# ApplyLowDepthAnd operation

Namespace: Microsoft.Quantum.Canon

Package: Microsoft.Quantum.Standard

Inverts a given target qubit if and only if both control qubits are in the 1 state, with T-depth 1, using measurement to perform the adjoint operation.

operation ApplyLowDepthAnd (control1 : Qubit, control2 : Qubit, target : Qubit) : Unit is Adj + Ctl


## Description

Inverts target if and only if both controls are 1, but assumes that target is in state 0. The operation has T-count 4, T-depth 1 and requires one helper qubit, and may therefore be preferable to a CCNOT operation, if target is known to be 0. The adjoint of this operation is measurement based and requires no T gates, and no helper qubit.

## Input

### control1 : Qubit

First control qubit

### control2 : Qubit

Second control qubit

### target : Qubit

Target auxiliary qubit; must be in state 0

## References

• Cody Jones: "Novel constructions for the fault-tolerant Toffoli gate", Phys. Rev. A 87, 022328, 2013 arXiv:1212.5069 doi:10.1103/PhysRevA.87.022328
• Peter Selinger: "Quantum circuits of T-depth one", Phys. Rev. A 87, 042302, 2013 arXiv:1210.0974 doi:10.1103/PhysRevA.87.042302