{"id":1250,"date":"2026-10-13T12:24:25","date_gmt":"2026-10-13T12:24:25","guid":{"rendered":"https:\/\/www.interviewbit.com\/varsity\/blog\/?p=1250"},"modified":"2026-10-13T12:24:29","modified_gmt":"2026-10-13T12:24:29","slug":"hadamard-gate","status":"publish","type":"post","link":"https:\/\/www.interviewbit.com\/varsity\/blog\/hadamard-gate\/","title":{"rendered":"The Hadamard Gate Explained Better Than Your Textbook"},"content":{"rendered":"\n<div class=\"wp-block-group vlf-insights is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"vlf-insights-title wp-block-paragraph\">Key Insights<\/p>\n\n\n\n<ul class=\"wp-block-list vlf-insights-list\">\n<li>The Hadamard gate (H) transforms |0\u27e9 and |1\u27e9 into equal superposition states |+\u27e9 and |\u2212\u27e9, making it a fundamental single-qubit operation.<\/li>\n\n\n\n<li>Its matrix explains these transformations directly, including the negative sign in H|1\u27e9, which represents a relative phase rather than a negative probability.<\/li>\n\n\n\n<li>On the Bloch sphere, the Hadamard gate provides an intuitive way to understand basis changes between the computational (Z) basis and the X basis.<\/li>\n\n\n\n<li>Applying H twice returns the qubit to its original state because H is its own inverse, making the operation reversible.<\/li>\n\n\n\n<li>The Hadamard gate creates coherent superposition, not randomness; the probabilistic outcome appears only when the qubit is measured.<\/li>\n\n\n\n<li>H is widely used in quantum circuits and algorithms, including creating the superpositions needed for algorithms such as Deutsch\u2013Jozsa and Grover, and can also work with gates such as CNOT to build entangled states.<\/li>\n<\/ul>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard gate, written as H, is one of the most important single-qubit gates in quantum computing. It transforms the computational-basis states |0\u27e9 and |1\u27e9 into equal superposition states, |+\u27e9 and |\u2212\u27e9. It can also reverse this transformation, making it useful for changing between quantum measurement bases.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But what is a Hadamard gate really doing to a qubit? We can understand the Hadamard gate explained in two complementary ways: mathematically, through its matrix and state transformations, and visually, through the Bloch sphere. This also explains why the H gate appears so often in quantum circuits, from creating superposition and changing measurement bases to algorithms such as Deutsch\u2013Jozsa and Grover.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">What Does the Hadamard Gate Do?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The simplest way to understand the Hadamard gate is that it takes a computational-basis state and creates an equal superposition of the two basis states.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1774\" height=\"887\" src=\"https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-transforming-the-computational-basis-states-0-1-1.png\" alt=\"Hadamard gate transforming the computational basis states |0\u27e9 and |1\u27e9 into the equal superposition states |+\u27e9 and |\u2212\u27e9\" class=\"wp-image-1252\" srcset=\"https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-transforming-the-computational-basis-states-0-1-1.png 1774w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-transforming-the-computational-basis-states-0-1-1-300x150.png 300w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-transforming-the-computational-basis-states-0-1-1-1024x512.png 1024w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-transforming-the-computational-basis-states-0-1-1-768x384.png 768w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-transforming-the-computational-basis-states-0-1-1-1536x768.png 1536w\" sizes=\"auto, (max-width: 1774px) 100vw, 1774px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">What Happens to |0\u27e9?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Applying H to |0\u27e9 gives: <strong>H|0\u27e9 = (|0\u27e9 + |1\u27e9)\/\u221a2 = |+\u27e9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The two states have equal amplitudes of 1\/\u221a2. If we measure the resulting state in the computational basis, we get 0 or 1 with equal probability.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Importantly, the qubit is not simply \u201crandom\u201d before measurement. The Hadamard transformation creates a definite quantum superposition, and the probabilistic outcome appears when we measure it.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What Happens to |1\u27e9?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Applying H to |1\u27e9 gives: <strong>H|1\u27e9 = (|0\u27e9 \u2212 |1\u27e9)\/\u221a2 = |\u2212\u27e9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The computational-basis measurement probabilities are still 50\u201350. The difference is the minus sign, which represents a relative phase. That phase does not change the immediate probabilities, but it can affect interference when the state goes through later gates.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The Hadamard Gate Matrix Explained<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The standard Hadamard gate matrix is: <strong>H = 1\/\u221a2 <\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This 2\u00d72 matrix describes the Hadamard operation mathematically and lets us calculate exactly how it transforms a single-qubit state.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1536\" height=\"1024\" src=\"https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-matrix-showing-how-the-h-gate-transforms-0-int-1.png\" alt=\"Hadamard gate matrix showing how the H gate transforms |0\u27e9 into |+\u27e9 and |1\u27e9 into |\u2212\u27e9 through matrix multiplication.