Proof of the Universality of Toffoli and Hadamard Gates
WEBJun 14, 2018 · Given those four catalyst states, Hadamard+Toffoli is universal because it can synthesize Hadamard+T+CNOT (which is universal). Note that it is important that the circuit not consume the catalyst states. This is what distinguishes Toffoli+H from the Clifford gate set (which can synthesize T gates only by consuming the magic states). Share. Cite.
Simulating Toffoli Gates with Fredkin Gates with no garbage bits
WEBAug 3, 2017 · Toffoli gates don't. Because of that, it's impossible to implement Toffoli gates with Fredkin gates without some source/dump of ON bits. See the paper 'The Classification of Reversible Bit Operations' by Scott Aaronson et al.
Derive unitary matrix for Tofolli gate - Physics Stack Exchange
WEBAug 14, 2018 · Apply the gates from your original circuit to the bottom half of this larger circuit. Look at the output amplitude display. It's the circuit's unitary matrix! (Actually it's only proportional to the matrix, but that's just as good.) Here …
Relationship between Toffoli gate and Deutsch gate
WEBAug 27, 2015 · The rotation R θ R θ in the Deutsch gate should be a rotation about the X X axis, not about the Z Z axis, i.e., k k, as e.g. described . Then, setting θ π θ π / one immediately obtains the Toffoli gate. Note that if R θ R θ were a phase shift, the Deutsch gate would not be universal, as it would be diagonal, and thus would only allow to ...
Smallest number of quantum gates to simulate other gates?
WEBToffoli simulates Fredkin. We write the Toffoli gate as. Relevant properties of the Toffoli gate are. FANOUT. XOR/CNOT. We also need to recognize that the Fredkin map can be equivalently written as $$\mathrm{Fred}(x,y,z)= (x, x(y\oplus z)\oplus y, …
Constructing a Toffoli gate with 2-and 1-qubit gates?
WEBI'm looking through Nielsen & Chuang's book on quantum computation and information and in part of it he says that any C2(U) C 2 (U) gate can be constructed from two qubit and one qubit gates. I can't figure out how to do this, or how to verify it (fig 4.8 in his book) I've attached a photo of the diagram:
2 following gates, inverse circuit - Physics Stack Exchange
WEBMar 25, 2013 · I have a circuit that has 4 wires and 2 following each other Toffoli gates. The first Toffoli gate occupies 3 wires from above, the following Toffoli gate occupies 3 wires from below. What will look like the inverse circuit of this entire circuit? Thanks much!
quantum information - How to write the matrices for Hadamard …
WEBJun 4, 2019 · Applying the Hadamard gate to the 'second qubit = Y' means performing: I⊗H. Applying the Hadamard gate to the 'first qubit = X' means performing: H⊗I. Bottom line: Make sure you know the convention for tagging qubits as 'first', 'second' or 'nth'
What meaning is Depth and T-Depth in Quantum Circuit?
WEBDec 2, 2020 · However, you have to distinguish between number of basic (or physical) gates and composed gates. For example, if you have one Toffoli gate, the depth can be one (composed gates) or 12 in basic gates H H, T T, T† T † and CNOT (see here how Toffoli gate can be constructed). T T -depth is a number of T T gates in row, or in general …
When is a unitary operator a quantum gate? - Physics Stack …
WEBOct 2, 2015 · Quantum gates are all unitary transformations on a state of qubits. Any unitary transformation can be considered a "gate", although the ones you mention are primitive ones from which others can be constructed. More complex ones are usually referred to as circuits. The two qubit gates, H H, π 8 π 8 and CNOT C N O T are considered universal ...