1. Qubit & Quantum Gate
Present by ………
Name : Bijoy Maji
Roll No. : 455
Semester : 4th
Session : 2021-2023
Vidyasagar University

2. A. What is Qubit?
B. Making Qubit by different method
C. Measure and control Qubits
D. Quantum gate
E. Quantum State
F. Different type of Quantum Gate
G. Making Adder circuit
H. Conclusion
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Content:

3. [Basic unit of quantum information]
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Superposition state |Ψ⟩= α∣0⟩ +
β∣1⟩
Qubit means quantum bit. Just like binary bit or basic unit
of classical computer. Binary bit can only represent a single
value such as 0 or 1. It can be in one of two possible state.
Qubit can be represent ∣0⟩ or ∣1⟩ or super position of both
state.
What Is Qubit?
|α|2
+ |β|2
= 1

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Making two level quantum system.
Making Qubit
Non Solid State Platforms:
1. Photon Qubit
2. Trapped Ions Qubit
Solid State Platforms:
1. Superconductor (Transmon)
2. NV – Center in Diamonds
3. Semiconductor Quantum Dot
 How to build Qubit?

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 Based on Polarization of photon.
Photon Qubit:
 Polarization : It is orientation
of electromagnetic field
which can be vertical and
horizontal.
 This approach not only build
photonic quantum computer
but also connect quantum
computer and bit
information between them.
BACK

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BACK
Trapped Ions Qubit:
 This platform made of electric charge trapped
in alternative electric field.
 This is done in high vacuum such that these
ions are well isolated from environment and
can be well controlled.
 The kinetic energy is low enough so there are
in ground state. We can deliberately exited
them using laser and read out it examined
with camera.
 It is permissible candidate to make large
system.
The electric filed is shaded
region and ions are small gray
ball.
Many trap ions

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Basic Structure Implementation in Quantum Processor
Superconductor Qubit:

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 Quantization of LC oscillator. (Act as a artificial atom)
Superconductor Qubit:

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 Making Two level artificial atom by using Josephson Junction
Superconductor Qubit:

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BACK
Finally on Quantum processor:

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Diamond Removing Carbon atom Placing Nitrogen atom
Spin of the electron or Nitrogen atom is use as qubit.
NV-Center qubit is well coupled with light, they are prime candidate as local nodes for
quantum communication using photon to transmit quantum information
BACK
NV – Center in Diamond’s spin:
 NV (Nitrogen Vacancy) center in Diamond’s spin qubit:

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Semiconductor quantum dot qubit:
 In semiconductor quantum dot qubit , single electron enabling their spin to as
qubit.
 Electron in quantum dot required to operate at absolute zero temperature in
order to suppress change fluctuation in quantum dot’s state.

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Measure and control of a Qubit: :
Figure shows how we measure
and control qubit by resonator

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Quantum Gate:
 Quantum gates are nothing but a
unitary operation.
 For single-qubit gates, it’s
actually quite straightforward: we
apply a short pulse of microwave
radiation. If the frequency of the
microwave exactly matches the
resonant frequency of the qubit,
it will cause the qubit state to flip.
We can also create superposition
states in the same way by
adjusting how long the pulse
lasts.
 Need Of quantum gate:
Implementing arithmetic and logical operation on qubit.
Fig: Operation of Quantum Gate

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These three weird quantum properties enable the design of quantum algorithms which can compute in ways classical computers
cannot, making quantum computers more powerful for solving certain types of problems.
 Quantum Theory related to quantum Gate:
Superposition Entanglement Interference

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 Its quantum state can be written in terms of two levels, labeled and ,
which can be represented in the “computational basis” by two-
dimensional vectors:
Quantum States:

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Different Quantum Gates:

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 X (or 𝞼x): bit-flip
 Work:
The output would be the input vector rotated 180º about the x-
axis on the Bloch sphere
 Some Single Qubit Quantum Gate:
 Symbol:
 Matrix Representation:

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 Symbol:
 Matrix Representation:
 Work:
Pauli-Y gate rotates quantum states
180º about the Y-axis.
 Symbol:
 Matrix Representation:
 Work:
Pauli-Z gate rotates quantum states
180º about the Z-axis.
 Pauli Y gate:  Pauli Z gate:

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 Hadamard (H): creates a 50-50
superposition from |0⟩ and |1⟩
 Hadamard (H) Gate:
 Symbol:
 Matrix Representation:

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 Work:
if the control qubit is 0, does nothing
if the control qubit is 1, flip the target qubit
 CNOT (controlled not):
It is similar to XOR gate

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 Quantum Composer has a series of quantum
phase-shift gates that allow us to shift this phase
by the following:
The general phase-shift gate:
The 𝑃 𝜙 matrix is
𝑃 𝜙 =
1 0
0 𝑒𝑗𝜙
 Phase Shift Gate:
 General Phase shift gate

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Input Output
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
Fig For 1+1 circuit
 Making Adder Circuit:
 Where X gates are use to
encode the input qubit.

24. It is a very advance, first and power
technology. But is very difficult to
implementation. To stabilized qubit on its
quantum state we need very low
temperature. This technology is too much
expensive.
This technology can’t replace our modern
day computer but is will help to improve
out Cyber security, Drug simulation,
Weather prediction system. Quantum
computer do two and more computation
parallelly .
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 Conclusion:

25. 1. https://jonathan-hui.medium.com/qc-how-to-build-a-quantum-
computer-with-superconducting-circuit-4c30b1b296cd
2. https://medium.com/qubit-factory/basic-quantum-computing-
gates-using-ibm-qiskit-12e64c46a46e
3. https://quantum-computing.ibm.com/
4. https://en.wikipedia.org/wiki/Controlled_NOT_gate
5. https://quantumai.google/research/publications
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 Reference:

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