Quantum computing hardware basics: Question bank — Hardware deep dive

This page attacks the parent topic from the side: not "compute this" but "why is this statement true or false". Prerequisites worth reopening: Classical Bits vs Qubits, Bloch Sphere, Superposition and Entanglement, Unitary Operators and Reversible Computing, Boltzmann Distribution.

True or false — justify

A qubit in superposition is secretly already 0 or 1, we just don't know which

False — that is a hidden-variable picture. Interference experiments (paths cancelling) prove the qubit has no pre-decided value; the amplitude, not our ignorance, is physical. See Superposition and Entanglement.

Global phase

e^{iγ}

∣ ψ ⟩

changes what you measure

False — measurement depends only on

∣ α ∣^{2}, ∣ β ∣^{2}

, which are unchanged by a global phase; that is exactly why the Bloch Sphere has one fewer parameter.

Relative phase

ϕ

between

∣0 ⟩

and

∣1 ⟩

is also unobservable

False — relative phase moves the point around the Bloch equator and is detectable after a rotating gate (e.g. Hadamard-measure), which is why interference works at all.

T_{2}

can safely exceed

2 T_{1}

with good engineering

False — the derivation

\frac{1}{T _{2}} = \frac{1}{2 T _{1}} + \frac{1}{T _{ϕ}}

forces

T_{2} \leq 2 T_{1}

because relaxation itself scrambles phase; no engineering escapes the inequality.

Adding more physical qubits always increases usable computing power

False — noisy qubits below the error threshold make things worse; power depends on fidelity and the ratio

T_{2} / t_{g}

, not raw count. See Quantum Error Correction.

A quantum gate is reversible

True — gates are unitary, and

U^{†} U = I

means every

U

has an inverse

U^{†}

; the map can always be undone. See Unitary Operators and Reversible Computing.

Measurement is a unitary operation

False — measurement collapses the state and destroys probability amplitude information; it is the one non-unitary, irreversible step in the whole pipeline.

Cooling a qubit is just to reduce electrical resistance

False — the deep reason is

P_{1} / P_{0} = e^{- Δ E / k_{B} T}

: warmth thermally excites the qubit out of

∣0 ⟩

, breaking initialization (DiVincenzo criterion 2). See Boltzmann Distribution.

Two orthogonal qubit states point in opposite directions in real 3D space

True on the Bloch sphere —

∣0 ⟩

and

∣1 ⟩

sit at opposite poles (

180°

apart) even though they are orthogonal (

90°

) in Hilbert space; the factor

θ /2

is what maps the two pictures.

Entanglement lets you send information faster than light

False — measurement outcomes are locally random; correlations only appear when classical results are compared, and that comparison travels at

\leq c

. See Superposition and Entanglement.

Spot the error

n

qubits store

2^{n}

classical bits of readable information."

The error is readable. There are

2^{n}

complex amplitudes for computation, but measuring

n

qubits yields only

n

classical bits; the advantage is interference, not storage.

"A transmon uses a Josephson junction to make the two levels equally spaced so lasers can address them."

Backwards — the Josephson Junction provides anharmonicity (unequal spacing) so a pulse tuned to the

0 \to 1

gap does not also drive

1 \to 2

; and transmons use microwaves, not lasers.

"Error per gate

\approx t_{g} / T_{2}

, so a longer gate is always better because it's gentler."

Longer

t_{g}

raises

t_{g} / T_{2}

, giving more decoherence error per gate; gate time should be short relative to

T_{2}

, the opposite conclusion.

"Because probabilities are always positive, wrong answers can cancel out."

Probabilities cannot cancel — that is precisely why we need complex amplitudes, where

+ \frac{1}{2}

and

- \frac{1}{2}

sum to zero.

"The Hadamard gate measures the qubit into a random state."

A Hadamard is unitary and reversible — it creates a definite superposition

\frac{∣0 ⟩ + ∣1 ⟩}{2}

; nothing is measured or randomized until an actual readout.

"Dispersive readout works by absorbing the qubit's energy to see it."

No — it senses a frequency shift of a coupled resonator that depends on the qubit state, so it can (mostly) read

∣0 ⟩

∣1 ⟩

without directly draining the qubit.

