The matrix for this gate is: The truth table for the Tofolli (CCNOT) gate is: All the gates in this section are more advanced that the gates already presented. | Although developed and described within the context of Nuclear Magnetic Resonance (NMR) quantum computing these sequences should be applicable to other implementations of quantum computation. {\displaystyle v_{1}} ⟩ a

c it means that the time complexity for simulating a step in a quantum circuit (by means of multiplying the gates) that operates on generic entangled states is

The Hadamard gate has the characteristically quantum capacity to transform a definite quantum state, such as spin-up, into a murky one, such as a … Unfortunately, a working Deutsch gate has remained out of reach, due to lack of a protocol. For more information about the CH gate, see CHGate in the Qiskit Circuit Library. 2 {\displaystyle |+\rangle } ⟩

{\displaystyle |a|^{2}} | and i [ https://arxiv.org/abs/quant-ph/0002077, The project aims to investigate resilience of frames to erasures with reference to Biomedical Imaging. about the Y-axis:

00 ⟩ {\displaystyle |10\rangle }

⋅ 0 | So if you have complex number $$a + ib$$ the conjugagte is $$a - ib$$.

To determine how a qubit's state changes after being operated on by a gate, the matrix of the qubit's current state is multiplied by the matrix of the gate operating on the qubit.

| {\displaystyle |0\rangle } , ⟩ 1 = ⟩ |α〉 = A|α〉, and results in another ket. ⟩ I'm not sure I understand the Swap gate for 11. as follows: If two or more qubits are viewed as a single quantum state, this combined state is equal to the tensor product of the constituent qubits. 1 Viewing CNOT in this basis, the state of the second qubit remains unchanged, and the state of the first qubit is flipped, according to the state of the second bit.

n Φ 1 (5) in the computational basis. The simplest gate is known as the Identity gate: This gate does not change the state of a qubit and outputs whatever was inputted. {\displaystyle \pi /2} 2

at the Bloch sphere. {\displaystyle \Omega (n^{2}log(n))} A = 1

1 Unitary transformations that are not available in the set of gates natively available at the quantum computer (the primitive gates) can be synthesised, or approximated, by combining the available primitive gates in a circuit.

0 {\displaystyle \{|+\rangle ,|-\rangle \}} (For details see below.)

F {\displaystyle F}

Very important single-qubit gates are: the Hadamard gate H, the phase shift gate S, the π/8 (or T) gate, controlled-NOT (or CNOT) gate, and Pauli operators X, Y, Z. H

Special care must be taken when applying gates to constituent qubits that make up entangled states. 0