\" class=\"wp-image-1253\" srcset=\"https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-matrix-showing-how-the-h-gate-transforms-0-int-1.png 1536w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-matrix-showing-how-the-h-gate-transforms-0-int-1-300x200.png 300w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-matrix-showing-how-the-h-gate-transforms-0-int-1-1024x683.png 1024w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/hadamard-gate-matrix-showing-how-the-h-gate-transforms-0-int-1-768x512.png 768w\" sizes=\"auto, (max-width: 1536px) 100vw, 1536px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">How the Matrix Acts on |0\u27e9<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The |0\u27e9 state is represented as: <strong>|0\u27e9 = [1, 0]\u1d40<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So: <strong>H[1, 0]\u1d40 = 1\/\u221a2 [1, 1]\u1d40<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Converting this back into ket notation gives: <strong>H|0\u27e9 = (|0\u27e9 + |1\u27e9)\/\u221a2 = |+\u27e9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is the mathematical form of the superposition we saw earlier.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">How the Matrix Acts on |1\u27e9<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Similarly: <strong>|1\u27e9 = [0, 1]\u1d40<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore: <strong>H[0, 1]\u1d40 = 1\/\u221a2 [1, \u22121]\u1d40<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So: <strong>H|1\u27e9 = (|0\u27e9 \u2212 |1\u27e9)\/\u221a2 = |\u2212\u27e9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The negative amplitude is not a negative probability. Probabilities are calculated from the squared magnitude of amplitudes; the minus sign instead represents relative phase.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What the Negative Sign Actually Means?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The easiest way to think about the minus sign is as information about how the state will interfere with other quantum states.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So although |+\u27e9 and |\u2212\u27e9 both give 50\u201350 outcomes when measured directly in the computational basis, they are different quantum states. That difference becomes observable when they are combined with other operations.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The Hadamard Gate on the Bloch Sphere<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The Bloch sphere gives us a visual way to understand a single-qubit Hadamard transformation.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1536\" height=\"1024\" src=\"https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/bloch-sphere-showing-the-hadamard-gate-transforming-0-to-and-1.png\" alt=\"Bloch sphere showing the Hadamard gate transforming |0\u27e9 to |+\u27e9 and |1\u27e9 to |\u2212\u27e9, illustrating the change between the Z and X bases.\" class=\"wp-image-1255\" srcset=\"https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/bloch-sphere-showing-the-hadamard-gate-transforming-0-to-and-1.png 1536w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/bloch-sphere-showing-the-hadamard-gate-transforming-0-to-and-1-300x200.png 300w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/bloch-sphere-showing-the-hadamard-gate-transforming-0-to-and-1-1024x683.png 1024w, https:\/\/www.interviewbit.com\/varsity\/blog\/wp-content\/uploads\/2026\/10\/bloch-sphere-showing-the-hadamard-gate-transforming-0-to-and-1-768x512.png 768w\" sizes=\"auto, (max-width: 1536px) 100vw, 1536px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Where |0\u27e9 and |1\u27e9 Sit<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">On the Bloch sphere:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>|0\u27e9 sits at the north pole.<\/li>\n\n\n\n<li>|1\u27e9 sits at the south pole.<\/li>\n\n\n\n<li>|+\u27e9 and |\u2212\u27e9 lie along the X axis.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard gate maps the Z-basis states |0\u27e9 and |1\u27e9 to the X-basis states |+\u27e9 and |\u2212\u27e9.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What H Does Geometrically?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Rather than thinking of H only as a matrix, we can view it as a geometric transformation of the qubit&#8217;s Bloch vector. IBM describes the Hadamard as a \u03c0 rotation about an axis halfway between the X and Z axes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The important takeaway is simpler: H changes the basis in which we describe and measure the qubit. This is why the Hadamard gate is often described as a basis-change operation.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Why This Is More Than \u201cCreating Randomness\u201d?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A common beginner mistake is to think that H simply flips a coin.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It does not. The Hadamard transformation itself is deterministic. It creates a coherent superposition; randomness appears when that state is measured.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Why Does Applying H Twice Give You the Original State?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">One of the most useful properties of the Hadamard gate is that it is its own inverse.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">H is Its Own Inverse<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Mathematically: <strong>H\u00b2 = HH = I<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Multiplying the Hadamard matrix by itself gives the identity matrix:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1\/2 = <\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So: <strong>H\u207b\u00b9 = H<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This means applying H twice cancels its first application.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What This Means for a Qubit?