Seminar PPT on Quantum Bits

1. QUBITS
(Quantum Bits)
by:
20BEC064

2. Introduction
• Qubits are the basic building blocks of
quantum computing, and they differ from
classical bits in that they can be in a state of
superposition, meaning they can represent
both 0 and 1 simultaneously. This property
allows quantum computers to perform
certain calculations much faster than classical
computers.

3. Properties of
Qubits
• Superposition:
• A qubit can exist in a superposition of states,
which means it can be in multiple states at
the same time. This is in contrast to classical
bits, which can only be in one state (either 0
or 1) at any given time.

4. Properties of
Qubits
• Entanglement:
• Qubits can also be entangled, which means
that the state of one qubit is dependent on
the state of another qubit, even if they are
physically separated. This property allows for
the creation of quantum states that cannot
be created with classical bits.

5. Collapse of
wave function
• Measurement:
• When a qubit is measured, it collapses into
one of its possible states, with the probability
of each state being determined by its
superposition. This means that the act of
measurement can change the state of the
qubit, which has important implications for
quantum computing algorithms.

6. Qubits Notation
• In this notation, a qubit can be in a
superposition of two states, commonly
referred to as the |0> state and the |1>
state.
• The notation for a qubit in a
superposition state can be written as:
• α|0> + β|1>
• Here, α and β are complex numbers
known as the probability amplitudes
that represent the probability of finding
the qubit in the |0> and |1> states,
respectively. The probabilities are
calculated by taking the square of the
absolute value of the probability
amplitudes, i.e., |α|^2 and |β|^2.

7. Qubits Bloch Sphere
Representation
• The Bloch sphere is a geometrical representation of
the quantum state of a qubit. It is a three-dimensional
sphere with the north and south poles representing
the |0> and |1> states, respectively. The equator of
the sphere represents the superposition states,
where the qubit can be in a combination of the |0>
and |1> states.
• To represent a qubit on the Bloch sphere, we need to
calculate its coordinates on the surface of the sphere.
The coordinates are determined by the probability
amplitudes of the qubit, which can be written as:
• α|0> + β|1>
• where α and β are complex numbers.

8. Qubits Bloch Sphere
Representation
• To calculate the coordinates of the qubit on the Bloch sphere,
we need to determine the angles θ and φ, which are defined as
follows:
• θ = 2 * cos^-1(|α|)
• φ = arg(β)
• Here, cos^-1 is the inverse cosine function, |α| is the absolute
value of α, and arg(β) is the argument or phase of β.
• Once we have calculated the values of θ and φ, we can locate
the qubit on the surface of the Bloch sphere. The point on the
sphere will be located at an angle of θ from the north pole and
an angle of φ from the x-axis.
• The Bloch sphere is a useful tool for visualizing the quantum
state of a qubit, and it is often used in quantum computing and
quantum information processing.

9. Quantum Gates
• Quantum gates are the building blocks of
quantum circuits, just like classical gates
are the building blocks of classical circuits.
Quantum gates are used to manipulate
the state of a qubit or a collection of
qubits to perform quantum operations like
computation and communication.

10. Quantum Gates
• There are many types of quantum gates, each of which performs a specific
operation on the quantum state. Some of the commonly used quantum gates
are:
• Pauli gates: These gates are named after Wolfgang Pauli and include the X, Y, and
Z gates. They are used to flip the state of a qubit along the x, y, or z-axis of the
Bloch sphere.
• Hadamard gate: This gate is used to create a superposition state of a qubit by
rotating it halfway between the |0> and |1> states.
• CNOT gate: This gate is a two-qubit gate that flips the second qubit if the first
qubit is in the |1> state.
• SWAP gate: This gate is used to exchange the states of two qubits.
• Controlled gates: These gates include the Controlled-NOT (CNOT) gate,
Controlled-Hadamard (CH) gate, and Controlled-Rotation gate. These gates are
used to apply an operation on a target qubit only when a control qubit is in a
specific state.

