Quantum – Circuits – AH2
AH2 Gate The quantum AH2 gate is the Haadmard gate for a multipart qubit with 2 qubits. The Haadamard operation, H, applies to the first qubit as follows: Next: CZ gate Previous: CNOT gate
Quantum – Circuits – CNOT
CNOT Gate The quantum CNOT gate, controlled not, inverts the second qubit in a multipart qubit whenever the first qubit is jv. The first qubit is the control. Examples of Quantum CNOT Gate Note that all gates are unitary and as such the quantum CNOT gate is reversible. See the Bellagio circuit for examples of […]
Quantum – Gates – Haadamard – H
This post shows how R2 Wave Numbers are used with the Haadamard gate. Note that part 1 of the Bellagio circuit uses Haadamard gates. H Gate The Haadmard gate puts |j^> and |jv> into superposition. It does this by splitting |j^> to |j^> + |jv> and |jv> to |j^> + –|jv>. Similarly to other gates, […]
Quantum – Gates – Pauli and σf
This post shows how R2 Wave Numbers are used with Pauli gates. It also introduces the σf gate which flips the Opposite Signs of both bits of a qubit. Pauli σx Gate The purpose of the Pauli σx gate is to bit-flip a qubit. It does this by inverting the bits up and down […]
Quantum – Gates – Introduction
Gates Quantum gates perform operations on qubits and need to relate to the physical process that manipulates qubits. An element of 0 in a gate operating on a 1^ in a qubit is the equivalent of saying stop or that the wave has no probability of getting to that hemisphere. Dirac’s Notation Quantum theory is […]
Quantum – Theory – Superposition
Definition: Superposition represents any state of the qubit that is a linear combination of basis states |j^> and |jv> where both components are non-zero. States that are not in superposition: Note that although the state is mathematically possible, a qubit cannot physically exist in this state. Also, this state breaches Born’s rule which states that: […]
Quantum – Theory – Matrices
Introduction Wave Number matrices allow for the addition and multiplication of quantum states. Opposite Values and flipping work together to get differences and consequently eliminate the need for subtraction. As in classical maths, there is no such thing as division with matrices. Multiply matrix a by the inverse of matrix b in order to divide […]
Quantum – Theory – Single, Multipart and Mega Qubits
This post covers the features of single and multipart qubits. Single Qubit Features Flip Operation Multipart Qubit Features Superposition and Entanglement and Mega Qubits Next: Matrices Previous: Basis and Born’s Rule
Quantum – Theory – Basis & Born’s Rule
This post describes Born’s rule that defines the probability of the collapse of qubits to a quantum basis. z-axis Basis Define the z-axis basis states, {|j^>, |jv>}, as: which are orthogonal because their inner product = 0: <j^|jv> = [1^ 0]. = 1^*0 + 0*1^ = 0 Born’s Rule In Wave Numbers, […]
Quantum – Theory – Bra-Kets or Dirac’s Notation
This post reviews the theory and format of quantum bra-kets and ket-bras, which is also known as Dirac’s notation. Ket-bras are outer products in comparison to bra-kets which are inner products. Definition Wikipedia defines a bra-ket as follows: ‘In quantum mechanics, bra-ket notation, or Dirac notation, is used ubiquitously to denote quantum states…. A ket […]