Qubits Under Pressure: A Research-Level Quiz

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1. Frag 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

2. Frag 2

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

   • QMA
   • BQP
   • PostBQP
   • QIP

3. Frag 3

   What are the parameters of the Steane code?

   • [[15,1,3]]
   • [[9,1,3]]
   • [[7,1,3]]
   • [[4,2,2]]

4. Frag 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)

5. Frag 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%

6. Frag 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

7. Frag 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

8. Frag 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

9. Frag 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

10. Frag 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