11. Quantum Gates

12. Types of Qubits
• There are several types of qubits used in quantum computing,
each with its advantages and limitations. Here are three of the
most common types:
• Superconducting qubits: Superconducting qubits are made from
tiny electrical circuits and are one of the most widely used types
of qubits in quantum computing. They can be fabricated using
standard microfabrication techniques and can be operated at
relatively high temperatures. However, they are susceptible to
noise and have a relatively short coherence time.
• Trapped ion qubits: Trapped ion qubits are made by trapping
individual ions and manipulating their quantum states using
lasers. They have long coherence times and are relatively
immune to noise, but they require complex and expensive
equipment to operate.
• Photonic qubits: Photonic qubits are encoded in the
polarization states of individual photons. They are immune to
decoherence and have long coherence times, but they are
challenging to manipulate and detect. Photonic qubits are
primarily used in quantum communication applications, such as
quantum cryptography.

13. Quantum
Supremacy
• Quantum supremacy refers to the ability of a quantum
computer to solve a problem that is infeasible for classical
computers, even the most powerful supercomputers. This
concept was introduced by John Preskill in 2012.
• To achieve quantum supremacy, a quantum computer must
demonstrate that it can perform a specific computation or task
that cannot be efficiently solved by classical computers. This is
typically done by running a quantum algorithm on a quantum
computer and comparing its performance with the best-known
classical algorithm.
• In 2019, Google claimed to have achieved quantum supremacy
by performing a computation on a quantum computer that
would take a classical computer thousands of years to
complete. The computation involved generating random
numbers, and Google's quantum computer completed it in
about 200 seconds.

14. Challenges and
Limitations of
Quantum Bits
• Quantum bits, or qubits, are essential building blocks
of quantum computers and quantum information
processing. However, there are several challenges and
limitations that need to be overcome before quantum
computing can become a practical reality.
• Decoherence: Qubits are very sensitive to their
environment, and even minor interactions with other
particles can cause them to lose their quantum state.
This phenomenon, known as decoherence, can make it
difficult to maintain the coherence of qubits and
perform accurate computations.
• Error Correction: Errors can arise due to various
sources like noise, imperfections, and environmental
disturbances, making it challenging to perform error-
free operations. Therefore, developing efficient error-
correction schemes that can detect and correct errors
in real-time is one of the biggest challenges in
quantum computing.

15. Challenges and
Limitations of
Quantum Bits
• Scalability: Current quantum computers have
only a few tens of qubits, which is not enough to
perform complex computations or simulations.
To build large-scale quantum computers,
researchers must develop scalable architectures
and qubit technologies that can support large
numbers of qubits.
• Control and Readout: Quantum computers
require precise control and measurement of
qubits, which can be challenging. The required
hardware and software to control the qubits and
read out the results need to be developed
further.
• Cost and Access: Building and maintaining
quantum computers are expensive, and access to
quantum computers is limited. This makes it
difficult for researchers and companies to
develop and test quantum algorithms and
applications.

16. Quantum
Supremacy
• However, the term quantum supremacy is somewhat
controversial, as it implies that quantum computers are
superior to classical computers in all respects. While quantum
computers are expected to excel at certain types of problems,
they may not necessarily outperform classical computers on all
tasks. Additionally, some researchers argue that the term
"quantum advantage" may be more appropriate, as it does not
imply superiority over classical computers but instead
acknowledges the potential of quantum computers to provide
significant speedup for certain tasks.
• Overall, achieving quantum supremacy or quantum advantage
is an important milestone for the development of quantum
computing and demonstrates the potential of this technology to
revolutionize various fields, including cryptography, materials
science, and drug discovery.

17. References
• https://qiskit.org/documentation/stubs/qiskit.circuit.Qubit.html
• https://quantum-computing.ibm.com/composer/docs/iqx/guide/the-qubit
• https://quantumcomputingreport.com/
• https://quantumcomputing.stackexchange.com/
• https://quantum.country/qcvc
• https://www.microsoft.com/en-us/quantum/
• https://www.amazon.com/Quantum-Computing-Applied-Jack-D-Hidary/dp/3030239219