Why is Toffoli gate universal?

The Toffoli gate θ(3) is universal in the sense that we can build a circuit to compute any reversible function using Toffoli gates alone (if we can fix input bits and ignore output bits).

What is reversible gate?

A reversible logic gate is a memory-less logic element that realizes an injective logical function. Fredkin gate, Toffoli gate, interaction gate, and switch gate are typical ones. Reducing the total amount of garbage signals is an important problem in designing reversible logic circuits.

What is controlled Z gate?

The controlled-Z or cz gate is another well-used two-qubit gate. Just as the CNOT applies an X to its target qubit whenever its control is in state |1⟩ , the controlled-Z applies a Z in the same case.

Is NAND gate reversible?

He goes on to describe the behaviour of what he calls a reversible NAND gate: It has three inputs and three outputs. Of the outputs, two, A’ and B’, are the same as two of the inputs, A and B, but the third input works this way. C’ is the same as C unless A and B are both 1, in which case C it changes whatever C is.

What is the T gate?

The T gate is a single-qubit operation given by: T = ( 1 0 0 exp ⁡ ( i π 4 ) ) \ T = \begin{pmatrix} 1 & 0 \ 0 & \exp \left ( \frac{i \pi}{4} \right ) \end{pmatrix} T=(100exp(4iπ)) The T gate is related to the S gate by the relationship S = T 2 \ S=T^{2} S=T2.

What is NAND logic gate?

In digital electronics, a NAND gate (NOT-AND) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results.

What are the reversible operators?

One clear example of a reversible operator is negation. A not gate, or N gate (where the N stands for negation), is reversible because we simply switch or flip the polarity of a state a (true to false and false to true).

What does a Toffoli gate do?

In logic circuits, the Toffoli gate (also CCNOT gate), invented by Tommaso Toffoli, is a universal reversible logic gate, which means that any classical reversible circuit can be constructed from Toffoli gates. It is also known as the “controlled-controlled-not” gate, which describes its action.

Is CZ a Clifford gate?

CZGate¶ Controlled-Z gate. This is a Clifford and symmetric gate. In the computational basis, this gate flips the phase of the target qubit if the control qubit is in the |1⟩ state.

What is Quantum cost in reversible logic?

Quantum cost (QC) refers to the cost of the circuit in terms of the cost of a. primitive gate. It is calculated knowing the number of primitive reversible logic gates (1*1 or 2*2) required to realize the circuit.

Which logic gate gives reversible?

2 Answers. A logic gate is reversible if we can recover input data from the output. Eg. NOT gate.