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Explain Deutsch's Algorithm and its purpose.
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Deutsch's Algorithm determines if a given function is constant or balanced with a single query by using Hadamard gates and an oracle.
What is meant by the term 'relative phase' in quantum computing?
Relative phase refers to the impact on computational power due to the phase difference between quantum states.
What is the exponential form of a complex number?
The exponential form of a complex number is r * e^(iθ).
What are the mathematical representations of |0⟩ and |1⟩ in a quantum computer?
|0⟩ = [1,0], |1⟩ = [0,1]
Describe the function of the CNOT gate.
The CNOT gate applies the X gate to the target qubit only if the control qubit is in state |1⟩.
What allows Superdense Coding to transmit 2 classical bits using 1 qubit?
Superdense Coding utilizes pre-shared entanglement between the sender and receiver.
Define superposition in the context of qubits.
Superposition refers to a qubit being in both states |0⟩ and |1⟩ simultaneously.
What is the physical representation of a qubit?
A qubit is often represented by quantum particles like photons that can exist in two states.
What does the X gate do in quantum computing?
The X gate flips the states |0⟩ and |1⟩.
What is the Bloch Sphere used for in quantum computing?
The Bloch Sphere is a visual representation of a qubit's state and phase.
What is the primary goal of the Bernstein-Vazirani Algorithm?
The Bernstein-Vazirani Algorithm finds a secret string S using a phase oracle by querying the function once.
Describe what phase kickback is.
Phase kickback refers to a phenomenon used in quantum algorithms where the phase of a control qubit is altered by an operation on a target qubit.
Explain the concept of quantum entanglement.
Quantum entanglement is a phenomenon where the measurement of one qubit instantaneously affects the state of another, regardless of distance.
What is the difference between maximally and partially entangled states?
Maximally entangled states (like Bell States) have the highest correlation between qubits, while partially entangled states affect probabilities of measurements but do not have maximum correlation.
Explain the significance of Hermitian matrices in quantum computing.
Hermitian matrices are equal to their own conjugate transpose (H = H†). They are used to describe observables in quantum mechanics.
What is the probability of measuring a qubit in state |0⟩ if the state is α|0⟩ + β|1⟩?
The probability is |α|^2.
What is the purpose of the Quantum Fourier Transform in Shor's Algorithm?
The Quantum Fourier Transform is used to find the period of a function, which is essential for the factorization process.
Describe what a unitary matrix is.
A matrix is unitary if it maintains vector length during transformation, such that UU† = I.
How are complex conjugates calculated?
To find the complex conjugate, you flip the sign of the imaginary part of a complex number.
How is the magnitude of a complex number a + bi calculated?
√(a^2 + b^2)
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