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">For example: <strong>H(H|0\u27e9) = |0\u27e9 <\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">And : <strong>H(H|1\u27e9) = |1\u27e9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard gate therefore provides a reversible transformation between the computational and X bases.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Why is the Hadamard Gate Important in Quantum Computing?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard gate is important because it performs several fundamental operations used throughout quantum circuits.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Creating Superposition<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">H is one of the standard ways to create an equal superposition from |0\u27e9 or |1\u27e9. This becomes particularly powerful when several qubits are placed into superposition.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Changing Between Measurement Bases<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard connects the computational, or Z, basis with the X basis. This makes it useful when a circuit needs to measure or manipulate information from a different basis.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Building Larger Quantum Circuits<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Hadamard gates are frequently combined with multi-qubit operations such as CNOT. For example, applying H to one qubit and then using a CNOT can create an entangled state. The important point is that H itself is a single-qubit operation; it does not create entanglement on its own.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Role in Quantum Algorithms<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard gate also appears in several important quantum algorithms.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In Deutsch-Jozsa, Hadamard gates help prepare the superposition of possible inputs. In Grover&#8217;s algorithm, they are used to create and manipulate the superposition underlying the search process.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So the Hadamard gate is not just a basic teaching example. It is a building block for larger quantum algorithms and circuits.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Hadamard Gate Circuit Diagram and Qiskit Example<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Hadamard Gate Circuit Diagram<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A simple quantum circuit containing a Hadamard gate looks like:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">q: \u2500\u2500H\u2500\u2500<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The horizontal line represents the qubit, while the H box represents the Hadamard operation applied to it. In a circuit, operations are read from left to right. IBM&#8217;s Qiskit documentation uses the same H-gate circuit representation.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Apply an H Gate in Qiskit<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard gate can be applied in Qiskit using qc.h(0):<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>from qiskit import QuantumCircuit\nqc = QuantumCircuit(1)\nqc.h(0)\nprint(qc)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">Here, QuantumCircuit(1) creates a circuit with one qubit, and qc.h(0) applies the H gate to qubit 0.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">What Output Should You Expect?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The circuit starts in |0\u27e9. After applying H, the state becomes: <strong>|+\u27e9 = (|0\u27e9 + |1\u27e9)\/\u221a2<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you measure this state in the computational basis repeatedly on an ideal simulator, the results should approach 50% 0 and 50% 1. Actual quantum hardware can produce slightly different counts because of noise and other imperfections.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Common Hadamard Gate Mistakes<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Thinking H is the Same as a Random Coin Flip<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">H does not introduce randomness into the quantum state. The transformation is deterministic; measurement is what produces probabilistic outcomes.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Ignoring the Minus Sign in H|1\u27e9<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The minus sign in H|1\u27e9 represents relative phase. Ignoring it can lead to incorrect predictions about interference in later parts of a circuit.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Confusing Superposition With Entanglement<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">H creates superposition on a single qubit. It does not automatically create entanglement. Entanglement involves correlations between multiple quantum systems.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Assuming H Always Produces 50\u201350 Measurement Results<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">H produces equal computational-basis probabilities when applied to |0\u27e9 or |1\u27e9. For other input states or measurement bases, the probabilities can be different.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard gate is a fundamental building block of quantum computing, connecting computational-basis states with superposition and enabling the interference that powers many quantum algorithms. Understanding how it works is an important step toward building and reasoning about larger quantum circuits.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ready to take these concepts beyond the basics? Explore the <a href=\"https:\/\/www.interviewbit.com\/varsity\/iit-delhi\/quantum-computing\">Applied Quantum Computing &amp; AI programme by IIT Delhi<\/a>, delivered on Varsity by InterviewBit, that helps you build practical skills in modern quantum computing through hands-on projects and industry-focused capstones.