Embedding Functions Into Reversible Circuits: A Probabilistic Approach to the Number of Lines

In order to compute a non-invertible function on a reversible circuit, one needs to "embed" the function into a larger function which has some garbage bits, corresponding to additional lines. The problem of determining the minimal number of garbage bits that are needed to embed a given function has attracted extensive research, largely motivated by quantum computing, where the number of lines equals the number of qubits. However, all approaches that are known have either no theoretical quality guarantees (bounds on approximation factors) or require exponential runtime. We present an efficient probabilistic approximation algorithm with theoretical bounds.