liveBook · Manning

Satisfiability problem

As explained in Quantum Programming in Depth

The Boolean satisfiability problem is the problem of finding an assignment to Boolean variables that makes a given Boolean expression true.

The Boolean satisfiability problem asks for an assignment of Boolean-variable values that makes a given Boolean expression true. It provides a compact search problem for translating a classical task into quantum terms. section 6.0

A quantum treatment follows this workflow:

  • Convert the classical satisfiability task into a quantum formulation. section 6.0
  • Apply a quantum search algorithm, such as Grover’s algorithm. section 6.0
  • Evaluate the quantum program and compare it with the best classical algorithm on large instances. section 6.0
Figure 6.1 To solve a classical problem on a quantum computer, we start by converting the problem to its “quantum” formulation to which we can apply a quantum algorithm. After this, we implement the algorithm itself as a quantum program. Finally, we evaluate the performance of the quantum program and compare it to that of the best classical algorithm for solving the same problem. This way, we can see whether this quantum algorithm offers a practical advantage over the classical approaches.
figure

Follow the pipeline from classical problem formulation through quantum implementation to performance comparison. section 6.0

How Quantum Programming in Depth covers it

How deep it goes
Defines the problem and its quantum workflow, while deferring algorithm implementation and performance analysis to later treatment.
Examples
Uses assignments satisfying Boolean expressions and a workflow figure covering formulation, implementation, execution, and comparison.
What it assumes
Assumes no specialized domain knowledge because the classical problem description remains simple.
What you can do after
Understand how to formulate satisfiability for quantum search and evaluate its quantum and classical approaches.
How it connects
Connects Boolean satisfiability with reversible computing, Grover’s search algorithm, quantum algorithms, and classical performance comparison.

Related concepts

This explainer was generated by Manning's knowledge graph from the text of Quantum Programming in Depth. The section links point to the parts of the book it draws on.