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Frequently Asked Questions<\/h2>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Why does the Hadamard gate create superposition?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">H transforms the computational-basis states into combinations of |0\u27e9 and |1\u27e9 with equal amplitudes. This creates a coherent superposition rather than a classical random mixture.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">What is the difference between Hadamard and Pauli-X?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Pauli-X swaps |0\u27e9 and |1\u27e9. The Hadamard instead transforms them into |+\u27e9 and |\u2212\u27e9, making H a superposition and basis-change operation.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Does the Hadamard gate create entanglement?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">No. H is a single-qubit gate and does not create entanglement by itself. Entanglement requires interactions or multi-qubit operations that create correlations between qubits.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Where is the Hadamard gate used in quantum algorithms?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Hadamard gates are used to create and manipulate superpositions in algorithms including Deutsch\u2013Jozsa and Grover&#8217;s algorithm, as well as in many larger quantum circuits.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Why is the Hadamard gate important in quantum computing?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">H combines several fundamental capabilities: creating superposition, changing measurement bases, enabling interference, and serving as a building block for quantum circuits and algorithms.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">What quantum algorithms use the Hadamard gate?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard gate is used in several important quantum algorithms, including Deutsch\u2013Jozsa and Grover\u2019s algorithm. Its ability to create and manipulate superposition makes it useful for preparing and transforming the quantum states these algorithms operate on.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Can a Hadamard gate be used with a CNOT gate?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. Hadamard and CNOT gates are commonly combined to create entangled two-qubit states. For example, applying H to one qubit followed by CNOT can produce a Bell state, making the combination an important pattern in quantum circuits.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">What is the difference between the Hadamard gate and the Pauli-X gate?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The Pauli-X gate flips the computational-basis states, while the Hadamard gate transforms them into superposition states. In simple terms, X changes |0\u27e9 to |1\u27e9, whereas H changes |0\u27e9 to |+\u27e9 and |1\u27e9 to |\u2212\u27e9.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">Can the Hadamard gate be applied to an already superposed qubit?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. The Hadamard gate can be applied to any single-qubit state, including an existing superposition. The resulting state depends on the input amplitudes and phases, so applying H does not always produce a 50\/50 measurement probability.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\">How is the Hadamard gate different from the CNOT gate?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The Hadamard gate is a single-qubit operation that changes the qubit&#8217;s state and can create superposition. CNOT is a two-qubit controlled operation that flips a target qubit based on the control qubit. They serve different roles but are often used together in quantum circuits.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Resources<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"https:\/\/quantum.cloud.ibm.com\/learning\/en\/courses\/use-a-qc-today\/quantum-mechanics-basics\">IBM Quantum Learning \u2014 Quantum Mechanics Basics<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/quantum.cloud.ibm.com\/learning\/en\/modules\/quantum-mechanics\/superposition-with-qiskit\">IBM Quantum Learning \u2014 Superposition with Qiskit<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/docs.quantum.ibm.com\/api\/qiskit\/qiskit.circuit.library.HGate\">Qiskit Documentation \u2014 Hadamard Gate (HGate)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.quantum-inspire.com\/kbase\/hadamard\/\">Quantum Inspire \u2014 Hadamard Gate<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/pennylane.ai\/glossary\/what-is-a-hadamard-gate\">PennyLane \u2014 What Is a Hadamard Gate?<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Quantum_logic_gate\">Wikipedia \u2014 Quantum Logic Gate<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Key Insights The Hadamard gate, written as H, is one of the most important single-qubit gates in quantum computing. It transforms the computational-basis states |0\u27e9 and |1\u27e9 into equal superposition states, |+\u27e9 and |\u2212\u27e9. It can also reverse this transformation, making it useful for changing between quantum measurement bases. But what is a Hadamard gate [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":1287,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-1250","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantum-computing"],"blocksy_meta":{"styles_descriptor":{"styles":{"desktop":"","tablet":"","mobile":""},"google_fonts":[],"version":8}},"acf":{"reviewed_by":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Hadamard Gate Explained: Matrix, Superposition &amp; Qiskit<\/title>\n<meta name=\"description\" content=\"Learn the Hadamard gate with simple examples, its matrix, Bloch sphere, superposition, quantum circuits, and Qiskit implementation.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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