Qubits Under Pressure: A Research-Level Quiz

Which gate set is universal for quantum computation?

Clifford gates plus the T gate

Pauli gates plus the phase gate S

Pauli gates plus Hadamard

CNOT plus all Pauli gates

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That's right!

Right! Adding the non-Clifford T gate to the Clifford group gives a dense set of unitaries, making Clifford+T universal.

Not quite!

The answer is Clifford gates plus T. Clifford circuits alone can be simulated efficiently on a classical computer (Gottesman–Knill), so a non-Clifford gate is needed.

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Which complexity class is defined by bounded-error polynomial-time quantum computation?

QMA

BQP

PostBQP

QIP

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That's right!

Correct! BQP contains problems a quantum computer solves in polynomial time with error at most 1/3.

Not quite!

It's BQP. QMA is the quantum analogue of NP with a quantum witness, PostBQP equals PP, and QIP equals PSPACE.

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What are the parameters of the Steane code?

[[15,1,3]]

[[9,1,3]]

[[7,1,3]]

[[4,2,2]]

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That's right!

Yes! The Steane code encodes 1 logical qubit in 7 physical qubits with distance 3, built from the classical Hamming code.

Not quite!

The Steane code is [[7,1,3]], a CSS code from the [7,4,3] Hamming code. [[5,1,3]] is the perfect code and [[9,1,3]] is Shor's code.

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Scratch the card to reveal a fact about quantum computing

Richard Feynman proposed in 1981 that simulating quantum physics efficiently might require a computer that is itself quantum.

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What query complexity does Grover's algorithm achieve for unstructured search over N items?

O(log N)

O(N/2)

O(N^(1/3))

O(√N)

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That's right!

Correct! Grover uses O(√N) queries, and the BBBV lower bound shows this is optimal.

Not quite!

It's O(√N), a quadratic speedup that is provably optimal. N^(1/3) arises for the collision problem, not search.

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In the surface code, what kind of error-correction threshold is often quoted under circuit-level depolarizing noise?

About 1%

About 0.001%

About 10%

About 25%

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That's right!

Right! The surface code tolerates physical error rates near 1% under circuit-level noise, which is why it dominates hardware roadmaps.

Not quite!

It's about 1%. Higher values like ~10% apply only to idealised code-capacity noise with perfect measurements.

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Flip the card to reveal a fact about quantum computing

Estimates suggest breaking 2048-bit RSA would need around 20 million noisy physical qubits running for roughly eight hours.

Did you know?

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The Gottesman–Knill theorem states that which circuits can be efficiently classically simulated?

Circuits of matchgates only

Stabilizer circuits

Circuits with low T-count

Circuits of depth one

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That's right!

Correct! Stabilizer preparation, Clifford gates and Pauli measurements can be tracked in polynomial time with the stabilizer formalism.

Not quite!

It's stabilizer circuits. Matchgates are also classically simulable, but by a different result (Valiant, Terhal–DiVincenzo).

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What subroutine gives Shor's algorithm its exponential speedup?

Amplitude amplification

Quantum walk on a graph

Quantum Fourier transform for period finding

Adiabatic evolution to a ground state

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That's right!

Yes! Phase estimation with the QFT finds the period of modular exponentiation, which reveals the factors.

Not quite!

It's the QFT for period finding. Amplitude amplification gives only quadratic speedups, as in Grover's algorithm.

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Which result says no fault-tolerant code has a transversal universal gate set?

Solovay–Kitaev theorem

No-cloning theorem

Threshold theorem

Eastin–Knill theorem

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That's right!

Correct! Eastin–Knill forces tricks like magic state distillation or code switching to reach universality.

Not quite!

It's the Eastin–Knill theorem. Solovay–Kitaev concerns efficient gate approximation, and the threshold theorem concerns scalable error correction.

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Drag the slider to reveal a fact about quantum computing

How cold is a superconducting qubit?

Dilution refrigerators keep superconducting qubits near 10 millikelvin, colder than the cosmic microwave background of outer space.

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Why is the transmon less sensitive to charge noise than the Cooper-pair box?

A large E_J/E_C ratio flattens its energy bands

It uses no Josephson junction at all

Its qubit states are spatially separated

It operates far above the gap frequency

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That's right!

Right! Shunting with a large capacitor raises E_J/E_C, making charge dispersion fall exponentially while anharmonicity drops only slowly.

Not quite!

The large E_J/E_C ratio flattens the bands in offset charge, suppressing charge noise exponentially at the cost of some anharmonicity.

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What does the Solovay–Kitaev theorem guarantee for approximating a single-qubit unitary to precision ε?

