Quantum logic gate

Quantum logic gate

In <a href="/en/Quantum_computing" title="Quantum computing" class="wl">quantum computing</a> and specifically the <a href="/en/Quantum_circuit" title="Quantum circuit" class="wl">quantum circuit</a> <a href="/en/Model_of_computation" title="Model of computation" class="wl">model of computation</a>, a quantum logic gate (or simply quantum gate) is a basic quantum circuit operating on a small number of <a href="/en/Qubit" title="Qubit" class="wl">qubits</a>. They are the building blocks of quantum circuits, like classical <a href="/en/Logic_gate" title="Logic gate" class="wl">logic gates</a> are for conventional digital circuits.

<div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none" about="#mwt1">Basic circuit in quantum computing</div>
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Unlike many classical logic gates, quantum logic gates are <a href="/en/Reversible_computing" title="Reversible computing" class="wl">reversible</a>. It is possible to perform classical computing using only reversible gates. For example, the reversible <a href="/en/Toffoli_gate" title="Toffoli gate" class="wl">Toffoli gate</a> can implement all Boolean functions, often at the cost of having to use <a href="/en/Ancilla_bit" title="Ancilla bit" class="wl">ancilla bits</a>. The Toffoli gate has a direct quantum equivalent, showing that quantum circuits can perform all operations performed by classical circuits.

Quantum gates are <a href="/en/Unitary_operators" title="Unitary operators" class="mw-redirect wl">unitary operators</a>, and are described as <a href="/en/Unitary_matrix" title="Unitary matrix" class="wl">unitary matrices</a> relative to some <a href="/en/Basis_(linear_algebra)" title="Basis (linear algebra)" class="wl">basis</a>. Usually we use the computational basis, which unless we compare it with something, just means that for a d-level quantum system (such as a <a href="/en/Qubit" title="Qubit" class="wl">qubit</a>, a <a href="/en/Quantum_register" title="Quantum register" class="wl">quantum register</a>, or <a href="/en/Qutrit" title="Qutrit" class="wl">qutrits</a> and <a href="/en/Qudit" title="Qudit" class="mw-redirect wl">qudits</a><a href="#cite_note-Williams-1" style="counter-reset: mw-Ref 1;">[1]</a>: 22–23 ) we have labeled the orthogonal basis vectors <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |0\rangle ,|1\rangle ,\dots ,|d-1\rangle }">
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</math><img loading="lazy"src="https://wikimedia.org/api/rest_v1/media/math/render/svg/157ee648c5e3be82aab0eacba4e6b1fe8a815a71" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:18.41ex; height:2.843ex;" alt="{\displaystyle |0\rangle ,|1\rangle ,\dots ,|d-1\rangle }">, or use <a href="/en/Binary_number" title="Binary number" class="wl">binary notation</a>.

<figure class="mw-halign-right wiki-thumb"><a href="/en/File:Quantum_Logic_Gates.png" class="mw-file-description image media-thumb" data-hash="File:Quantum_Logic_Gates.png"><img loading="lazy" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Quantum_Logic_Gates.png/500px-Quantum_Logic_Gates.png" decoding="async" data-file-width="2443" data-file-height="3003" data-file-type="bitmap" height="615" width="500" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Quantum_Logic_Gates.png/750px-Quantum_Logic_Gates.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Quantum_Logic_Gates.png/1000px-Quantum_Logic_Gates.png 2x" alt="Quantum_Logic_Gates.png"></a><figcaption>Common quantum logic gates by name (including abbreviation), circuit form(s) and the corresponding unitary matrices.</figcaption></figure>

In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits. Unlike many classical logic gates, quantum logic gates are reversible. It is possible to perform classical computing using only reversible gates. For example, the reversible Toffoli gate can implement all Boolean functions, often at the cost of having to use ancilla bits. The Toffoli gate has a direct quantum equivalent, showing that quantum circuits can perform all operations performed by classical circuits. Quantum gates are unitary operators, and are described as unitary matrices relative to some basis. Usually we use the computational basis, which unless we compare it with something, just means that for a d-level quantum system we have labeled the orthogonal basis vectors 
  
    
      
        
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    {\displaystyle |0\rangle ,|1\rangle ,\dots ,|d-1\rangle }
  
, or use binary notation. 