1
Imortant Questions and Answers
CP25C07-Quantum Computing
Syllabus
1. Physical properties and mathematical foundations
Double Slit Experiment; Light: Particle Vs Wave; Heisenberg Uncertainty Principle.
Vector spaces – basis; Inner product; Outer product; Tensor product; Linear operators.
2. Quantum computing postulates and gates
Review of postulates, Bloch sphere, Single qubit states and gates, superposition; Two
Qubit States and Gates - Bell States, Entanglement, CNOT gate, Phase oracles, Pauli
Gates.
3. Quantum computing circuits
Dirac’s notation for quantum computing, Computational Basis, Orthonormality, Hadamard
and Phase Gates- building quantum circuits.
4. Fundamental Quantum Algorithms
Deutsch–Josza Algorithm, Grover search algorithm: Problem definition, Amplitude
amplification, Grover oracle, diffuser, multiple solutions in the search space.
5. Programming on a real quantum computer
Coding a real time quantum computer via IBMQ to carry out basic quantum measurement
and state analysis.
S.No. Description
Unit-I
Physical properties and mathematical foundations
Basic Concepts
V.
U
m
ap
at
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Pr
of
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C
N
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es
, 2
Physical Properties and Mathematical Foundations
S. Basic Concept Definition and Equation (Plain Text)
No.
Light passing through two slits produces interference fringes.
1 Double-Slit Experiment
Fringe width: β = λD/d
2 Particle Nature of Light Light consists of photons. Photon energy: E = hν = hc/λ
3 Wave Nature of Light Light exhibits interference and diffraction. Wave equation: c = λν
Position and momentum uncertainties satisfy: Δx × Δp ≥ ℏ/2 =
4 Wave–Particle Duality Light exhibits both particle and wave properties.
Heisenberg Uncertainty
5
Principle h/(4π)
A set of vectors closed under vector addition and scalar
6 Vector Space
multiplication. Qubit: |ψ⟩ = α|0⟩ + β|1⟩
A linearly independent set of vectors spanning a vector space. Qubit
7 Basis
Produces a scalar from two vectors: ⟨φ|ψ⟩. Normalization: ⟨ψ|ψ⟩ =
basis:
8 Inner Product
1
Combines states of multiple systems: |ψ⟩ ⊗ |φ⟩. Example: |0⟩ ⊗ |1⟩
9 Outer Product Produces an operator or matrix: |ψ⟩⟨φ|
10 Tensor Product
= |01⟩
11 Linear Operator A transformation satisfying: A(a|ψ⟩ + b|φ⟩) = aA|ψ⟩ + bA|φ⟩
12 Qubit Normalization Total measurement probability equals one: |α|² + |β|² = 1
Important Symbols and Notations
Meaning
Symbol
λ Wavelength
ν Frequency
h Planck’s constant
c Speed of light in vacuum
D Distance from slits to screen
V.
d Separation between slits
U
m
Δx Uncertainty in position
ap
ℏ
Δp Uncertainty in momentum
at
h
Reduced Planck’s constant = h/(2π)
y,
⟨ψ|
|ψ⟩ Ket representing a quantum state
Pr
of
Bra representing the conjugate transpose of a ket
./E
C
N
ot
es
, 3
α, β Probability amplitudes
Multiple Choice QA
1. In the Double-Slit Experiment, the formation of interference fringes demonstrates the:
A) Particle nature of light only
B) Wave nature of light
C) Magnetic nature of light
D) Gravitational nature of light
Answer: B) Wave nature of light
Reason: The bright and dark interference fringes are produced by the constructive and destructive
interference of light waves.
2. Which statement correctly describes the wave-particle duality of light?
A) Light behaves only as a wave
B) Light behaves only as a particle
C) Light exhibits both wave and particle properties
D) Light has neither wave nor particle properties
Answer: C) Light exhibits both wave and particle properties
Reason: Light exhibits wave properties through interference and diffraction, and particle properties
through phenomena such as the photoelectric effect.
3. According to Heisenberg’s Uncertainty Principle, which quantities cannot be simultaneously
measured with arbitrary precision?
V.
A) Mass and energy
U
m
ap
B) Position and momentum
at
h
C) Temperature and pressure
y,
Pr
of
./E
C
N
ot
es
, 4
D) Speed and time
Answer: B) Position and momentum
Reason: The uncertainties in position and momentum satisfy
4. In a vector space, a basis is a set of vectors that:
A) Contains only zero vectors
B) Is always linearly dependent
C) Is linearly independent and spans the space
D) Contains infinitely many vectors in every case
Answer: C) Is linearly independent and spans the space
Reason: Every vector in the space can be expressed uniquely as a linear combination of the basis
vectors.
5. Which statement about the tensor product of two quantum states is correct?
A) It combines the states to describe a composite system
B) It always produces a scalar
V.
C) It is identical to the inner product
U
m
ap
D) It always gives the zero vector
at
hy,
Answer: A) It combines the states to describe a composite system
Pr
of
Reason: The tensor product combines individual state spaces to represent a joint system. For example,
./E
C
N
ot
es
Imortant Questions and Answers
CP25C07-Quantum Computing
Syllabus
1. Physical properties and mathematical foundations
Double Slit Experiment; Light: Particle Vs Wave; Heisenberg Uncertainty Principle.
