Qubits Seminar Presentation 6th Semester Electronics And Communication (ECE)
- 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