not gate




{\displaystyle |11\rangle } So a conductive path will be established between Vcc and output, which makes the output logic High. A If we measure one of the qubits to be for example Gates that are their own unitary inverses are called Hermitian or self-adjoint operators. x | {\displaystyle q} ⟩ F

True or 1, the NPN transistor will switch on & a conductive path from the output to ground is created. 0 2 . {\displaystyle \dagger } is the probability amplitude for measurable state

{\displaystyle -|1\rangle } ( n

0



a | Unitary transformations (functions) that only consist of gates can themselves be fully described as matrices, just like the primitive gates. creates a superposition).

a 2

⟩ unchanged and maps ⟩

ϕ | {\displaystyle 2^{n}}

K

Digital inverter quality is often measured using the voltage transfer curve (VTC), which is a plot of output vs. input voltage. n {\displaystyle |0\rangle } representing the gate. n | 1 {\displaystyle |10\rangle }

⟩ 0 The Boolean expression of the NOT gate is Z =X ̅. {\displaystyle {\frac {|0\rangle +|1\rangle }{\sqrt {2}}}} There are three different symbols used for NOT gate: The American National standard Institute symbol, it is most commonly used: The International Electrotechnical Commission symbol: Deutsches Institut für Normung symbol for NOT gate, which is used in Germany: The truth table is a logic table containing the input combinations and their corresponding outputs.

is the analytical representation of NOT gate: If no specific NOT gates are available, one can be made from the universal NAND or NOR gates.[2]. ⟩

1

{\displaystyle |01\rangle } g All rights reserved. y

⟩ 0 n b Quantum algorithms often contain both a classical and a quantum part. with Moreover, for unitaries on a constant number of qubits, the Solovay–Kitaev theorem guarantees that this can be done efficiently. ) This can be done by combining the gate with an identity matrix such that their tensor product becomes a gate that act on N qubits.

It is also known as the name of an inverter because it inverts or reverses the input. H = {\displaystyle |1\rangle } See measurement for details.

Try the following interactive example to see for yourself how a NOT gate behaves. {\displaystyle e^{i\phi }|1\rangle }

The vector representation of two qubits is: The action of the gate on a specific quantum state is found by multiplying the vector
− 2 Measurement is then a probabilistic projection, or the shadow, of the points at the surface of this complex sphere onto the basis vectors that span the space (and labels the outcomes). 2

is a unitary matrix, F | 0 | If the applied input is low then the output becomes high and vice versa.

Measurement (sometimes called observation) is irreversible and therefore not a quantum gate, because it assigns the observed variable to a single value. consists of two gates H

1

⟩ | It acts in the manner of the logical operation "and" followed by negation. + {\displaystyle R_{\phi }}

{\displaystyle |0\rangle } Measurement of quantum registers results in binary values that the classical computer can use in its computations.



0 The tensor product is denoted by the symbol 0



{\displaystyle \pi } n In this article, we always use the computational basis, which means that we have labeled the
Originally it was solved by giving up the assumption of local realism, but other interpretations have also emerged. − The inverter is a basic building block in digital electronics. 0 The logic symbol of the NOT gate is shown in below figure. mod Ω

{\displaystyle n} 2

so that we can act on quantum states that span two qubits: The gate then the controlled-U gate is a gate that operates on two qubits in such a way that the first qubit serves as a control.

q 2

2 {\displaystyle B_{k}}

2

Unitary inverses can also be used for uncomputation. There are three different symbols used for NOT gate: ANSI. ] |

|

Any state that can be written as a tensor product from the constituent subsystems are called separable states.

| )

with probability − to about the Z-axis: to {\displaystyle |2^{n}-1\rangle }

and 1

| {\displaystyle {\frac {1}{\sqrt {2^{n}}}}\sum _{k=0}^{2^{n}-1}|k\rangle } k A NOT gate, often called an inverter, is a nice digital logic gate to start with because it has only a single input with simple behavior. Similarly, a false input results in a true output.

. mod

. 1 If a function

{\displaystyle \Omega (n^{2}log(n))}

n

0 ⊗ and The Toffoli gate, named after Tommaso Toffoli; also called CCNOT gate or Deutsch ( 1 where I is the identity matrix, H is a unitary matrix (like all other quantum logical gates). {\displaystyle H} {\displaystyle F(|a\rangle \otimes |b\rangle )=|a+b{\pmod {2^{n}}}\rangle \otimes |a\rangle }

possible states; 2 B

⟩ {\displaystyle {\sqrt {\mbox{SWAP}}}} ,

In digital logic, an inverter or NOT gate is a logic gate which implements logical negation. , the phase gate (written S, though S is sometimes used for SWAP gates) where a 0 ⟩ 2



can now be applied to any two-qubit state, entangled or otherwise. =

b |

We will discuss this schematic for both cases of input logic. ⟩ − A , which means that a measurement will have equal probabilities to become 1 or 0 (i.e.

( ⟩ ⟩ 1 A NOT gate is a special type of gate in that it has only one input and only one output. | = ⊗

basis vectors of an The tensor product (or kronecker product) of two quantum gates is the gate that is equal to the two gates in parallel.[11][12].

|

NOT gate is a single input single output gate. [24], The effect of measurement on entangled states, Measurement on registers with pairwise entangled qubits.

, {\displaystyle G} {\displaystyle m}

{\displaystyle 2^{n}} 256 0 U The resulting gate C will have the same dimensions as A and B. ⟩ n Measurement can even be randomly and concurrently interleaved qubit by qubit, since the measurements assignment of one qubit will limit the possible value-space from the other entangled qubits. Each of the symbols below can be used to represent a NOT gate. e we have, after recursive application on itself, Similarly if the function

⟩ b 11 00

{\displaystyle |\Psi \rangle } w {\displaystyle F^{\dagger }F=FF^{\dagger }=I} n



. 0 V A , it is represented by the matrix: The CNOT (or controlled-X) gate can be described as the gate that maps [



| i ⟩

{\displaystyle |\psi \rangle =\bigotimes _{i=0}^{n-1}|\psi _{i}\rangle }

| 0 0





A s NOT gate IC is an inverter, the output is represented by a “ ͞ … ), create a quantum state that have equal probability of being observed in any of its four possible outcomes; 00, 01, 10 and 11. ⟩



The source of NMOS is connected with GND.

a .

{\displaystyle |0_{10}\rangle =|0\dots 00_{2}\rangle ,|1_{10}\rangle =|0\dots 01_{2}\rangle ,|2_{10}\rangle =|0\dots 10_{2}\rangle ,\cdots ,|2^{n}-1\rangle =|111\dots 1_{2}\rangle } ) The output O is taken across the resistor R2 & input is applied to the base of the transistor through resistor R1. 1 2 and 2

{\displaystyle n}

| gate performs half-way of a two-qubit swap. n {\displaystyle {\begin{bmatrix}1&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0\\0&0&1&0&0&0&0&0\\0&0&0&1&0&0&0&0\\0&0&0&0&1&0&0&0\\0&0&0&0&0&0&1&0\\0&0&0&0&0&1&0&0\\0&0&0&0&0&0&0&1\\\end{bmatrix}}}, The Ising gate (or XX gate) is a 2-qubit gate that is implemented natively in some trapped-ion quantum computers. x

In the quantum computing domain, it is generally assumed that the basis vectors constitute an orthonormal basis. It cannot be described as a tensor product of two qubits. 0

Unlike with the bits of classical computers, quantum states can have non-zero probability amplitudes in multiple measurable values simultaneously. {\displaystyle |\psi _{1}\rangle }

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