Vector spaces – basis; Inner product; Outer product; Tensor product; Linear operators.
2. Quantum computing postulates and gates
Review of postulates, Bloch sphere, Single qubit states and gates, superposition; Two
Qubit States and Gates - Bell States, Entanglement, CNOT gate, Phase oracles, Pauli
Gates.
3. Quantum computing circuits
Dirac’s notation for quantum computing, Computational Basis, Orthonormality, Hadamard
and Phase Gates- building quantum circuits.
4. Fundamental Quantum Algorithms
Deutsch–Josza Algorithm, Grover search algorithm: Problem definition, Amplitude
amplification, Grover oracle, diffuser, multiple solutions in the search space.
5. Programming on a real quantum computer
Coding a real time quantum computer via IBMQ to carry out basic quantum measurement
and state analysis.
S.No. Description
Unit-I
Physical properties and mathematical foundations
Basic Concepts
V.
U
m
ap
at
hy,
Pr
of
./E
C
N
ot
es
, 2
Physical Properties and Mathematical Foundations
S. Basic Concept Definition and Equation (Plain Text)
No.
Light passing through two slits produces interference fringes.
1 Double-Slit Experiment
Fringe width: β = λD/d
2 Particle Nature of Light Light consists of photons. Photon energy: E = hν = hc/λ
3 Wave Nature of Light Light exhibits interference and diffraction. Wave equation: c = λν
Position and momentum uncertainties satisfy: Δx × Δp ≥ ℏ/2 =
4 Wave–Particle Duality Light exhibits both particle and wave properties.
Heisenberg Uncertainty
5
Principle h/(4π)
A set of vectors closed under vector addition and scalar
6 Vector Space
multiplication. Qubit: |ψ⟩ = α|0⟩ + β|1⟩
A linearly independent set of vectors spanning a vector space. Qubit
7 Basis
Produces a scalar from two vectors: ⟨φ|ψ⟩. Normalization: ⟨ψ|ψ⟩ =
basis:
8 Inner Product
1
Combines states of multiple systems: |ψ⟩ ⊗ |φ⟩. Example: |0⟩ ⊗ |1⟩
9 Outer Product Produces an operator or matrix: |ψ⟩⟨φ|
10 Tensor Product
= |01⟩
11 Linear Operator A transformation satisfying: A(a|ψ⟩ + b|φ⟩) = aA|ψ⟩ + bA|φ⟩
12 Qubit Normalization Total measurement probability equals one: |α|² + |β|² = 1
Important Symbols and Notations
Meaning
Symbol
λ Wavelength
ν Frequency
h Planck’s constant
c Speed of light in vacuum
D Distance from slits to screen
V.
d Separation between slits
U
m
Δx Uncertainty in position
ap
ℏ
Δp Uncertainty in momentum
at
h
Reduced Planck’s constant = h/(2π)
y,
⟨ψ|
|ψ⟩ Ket representing a quantum state
Pr
of
Bra representing the conjugate transpose of a ket
./E
C
N
ot
es
, 3
α, β Probability amplitudes
Multiple Choice QA
1. In the Double-Slit Experiment, the formation of interference fringes demonstrates the:
A) Particle nature of light only
B) Wave nature of light
C) Magnetic nature of light
D) Gravitational nature of light
Answer: B) Wave nature of light
Reason: The bright and dark interference fringes are produced by the constructive and destructive
interference of light waves.
2. Which statement correctly describes the wave-particle duality of light?
A) Light behaves only as a wave
B) Light behaves only as a particle
C) Light exhibits both wave and particle properties
D) Light has neither wave nor particle properties
Answer: C) Light exhibits both wave and particle properties
Reason: Light exhibits wave properties through interference and diffraction, and particle properties
through phenomena such as the photoelectric effect.
3. According to Heisenberg’s Uncertainty Principle, which quantities cannot be simultaneously
measured with arbitrary precision?
V.
A) Mass and energy
U
m
ap
B) Position and momentum
at
h
C) Temperature and pressure
y,
Pr
of
./E
C
N
ot
es
, 4
D) Speed and time
Answer: B) Position and momentum
Reason: The uncertainties in position and momentum satisfy
4. In a vector space, a basis is a set of vectors that:
A) Contains only zero vectors
B) Is always linearly dependent
C) Is linearly independent and spans the space
D) Contains infinitely many vectors in every case
Answer: C) Is linearly independent and spans the space
Reason: Every vector in the space can be expressed uniquely as a linear combination of the basis
vectors.
5. Which statement about the tensor product of two quantum states is correct?
A) It combines the states to describe a composite system
B) It always produces a scalar
V.
C) It is identical to the inner product
U
m
ap
D) It always gives the zero vector
at
hy,
Answer: A) It combines the states to describe a composite system
Pr
of
Reason: The tensor product combines individual state spaces to represent a joint system. For example,
./E
C
N
ot
es
