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Quantum Computing Fundamentals
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Quantum Computing Fundamentals
Quantum Computing Fundamentals
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1
Question
Quantum Parallelism
Page 1
Answer
Qbits can be simultaneous arbitrary mix of both states simultaneously
2
Question
Difference between qBits and Classical Bits
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Answer
Classical Bits: two defined states 0 or 1; are resistant to interference; can be independently copied. qBits: arbitrary superposition vectors (∣0⟩,∣1⟩); can be entangled; are very prone to interference; and cannot be copied due to the No-Cloning Theorem.
3
Question
Heisenberg Uncertainty Principle
Page 1
Answer
It is impossible to determine position (x) and momentum (p), with arbitrary precision simultaneously. Formula: Δx⋅Δp≥ℏ/2.
4
Question
The Concept of Measurement
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Answer
a quantum mechanical operation that determines the instantaneous value of a physical quantity, yielding a real result (observable). Before Measurement: The system's state is not fixed and can exist in a superposition of basis states. After Measurement: The wave function collapses; the system is forced into one definite basis state, and superposition is destroyed.
5
Question
Decoherence
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Answer
The collapse of superposition caused by interaction with the environment (noise), limiting the time available to run quantum algorithms.
6
Question
Types of memory in classical computers
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Answer
SRAM, DRAM, Flash/SSD, HDD
7
Question
Von Neumann Architecture
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Answer
separation of the logic unit (ALU) and the memory.
8
Question
Neumann Memory Wall
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Answer
information must be transported from the memory to the ALU for the minimum energy performance
9
Question
Anwendungen von QC
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Answer
random generators, search aögorithms, secure encryption
10
Question
Wave Functions and Probability Densities in a 1D Potential Well
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Answer
Wave Functions and Probability Densities in a 1D Potential Well
11
Question
Proximity effect
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Answer
when a superconductor and a normal conductor come in contact, cooper pairs can enter the normal conductor up until a characteristic length, creation of Josephson junctions
12
Question
Niobium (Nb)
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Answer
high critical temperature T = 9.3K, providing a noise-reducing energy gap. As a Type II superconductor with high magnetic field resistance, it easily forms sub-100 nm qubit circuits.
13
Question
Bandgap increase for T → 0K
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Answer
At low temperatures, the band gap in semiconductors increases due to a decrease of interatomic distances. The Sub Threshold Slope decreases, it saturates and does not go any lower. The classic Boltzmann theory can no longer be applied.
14
Question
Theoretical Simultaneous Determination of Position and Momentum
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Answer
Theoretical Example: One could try creating an independent but identical copy of a quantum system, measuring position on the first copy and momentum on the second. Why it's impossible: The No-Cloning Theorem proves that it is impossible to create an independent, identical copy of an arbitrary unknown quantum state.
15
Question
Density of States in 2D Space
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Answer
Volume of a state (VEZ): (2π/L)^2. Total volume of all states (V(k)): πk^2. Number of States (N(k)) 2⋅ V(k) /VEZ = k^2L^2/2π
16
Question
No-Cloning Theorem
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Answer
it is impossible to create an independent, identical copy of an unknown quantum state, because measurement/copying changes the original state.
17
Question
DiVincenzo Criteria
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Answer
The system must be scalable, qBits must be initializable to a defined basis state, Long coherence, Availability of a universal set of quantum gates (CNOT, Hadamard, etc.), a reliable measurement method must exist.
18
Question
Mobility (log μ)
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Answer
is highest in between (a peak), because impurity scattering dominates at low T and phonon scattering dominates at high T — the curve rises then falls, forming a mountain shape.
19
Question
Meissner–Ochsenfeld Effect
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Answer
Below a specific critical temperature, all electric and magnetic fields are expelled from the interior of the material
20
Question
Superconductors (Fields and Resistance)
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Answer
Fields: There are no electric or magnetic fields inside a superconductor due to the Meißner-Ochsenfeld Effect. Resistance: Below the critical temperature, electrons form Cooper pairs. These pairs behave like bosons in a collective ground state and cannot be scattered by the lattice, leading to zero electrical resistance
21
Question
Superconductors: Type I
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Answer
These are ideal diamagnets where the magnetic flux density inside is zero. Superconductivity is destroyed immediately once a critical temperature, field strength, or current density is exceeded.
22
Question
Superconductors: Type II
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Answer
These are not ideal diamagnets. Magnetic flux is only zero up to a first critical field strength (Hc,1); above this, flux penetrates the material in the form of vortices without destroying superconductivity until a second critical field strength (Hc,2) is reached
23
Question
Electron Interaction Interpretation
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Answer
The interaction between the two electrons is interpreted as a collision mediated by a phonon (lattice deformation). What must apply: The conservation of momentum must be fulfilled (K=k1+k2=k1′+k2′). Formation is most favored when the total momentum K=0.
24
Question
Layer Thickness and Superconductivity
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Answer
Many materials lose their ability to superconduct if the layer becomes too thin (low dimensions). Example: Niobium (Nb) progressively loses its superconducting properties at thicknesses below 80 nm.
25
Question
Unitary Matrix Definition
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Answer
A matrix A is unitary if the product of the matrix and its adjoint (Hermitian transpose A†) results in the identity matrix (A†⋅A=I). This implies that the adjoint matrix is equal to the inverse of the matrix (A†=A^−1), meaning the operation is reversible
26
Question
CNOT
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Answer
CNOT is the unitary equivalent to XOR. Is the first bit a 1, the second bit will be negated. Is the first bit 0, the second one will stay unchanged. → CNOT is used to entangle two qBits
27
Question
Mathematical Representation
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Answer
|x, y⟩ ↦ |x, x ⊕ y⟩, where ⊕ is the XOR (addition modulo 2) operation
28
Question
CNOT on a superposition
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Answer
CNOT 1/√2 (|00⟩ + |10⟩) = 1/√2 (|00⟩ + |11⟩)
29
Question
Identity I
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Answer
Leaves the state unchanged
30
Question
Projector P0
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Answer
Keeps only the |0⟩ component, projects out |1⟩