词: 逻辑门量子门量子比特
摘要:

                              
                                     Toffoli门是一个操作三个量子比特的的量子逻辑门，其为一种通用可逆逻辑门。 
主要表征为：operation CCNOT (control1 : Qubit, control2 : Qubit, target : Qubit) :

<div style="width:595.0pt;margin-bottom:72.0pt;margin-top:72.0pt;margin-left:90.0pt;margin-right:90.0pt;">
 <p style="text-align:left;"><span style="font-family:'Arial';font-size:10.0pt;color:#333333;background-color:#ffffff;">Noisy Intermediate-Scale Quantum</span></p>
 <p><a href="http://ai.googleblog.com/2018/07/announcing-cirq-open-source-framework.html"><span style="font-family:'Roboto';font-size:18.0pt;color:#4184f3;text-decoration:underline;">Announcing Cirq: An Open Source Framework for NISQ Algorithms</span> </a></p>
 <p><a href="https://ai.googleblog.com/2018/07/announcing-cirq-open-source-framework.html"><span style="font-family:'PingFang SC';font-size:12.0pt;color:#0000ff;text-decoration:underline;background-color:#ffffff;">https://ai.googleblog.com/2018/07/announcing-cirq-open-source-framework.html</span> </a></p>
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 <p><span style="font-family:'PingFang SC';font-size:12.0pt;color:#191919;background-color:#ffffff;">GitHub</span><span style="font-family:'PingFang SC';font-size:12.0pt;color:#191919;background-color:#ffffff;">传送门：</span></p>
 <p style="text-align:left;"><span style="font-family:'PingFang SC';font-size:12.0pt;color:#191919;background-color:#ffffff;">https://github.com/quantumlib/cirq</span></p>
 <p><span style="font-family:'PingFang SC';font-size:12.0pt;color:#191919;background-color:#ffffff;">OpenFermion-Cirq</span><span style="font-family:'PingFang SC';font-size:12.0pt;color:#191919;background-color:#ffffff;">传送门：</span></p>
 <p><a href="https://github.com/quantumlib/OpenFermion-Cirq"><span style="font-family:'PingFang SC';font-size:12.0pt;color:#0000ff;text-decoration:underline;background-color:#ffffff;">https://github.com/quantumlib/OpenFermion-Cirq</span> </a></p>
 <p><span style="font-family:'PingFang SC';font-size:12.0pt;background-color:#ffffff;">x</span><span style="font-family:'PingFang SC';font-size:12.0pt;background-color:#ffffff;">门：交换门</span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">Z</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">门：</span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">（</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">x,y)=>(x,-y)</span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">Y</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">门</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">:</span></p>
 <p style="text-align:left;"><img src="/user/files/U7W6pdALcEZ8zN6uf8eEpYxj2YsRug3MaBQyUUs1qKw.png" width="169.5pt" height="100%"></p>
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 <p><span style="font-family:'-apple-system';font-size:12.0pt;font-weight:bold;color:#4f4f4f;background-color:#ffffff;">三，对三量子进行操作的逻辑门</span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">【</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">Toffoli</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">门</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">CCNOT(Controlled-Controlled-NOT gate)</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">】</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> </span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">Toffoli</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">门是一个操作三个量子比特的的量子逻辑门，其为一种通用可逆逻辑门。</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> </span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">主要表征为：</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">operation CCNOT (control1 : Qubit, control2 : Qubit, target : Qubit) : () </span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">其前两个量子比特是</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> |1</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">〉，则对第三个量子比特进行类似于经典的逻辑非门处理，反之则不做操作。前两个是操作子，后一个是观测子。</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> </span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">整体输入输出表达式可以观测为以下：</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> </span></p>
 <p><img src="/user/files/hcXAoNnBp1W7xURBdiJ3wIxZx5PkdTKAcy1hqE-3gGw.jpeg" width="309.0pt" height="100%"></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> </span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">即对第一和第二个量子位同时</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> |1</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">〉的时候，对第三个量子位进行逻辑反转操作。</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> </span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">|a,b,c</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">〉</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">-> |a,b,c </span><span style="font-family:'-apple-system';font-size:12.0pt;font-weight:bold;color:#4f4f4f;background-color:#ffffff;">+</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> (ab)</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">〉</span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">【</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">Fredkin</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">门三位受控互换门</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">CSWAP</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">】</span></p>
 <p><img src="/user/files/_-aTSgUQwU5Bcsz_9nfL10ZWZwf2_yHcq-bFzX1Jbpk.jpeg" width="192.0pt" height="100%"></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> </span></p>
 <p><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">即对第一为</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> |1</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">〉，且第二和第三个量子位不同时为</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;"> |1</span><span style="font-family:'-apple-system';font-size:12.0pt;color:#4f4f4f;background-color:#ffffff;">〉的时候，两个量子位相互交换。</span></p>
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