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This shows you the differences between two versions of the page.

--- projects:quantum:category-qc-foundation [2025/04/16 15:38] – kymki
+++ projects:quantum:category-qc-foundation [2025/04/30 09:26] (current) – [Emmanuel Jeandel, Simon Perdrix & Renaud Vilmart (2020)] kymki
@@ Line 1: / Line 1: @@
+<html>
+<head>
+  <meta charset="UTF-8">
+  <meta name="viewport" content="width=device-width, initial-scale=1.0">
+  <title>Ramble Meter</title>
+  <style>
+    /* Container for the entire Ramble Meter */
+    .ramble-meter-container {
+      display: flex;
+      align-items: center;
+      justify-content: center;
+      margin: 20px 0;
+    }
+    /* Ramble Meter */
+    .ramble-meter {
+      position: relative;
+      width: 200px; /* Scaled down */
+      height: 40px; /* Scaled down */
+      background: linear-gradient(to right, green, yellow, orange, red);
+      border-radius: 20px;
+      overflow: hidden;
+      box-shadow: 0 2px 8px rgba(0, 0, 0, 0.3);
+    }
+    /* Needle */
+    .needle {
+      position: absolute;
+      top: 5px; /* Adjust for centering */
+      left: 50%; /* Default position */
+      width: 4px; /* Visible width */
+      height: 30px;
+      background: black;
+      border-radius: 2px;
+      z-index: 2;
+      box-shadow: 0 0 10px rgba(0, 0, 0, 0.5); /* Glow effect */
+    }
+    /* Label in the middle of the meter */
+    .meter-label {
+      position: absolute;
+      top: 50%;
+      left: 50%;
+      transform: translate(-50%, -50%);
+      font-family: Arial, sans-serif;
+      font-size: 12px; /* Adjusted for smaller size */
+      font-weight: bold;
+      color: #fff;
+      text-shadow: 0 2px 4px rgba(0, 0, 0, 0.5);
+      z-index: 3;
+    }
+    /* Tooltip styling */
+    .tooltip {
+      visibility: hidden;
+      width: 250px;
+      background-color: #222;
+      color: #fff;
+      text-align: center;
+      padding: 10px;
+      border-radius: 5px;
+      position: absolute;
+      top: 50%; /* Vertically aligned */
+      left: 110%; /* Position to the right of the meter */
+      transform: translateY(-50%);
+      font-size: 12px;
+      z-index: 10;
+      box-shadow: 0 2px 5px rgba(0, 0, 0, 0.3);
+    }
+    /* Show tooltip on hover */
+    .ramble-meter:hover + .tooltip {
+      visibility: visible;
+    }
+    /* Wrapper for positioning the tooltip and meter */
+    .ramble-wrapper {
+      position: relative;
+      display: flex;
+      align-items: center;
+    }
+  </style>
+  <script>
+    document.addEventListener("DOMContentLoaded", () => {
+      const needle = document.querySelector(".needle");
+      const rambleMeter = document.querySelector(".ramble-meter");
+      const level = rambleMeter.getAttribute("data-level"); // Read the level from the attribute (0-100)
+      needle.style.left = `${Math.min(Math.max(level, 0), 100)}%`; // Clamp between 0 and 100
+    });
+  </script>
+</head>
+<body>
+  <!-- Ramble Meter -->
+  <div class="ramble-meter-container">
+    <div class="ramble-wrapper">
+      <div class="ramble-meter" data-level="10"> <!-- Adjust level here (0-100) -->
+        <div class="meter-label">Ramble Meter</div>
+        <div class="needle"></div>
+      </div>
+      <div class="tooltip">This post is very close to being completely finished. Not that rambly at all.</div>
+    </div>
+  </div>
+</body>
+</html>
 ===== Categorical Quantum Computing Series: Foundational Papers =====
@@ Line 56: / Line 161: @@
  [[https://lmcs.episciences.org/6532/pdf|Completeness of the ZX-Calculus]]
-This recent paper resolves a long-standing open question by proving the ZX-calculus is complete for all pure qubit quantum mechanics. The ZX-calculus (introduced by Coecke & Duncan in 2011) was known to be universal but not fully complete (certain true quantum equations had no diagrammatic proof using the original rules). Jeandel et al. provided the first complete axiomatisation: they show that any equality of linear maps (matrices) on qubits can be derived using ZX-diagram rewrite rules. The proof proceeds by first enriching the ZX-calculus with additional rewrite rules to make it complete for the Clifford+T fragment (a universal gate set), and then leveraging a translation to a related graphical language (the ZW-calculus) to reach completeness for arbitrary quantum operations. The result implies that the diagrammatic calculus now fully matches the expressive power of matrix mathematics – if two quantum circuits are mathematically equivalent, the ZX-calculus can prove it. This accomplishment marks a maturation of the categorical approach: the diagrammatic methods are not only convenient and intuitive but also no less powerful than algebraic methods. It has spurred further research and practical tools in quantum circuit optimization, equipping the field with a robust graphical proof technique for quantum computing theory.
+This recent paper resolves a long-standing open question by proving the ZX-calculus is complete for all pure qubit quantum mechanics. The ZX-calculus (introduced by Coecke & Duncan in 2011) was known to be universal but not fully complete (certain true quantum equations had no diagrammatic proof using the original rules). Jeandel et al. provided the first complete axiomatisation: they show that any equality of linear maps (matrices) on qubits can be derived using ZX-diagram rewrite rules. The proof proceeds by first enriching the ZX-calculus with additional rewrite rules to make it complete for the Clifford+T fragment (a universal gate set), and then leveraging a translation to a related graphical language (the ZW-calculus) to reach completeness for arbitrary quantum operations. The result implies that the diagrammatic calculus now fully matches the expressive power of matrix mathematics – if two quantum circuits are mathematically equivalent, the ZX-calculus can prove it. This accomplishment marks a maturation of the categorical approach: the diagrammatic methods are not only convenient and intuitive but also no less powerful than algebraic methods. It has generated further research and practical tools in quantum circuit optimization, now with graphical proof technique for quantum computing theory.