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+#import "@preview/fletcher:0.5.1": diagram, node, edge
+#import "@preview/gentle-clues:0.9.0": example
+#import "@preview/quill:0.3.0": quantum-circuit, lstick, rstick, ctrl, targ, mqgate, meter
+
+
+= Background
+== Quantum Computation and Quantum Circuits
+A quantum computer is a device that performs calculations by using certain phenomena of quantum mechanics.
+The algorithms that run on this device are specified in quantum circuits. 
+
+#example[
+  @example_qc shows a simple quantum circuit that implements a specific quantum algorithm.
+
+  #figure(
+    quantum-circuit(
+      lstick($|0〉$), $H$, mqgate($U$, n: 2, width: 5em, inputs: ((qubit: 0, label: $x$), (qubit: 1, label: $y$)), outputs: ((qubit: 0, label: $x$), (qubit: 1, label: $y plus.circle f(x)$))), $H$, meter(), [\ ],
+      lstick($|1〉$), $H$, 1, 1, 1
+    ),
+    caption: [A quantum circuit implementing the Deutsch-Jozsa algorithm]
+  ) <example_qc>
+]
+
+
+== Decision Diagrams
+Decision diagrams in general are directed acyclical graphs, that may be used to express control flow through a series of conditions.
+It consists of a set of decision nodes and terminal nodes.
+The decision nodes represent an arbitrary decision based on an input value and may thus have any number of outgoing edges.
+The terminal nodes represent output values and may not have outgoing edges.
+
+A @bdd is a specific kind of decision diagram, where there are two terminal nodes (0 and 1) and each decision node has two outgoing edges, depending solely on a single bit of an input value.
+@bdd[s] may be used to represent any boolean function.
+
+#example[
+  Example @bdd[s] implementing boolean functions with an arity of $2$ are show in @example_bdd_xor and @example_bdd_and.
+
+  #figure(
+    diagram(
+      node-stroke: .1em,
+      node((0, 0), [$x_0$], radius: 1em),
+      edge((0, 0), (-1, 1), [0], "->"),
+      edge((0, 0), (1, 1), [1], "->"),
+      node((-1, 1), [$x_1$], radius: 1em),
+      node((1, 1), [$x_1$], radius: 1em),
+      edge((-1, 1), (-1, 2), [0], "->"),
+      edge((-1, 1), (1, 2), [1], "->"),
+      edge((1, 1), (1, 2), [0], "->"),
+      edge((1, 1), (-1, 2), [1], "->"),
+      node((-1, 2), [$0$]),
+      node((1, 2), [$1$]),
+    ),
+    caption: [A @bdd for an XOR gate.]
+  ) <example_bdd_xor>
+
+  #figure(
+    diagram(
+      node-stroke: .1em,
+      node((1, 0), [$x_0$], radius: 1em),
+      edge((1, 0), (0, 2), [0], "->"),
+      edge((1, 0), (1, 1), [1], "->"),
+      node((1, 1), [$x_1$], radius: 1em),
+      edge((1, 1), (0, 2), [0], "->"),
+      edge((1, 1), (1, 2), [1], "->"),
+      node((0, 2), [$0$]),
+      node((1, 2), [$1$]),
+    ),
+    caption: [A @bdd for an AND gate.]
+  ) <example_bdd_and>
+]
+
+