"1000 physical qubits means 1000 logical qubits."

With current error rates, roughly ~1000 physical qubits may encode just one logical qubit via Quantum Error Correction; physical and logical counts differ by orders of magnitude.

Why questions

Why must gate operations be unitary and not any invertible matrix?

Only unitary maps preserve the norm

∣ α ∣^{2} + ∣ β ∣^{2} = 1

; a general invertible matrix would let total probability drift, which is physically forbidden. See Unitary Operators and Reversible Computing.

Why do independent decoherence rates add rather than multiply?

Independent decays each give an exponential factor, and

e^{- t / T_{1}} \cdot e^{- t / T_{ϕ}} = e^{- t (1/ T_{1} + 1/ T_{ϕ})}

; multiplying the survivals means adding the rates.

Why does relaxation (

T_{1}

) contribute only

\frac{1}{2 T _{1}}

to dephasing, not

\frac{1}{T _{1}}

Coherence lives in the off-diagonal density-matrix element, which scales with the amplitude not the population; amplitude decays at half the population rate, giving the factor

\frac{1}{2}

Why write the state with

cos \frac{θ}{2}

instead of

cos θ

θ \in [0, π]

sweeps the whole Bloch Sphere from north pole (

∣0 ⟩

) to south pole (

∣1 ⟩

), placing orthogonal states at opposite poles.

Why is

T_{2} / t_{g}

a better figure of merit than

T_{2}

alone?

It counts how many gates you can run before coherence dies; a long

T_{2}

with slow gates may allow fewer operations than a shorter

T_{2}

with fast gates.

Why can't we just clone a qubit to make measurement easier?

The no-cloning theorem forbids copying an unknown quantum state — a consequence of linearity/unitarity — so you cannot make backup copies to read repeatedly.

Why does entanglement matter for computation and not just correlation?

It lets the amplitudes of many qubits interfere jointly so wrong answers cancel across the whole register; product (unentangled) states cannot produce that global interference.

Edge cases

At exactly

θ = 0

, what does the phase

ϕ

do?

Nothing observable — at the north pole

sin \frac{θ}{2} = 0

, so

∣ ψ ⟩ = ∣0 ⟩

regardless of

ϕ

; the poles are the coordinate singularities of the Bloch Sphere.

T \to 0

, what happens to

P_{1} / P_{0} = e^{- Δ E / k_{B} T}

\to 0

, so the qubit is perfectly initialized in

∣0 ⟩

; this is the ideal limit that finite cold dilution fridges only approximate.

T \to \infty

(or room temperature), what is

P_{1} / P_{0}

\to 1

— both levels equally populated, the qubit fully scrambled and useless, which is why room-temperature operation fails for GHz-scale gaps.

T_{ϕ} \to \infty

(no pure dephasing), what is

T_{2}

Then

\frac{1}{T _{2}} = \frac{1}{2 T _{1}}

, so

T_{2} = 2 T_{1}

— the best possible coherence, limited purely by relaxation.

What is the state right after measurement of

α ∣0 ⟩ + β ∣1 ⟩

gives outcome 0?

It collapses to exactly

∣0 ⟩

; the superposition and all phase information are gone, so re-measuring always yields 0.

For a classical bit, how many real parameters describe its state, versus a qubit?

A classical bit has one discrete parameter (0 or 1); a pure qubit has two continuous real parameters

(θ, ϕ)

— the source of, but not directly the payoff of, quantum power. See Classical Bits vs Qubits.

If a gate takes longer than

T_{2}

, is the computation salvageable?

No — coherence has decayed past

1/ e

before the gate even finishes, so its output carries essentially random phase; gates must satisfy

t_{g} ≪ T_{2}

Recall One-line self-test

Cover every answer above, run the list top to bottom, and for each say your verdict and its reason aloud. Any item where the reason wobbles is your next study target — most of them trace back to just four facts: amplitudes (not probabilities) interfere, global phase is invisible, $T_{2} \leq 2 T_{1}$ , and $P_{1} / P_{0} = e^{- Δ E / k_{B} T}$ .