Abstract:

Problems of metaphor are rampant in quantum computing. On the one hand, the underlying phenomena are best described mathematically. They are so different from things in the world natural languages and drawings are intended to describe that constructing even approximate metaphors can be extremely challenging. On the other hand, metaphor is an extremely powerful technique for education; it is a primary way humans learn. So it is completely expected that quantum computing educators and textbooks would attempt to adapt visual metaphors from existing disciplines, like computer science and electrical engineering, to the new discipline of quantum computing. To do otherwise borders on negligence. However, in the view of the author, a computer scientist with no formal physics background, the results are mixed at best. This is completely to be expected, but it shouldn’t deter us from trying to do better.

We propose some different ideas that, while hardly the “final” or “best” answers, could at least move the discussion forward. By recognizing the deficiencies of existing metaphors in describing quantum phenomena, we hope to develop drawings and circuit diagrams better suited to depicting qbits and quantum circuits, in ways that will make quantum computing concepts more accessible to a broader audience beyond physics majors.

For example, one significant problem with existing quantum gate and circuit drawings arises from the inability of a single wire to elegantly convey the properties of a qbit in superposition. Consider for example the traditional presentation of a 2-qbit CNOT gate, using Dirac notation, linear algebra, and the standard circuit diagram. Everything is reasonably intuitive when the inputs are in one of the basis states {|0>,|1>}, because then the circuit behaves classically. This is exactly what anyone familiar with an introductory digital logic course would expect.

However, when the control input is in superposition, the result violates the viewer’s expectation that a wire with no intervening gates can nonetheless have a different result at the output than was supplied at the input, due to the quantum state property of entanglement. This hinders learning, and can generate frustration among students. We show how to present the CNOT example in a different way, this time representing the wires and gate using visual metaphors we believe more intuitively capture the notion of superposition on a wire. Drawn in this way, classical behavior is more easily seen as a special case of general quantum behavior that includes entanglement, without violating any previously learned assumptions about how circuits work that may have been internalized from earlier courses in more established disciplines.

Better metaphors can help in other areas as well, such as emphasizing the connection between the operation of the gate at a quantum level and the gate's mathematical description as a matrix, the Bloch Sphere (one of the better visual aids in quantum computing), and others.

Keywords:

Metaphors, quantum computing, quantum computing education, STEM education, mathematics.