Quantum Computing Exam #1
1. What is Moore's Law?
Moore's Law states that approximately every two years, the computing power,
specifically the number of transistors on an integrated circuit, doubles. Historically,
this increase in density has also been accompanied by a halving of prices since the
invention of these components.
2. What physical property may produce an end to Moore's Law and why?
Quantum tunneling is a physical property that may lead to the end of Moore's Law.
As transistors become increasingly smaller, the barriers separating their
components become so thin that electrons have a non-zero probability of passing
through these barriers even when they shouldn't have enough energy to do so. This
"tunneling" effect makes it impossible to precisely control the flow of electrons,
undermining the reliability of classical transistors and logic gates. We cannot know
the precise location of these electrons.
3. As computers become smaller, classical circuits with transistors, logic gates,
and Integrated Circuits face limitations. What do quantum computers use to
represent "bits" (actually called qubits)?
Quantum computers utilize subatomic particles such as atoms, electrons, photons,
and ions as their fundamental units of information, known as qubits. These qubits
leverage the intrinsic quantum mechanical properties of these particles, such as
their spin and energy states, to encode and process information.
4. Are there problems that classical computers can solve but quantum
computers cannot?
No, quantum computers are theoretically capable of solving any computational
problem that a classical computer can solve. In fact, for certain types of problems,
quantum computers offer the potential for significantly faster solutions.
5. Are there any problems that quantum computers can solve that classical
computers cannot? If not, what advantages do quantum computers have?
While classical computers can theoretically solve any problem a quantum
computer can, the critical difference lies in the time it takes to find a solution.
,Quantum computers excel at solving complex and currently intractable problems
for classical computers in a dramatically shorter, often exponentially lower, time
complexity. This opens up possibilities for tackling problems currently beyond the
reach of even the most powerful supercomputers.
6. What is quantum supremacy?
Quantum supremacy refers to the point at which a quantum computer can solve a
specific computational problem that no classical computer, even the most powerful
supercomputer, can solve within a reasonable timeframe (e.g., polynomial time). It
signifies a decisive advantage of quantum computers over classical computers for
certain classes of problems and is a key milestone in the development of quantum
computing technology. The race to achieve quantum supremacy has been a
prominent area of research, with entities like Google and IBM actively pursuing
this goal.
7. What does Shor's quantum algorithm do? What problem may this
produce?
Shor's algorithm is a quantum algorithm that can factor large numbers
exponentially faster than the best-known classical algorithms. This capability poses
a significant threat to current public-key cryptographic systems, such as RSA,
which rely on the computational difficulty of factoring large numbers for their
security. The development of practical quantum computers running Shor's
algorithm could potentially break many of the cryptographic codes used to secure
online communication and data.
8. What is Dirac's notation and what is it used for?
Dirac's notation, also known as bra-ket notation, is a standard notation used in
quantum mechanics to describe quantum states. A qubit, for example, can exist in a
definite state, represented as ∣0⟩ and ∣1⟩, analogous to the 0 and 1 of a classical bit.
Crucially, a qubit can also exist in a superposition, a combination of both states
simultaneously. Dirac's notation provides a concise and powerful way to represent
these quantum states and the mathematical operations performed on them.
9. What do we mean by "observation of quantum objects"?
"Observation of quantum objects," or quantum measurement, refers to the process
of extracting information about a quantum system. Unlike classical systems, the act
of measurement in quantum mechanics is not passive. It inevitably disturbs the
, quantum state of the system, causing it to "collapse" from a superposition of states
into a single, definite state corresponding to the measured value. This measurement
process can lead to a loss of other potential information that was encoded in the
superposition.
10. What are quantum coherence and decoherence?
Quantum coherence refers to the ability of a quantum system to maintain its
quantum mechanical properties, such as superposition and entanglement. It's the
"quantumness" of the system. Quantum decoherence is the process by which a
quantum system loses its coherence due to interaction with its surrounding
environment. Even slight changes in temperature or vibrations can cause the
delicate quantum states to become entangled with the environment, effectively
destroying the superposition and causing the system to behave more classically. If
a quantum system is not perfectly isolated, coherence is shared with the
environment and appears to be lost over time.
11. What are the three fundamental properties of quantum mechanics that
quantum computers use to store, represent, and perform operations on data
in such a way that they can compute exponentially faster than any classical
computer?
The three fundamental properties of quantum mechanics that underpin the power
of quantum computers are: Superposition, Entanglement, and Interference.
12. What is superposition?
Superposition is a fundamental principle of quantum mechanics that allows a
quantum system, such as a qubit, to exist in multiple states simultaneously. Instead
of being definitively 0 or 1 like a classical bit, a qubit in superposition can be a
combination of both ∣0⟩ and ∣1⟩ with certain probabilities. This allows quantum
computers to explore a vast number of possibilities concurrently.
13. What is entanglement?
Entanglement is a peculiar quantum mechanical phenomenon where two or more
quantum objects become linked together in such a way that their fates are
intertwined, regardless of the distance separating them. When a measurement is
performed on one entangled particle, the state of the other particle is
instantaneously determined, even if they are light-years apart. This strong
correlation is a powerful resource for quantum computation and communication.
