Composite Toffoli gate with two-round error detection

Understand

We introduce a fault-tolerant construction to implement a composite quantum operation of four overlapping Toffoli gates.

• The same construction can produce two independent Toffoli gates.
• This result lowers resource overheads in designs for quantum computers by more than an order of magnitude.
• The procedure uses Clifford operations and 64 copies of the non-Clifford gate $T = \exp[i \pi (I - \sigma^z) /8]$.