Exactly ε^(−1) gates from any set

O(log^c(1/ε)) gates from a dense set

Constant-depth circuits for every ε

O(1/ε²) gates from Clifford gates

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That's right!

Correct! Any dense, inverse-closed gate set approximates a unitary with only polylogarithmic overhead, with c around 3–4.

Not quite!

It's O(log^c(1/ε)) gates from a dense, inverse-closed set, so discretising gates costs only polylogarithmic overhead.

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Perfect! Every answer right!

10 of 10 right

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Question 1:
Which gate set is universal for quantum computation?
Clifford gates plus the T gate
Pauli gates plus the phase gate S
Pauli gates plus Hadamard
CNOT plus all Pauli gates
Right! Adding the non-Clifford T gate to the Clifford group gives a dense set of unitaries, making Clifford+T universal.
The answer is Clifford gates plus T. Clifford circuits alone can be simulated efficiently on a classical computer (Gottesman–Knill), so a non-Clifford gate is needed.
Question 2:
Which complexity class is defined by bounded-error polynomial-time quantum computation?
QMA
BQP
PostBQP
QIP
Correct! BQP contains problems a quantum computer solves in polynomial time with error at most 1/3.
It's BQP. QMA is the quantum analogue of NP with a quantum witness, PostBQP equals PP, and QIP equals PSPACE.
Question 3:
What are the parameters of the Steane code?
[[15,1,3]]
[[9,1,3]]
[[7,1,3]]
[[4,2,2]]
Yes! The Steane code encodes 1 logical qubit in 7 physical qubits with distance 3, built from the classical Hamming code.
The Steane code is [[7,1,3]], a CSS code from the [7,4,3] Hamming code. [[5,1,3]] is the perfect code and [[9,1,3]] is Shor's code.
Question 4:
What query complexity does Grover's algorithm achieve for unstructured search over N items?
O(log N)
O(N/2)
O(N^(1/3))
O(√N)
Correct! Grover uses O(√N) queries, and the BBBV lower bound shows this is optimal.
It's O(√N), a quadratic speedup that is provably optimal. N^(1/3) arises for the collision problem, not search.
Question 5:
In the surface code, what kind of error-correction threshold is often quoted under circuit-level depolarizing noise?
About 1%
About 0.001%
About 10%
About 25%
Right! The surface code tolerates physical error rates near 1% under circuit-level noise, which is why it dominates hardware roadmaps.
It's about 1%. Higher values like ~10% apply only to idealised code-capacity noise with perfect measurements.
Question 6:
The Gottesman–Knill theorem states that which circuits can be efficiently classically simulated?
Circuits of matchgates only
Stabilizer circuits
Circuits with low T-count
Circuits of depth one
Correct! Stabilizer preparation, Clifford gates and Pauli measurements can be tracked in polynomial time with the stabilizer formalism.
It's stabilizer circuits. Matchgates are also classically simulable, but by a different result (Valiant, Terhal–DiVincenzo).
Question 7:
What subroutine gives Shor's algorithm its exponential speedup?
Amplitude amplification
Quantum walk on a graph
Quantum Fourier transform for period finding
Adiabatic evolution to a ground state
Yes! Phase estimation with the QFT finds the period of modular exponentiation, which reveals the factors.
It's the QFT for period finding. Amplitude amplification gives only quadratic speedups, as in Grover's algorithm.
Question 8:
Which result says no fault-tolerant code has a transversal universal gate set?
Solovay–Kitaev theorem
No-cloning theorem
Threshold theorem
Eastin–Knill theorem
Correct! Eastin–Knill forces tricks like magic state distillation or code switching to reach universality.
It's the Eastin–Knill theorem. Solovay–Kitaev concerns efficient gate approximation, and the threshold theorem concerns scalable error correction.
Question 9:
Why is the transmon less sensitive to charge noise than the Cooper-pair box?
A large E_J/E_C ratio flattens its energy bands
It uses no Josephson junction at all
Its qubit states are spatially separated
It operates far above the gap frequency
Right! Shunting with a large capacitor raises E_J/E_C, making charge dispersion fall exponentially while anharmonicity drops only slowly.
The large E_J/E_C ratio flattens the bands in offset charge, suppressing charge noise exponentially at the cost of some anharmonicity.
Question 10:
What does the Solovay–Kitaev theorem guarantee for approximating a single-qubit unitary to precision ε?
Exactly ε^(−1) gates from any set
O(log^c(1/ε)) gates from a dense set
Constant-depth circuits for every ε
O(1/ε²) gates from Clifford gates
Correct! Any dense, inverse-closed gate set approximates a unitary with only polylogarithmic overhead, with c around 3–4.
It's O(log^c(1/ε)) gates from a dense, inverse-closed set, so discretising gates costs only polylogarithmic overhead.

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