1. What is Moore's Law?
Moore's Law states that approximately every two years, the computing power,
specifically the number of transistors on an integrated circuit, doubles. Historically,
this increase in density has also been accompanied by a halving of prices since the
invention of these components.
2. What physical property may produce an end to Moore's Law and why?
Quantum tunneling is a physical property that may lead to the end of Moore's Law.
As transistors become increasingly smaller, the barriers separating their
components become so thin that electrons have a non-zero probability of passing
through these barriers even when they shouldn't have enough energy to do so. This
"tunneling" effect makes it impossible to precisely control the flow of electrons,
undermining the reliability of classical transistors and logic gates. We cannot know
the precise location of these electrons.
3. As computers become smaller, classical circuits with transistors, logic gates,
and Integrated Circuits face limitations. What do quantum computers use to
represent "bits" (actually called qubits)?
Quantum computers utilize subatomic particles such as atoms, electrons, photons,
and ions as their fundamental units of information, known as qubits. These qubits
leverage the intrinsic quantum mechanical properties of these particles, such as
their spin and energy states, to encode and process information.
4. Are there problems that classical computers can solve but quantum
computers cannot?
No, quantum computers are theoretically capable of solving any computational
problem that a classical computer can solve. In fact, for certain types of problems,
quantum computers offer the potential for significantly faster solutions.
5. Are there any problems that quantum computers can solve that classical
computers cannot? If not, what advantages do quantum computers have?
While classical computers can theoretically solve any problem a quantum
computer can, the critical difference lies in the time it takes to find a solution.
,Quantum computers excel at solving complex and currently intractable problems
for classical computers in a dramatically shorter, often exponentially lower, time
complexity. This opens up possibilities for tackling problems currently beyond the
reach of even the most powerful supercomputers.
6. What is quantum supremacy?
Quantum supremacy refers to the point at which a quantum computer can solve a
specific computational problem that no classical computer, even the most powerful
supercomputer, can solve within a reasonable timeframe (e.g., polynomial time). It
signifies a decisive advantage of quantum computers over classical computers for
certain classes of problems and is a key milestone in the development of quantum
computing technology. The race to achieve quantum supremacy has been a
prominent area of research, with entities like Google and IBM actively pursuing
this goal.
7. What does Shor's quantum algorithm do? What problem may this
produce?
Shor's algorithm is a quantum algorithm that can factor large numbers
exponentially faster than the best-known classical algorithms. This capability poses
a significant threat to current public-key cryptographic systems, such as RSA,
which rely on the computational difficulty of factoring large numbers for their
security. The development of practical quantum computers running Shor's
algorithm could potentially break many of the cryptographic codes used to secure
online communication and data.
8. What is Dirac's notation and what is it used for?
Dirac's notation, also known as bra-ket notation, is a standard notation used in
quantum mechanics to describe quantum states. A qubit, for example, can exist in a
definite state, represented as ∣0⟩ and ∣1⟩, analogous to the 0 and 1 of a classical bit.
Crucially, a qubit can also exist in a superposition, a combination of both states
simultaneously. Dirac's notation provides a concise and powerful way to represent
these quantum states and the mathematical operations performed on them.
9. What do we mean by "observation of quantum objects"?
"Observation of quantum objects," or quantum measurement, refers to the process
of extracting information about a quantum system. Unlike classical systems, the act
of measurement in quantum mechanics is not passive. It inevitably disturbs the
, quantum state of the system, causing it to "collapse" from a superposition of states
into a single, definite state corresponding to the measured value. This measurement
process can lead to a loss of other potential information that was encoded in the
superposition.
10. What are quantum coherence and decoherence?
Quantum coherence refers to the ability of a quantum system to maintain its
quantum mechanical properties, such as superposition and entanglement. It's the
"quantumness" of the system. Quantum decoherence is the process by which a
quantum system loses its coherence due to interaction with its surrounding
environment. Even slight changes in temperature or vibrations can cause the
delicate quantum states to become entangled with the environment, effectively
destroying the superposition and causing the system to behave more classically. If
a quantum system is not perfectly isolated, coherence is shared with the
environment and appears to be lost over time.
11. What are the three fundamental properties of quantum mechanics that
quantum computers use to store, represent, and perform operations on data
in such a way that they can compute exponentially faster than any classical
computer?
The three fundamental properties of quantum mechanics that underpin the power
of quantum computers are: Superposition, Entanglement, and Interference.
12. What is superposition?
Superposition is a fundamental principle of quantum mechanics that allows a
quantum system, such as a qubit, to exist in multiple states simultaneously. Instead
of being definitively 0 or 1 like a classical bit, a qubit in superposition can be a
combination of both ∣0⟩ and ∣1⟩ with certain probabilities. This allows quantum
computers to explore a vast number of possibilities concurrently.
13. What is entanglement?
Entanglement is a peculiar quantum mechanical phenomenon where two or more
quantum objects become linked together in such a way that their fates are
intertwined, regardless of the distance separating them. When a measurement is
performed on one entangled particle, the state of the other particle is
instantaneously determined, even if they are light-years apart. This strong
correlation is a powerful resource for quantum computation and communication.
