Quantum computing hardware basics: Question bank — Hinglish deep dive

6.5.13 · D5 · Hardware › Advanced & Emerging Architectures › Quantum computing hardware basics

Yeh page parent topic ko side se attack karta hai: yeh nahi ki "compute karo" balki "yeh statement true ya false kyun hai". Kholne layak prerequisites: Classical Bits vs Qubits, Bloch Sphere, Superposition and Entanglement, Unitary Operators and Reversible Computing, Boltzmann Distribution.

True or false — justify

Superposition mein ek qubit secretly pehle se hi 0 ya 1 hota hai, bas humein pata nahi hota

False — yeh ek hidden-variable picture hai. Interference experiments (paths ka cancel hona) prove karte hain ki qubit ki koi pre-decided value nahi hoti; amplitude, hamari ignorance nahi, physical hai. Dekho Superposition and Entanglement.

∣ ψ ⟩

par global phase

e^{iγ}

measure kiya hua result change kar deta hai

False — measurement sirf

∣ α ∣^{2}, ∣ β ∣^{2}

par depend karta hai, jo global phase se change nahi hote; exactly isliye Bloch Sphere mein ek parameter kam hota hai.

∣0 ⟩

aur

∣1 ⟩

ke beech relative phase

ϕ

bhi unobservable hota hai

False — relative phase Bloch equator ke around point ko move karta hai aur ek rotating gate ke baad detectable hota hai (jaise Hadamard-measure), isliye interference kaam karta hai.

Acchi engineering se

T_{2}

safely

2 T_{1}

se zyada ho sakta hai

False — derivation

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

yeh force karta hai ki

T_{2} \leq 2 T_{1}

, kyunki relaxation khud phase scramble karta hai; koi bhi engineering is inequality se nahi bach sakti.

Zyada physical qubits add karna hamesha usable computing power badhata hai

False — error threshold se neeche noisy qubits cheezein badtар banate hain; power fidelity aur

T_{2} / t_{g}

ke ratio par depend karti hai, raw count par nahi. Dekho Quantum Error Correction.

Ek quantum gate reversible hota hai

True — gates unitary hote hain, aur

U^{†} U = I

ka matlab hai har

U

ka inverse

U^{†}

hota hai; map hamesha undo kiya ja sakta hai. Dekho Unitary Operators and Reversible Computing.

Measurement ek unitary operation hai

False — measurement state ko collapse karta hai aur probability amplitude information destroy karta hai; yeh poori pipeline mein ek maatra non-unitary, irreversible step hai.

Qubit ko cool karna sirf electrical resistance kam karne ke liye hai

False — deep reason yeh hai ki

P_{1} / P_{0} = e^{- Δ E / k_{B} T}

: warmth qubit ko

∣0 ⟩

se thermally excite kar deti hai, initialization tod deti hai (DiVincenzo criterion 2). Dekho Boltzmann Distribution.

Do orthogonal qubit states real 3D space mein opposite directions mein point karte hain

True Bloch sphere par —

∣0 ⟩

aur

∣1 ⟩

opposite poles par baithe hain (

180°

apart) chahe Hilbert space mein woh orthogonal (

90°

) hain; factor

θ /2

hi dono pictures ko map karta hai.

Entanglement se tum light se tez information bhej sakte ho

False — measurement outcomes locally random hote hain; correlations tabhi dikhte hain jab classical results compare hote hain, aur woh comparison

\leq c

par travel karta hai. Dekho Superposition and Entanglement.

Spot the error

n

qubits

2^{n}

classical bits of readable information store karte hain."

Error readable mein hai. Computation ke liye

2^{n}

complex amplitudes hote hain, lekin

n

qubits measure karne se sirf

n

classical bits milte hain; faida interference hai, storage nahi.

"Ek transmon Josephson junction use karta hai do levels ko equally spaced banane ke liye taaki lasers unhe address kar sakein."

Yeh ulta hai — Josephson Junction anharmonicity (unequal spacing) provide karta hai taaki

0 \to 1

gap pe tune kiya pulse

1 \to 2

bhi drive na kare; aur transmons microwaves use karte hain, lasers nahi.

"Error per gate

\approx t_{g} / T_{2}

, toh zyada lamba gate hamesha better hai kyunki woh gentle hota hai."

Lamba

t_{g}

matlab

t_{g} / T_{2}

badh jaata hai, giving zyada decoherence error per gate; gate time

T_{2}

ke relatively short honi chahiye, opposite conclusion.

"Kyunki probabilities hamesha positive hoti hain, galat answers cancel out ho sakte hain."

Probabilities cancel nahi ho sakti — exactly isliye hume complex amplitudes chahiye, jahan

+ \frac{1}{2}

aur

- \frac{1}{2}

sum karke zero ho jaate hain.

"Hadamard gate qubit ko ek random state mein measure karta hai."

Hadamard unitary aur reversible hai — yeh ek definite superposition

\frac{∣0 ⟩ + ∣1 ⟩}{2}

create karta hai; kuch bhi measure ya randomize nahi hota jab tak actual readout na ho.

"Dispersive readout qubit ki energy absorb karke use dekhne se kaam karta hai."

Nahi — yeh ek coupled resonator ki frequency shift sense karta hai jo qubit state par depend karta hai, isliye yeh qubit ko directly drain kiye bina (mostly)

∣0 ⟩

∣1 ⟩

read kar sakta hai.

"1000 physical qubits matlab 1000 logical qubits."

Current error rates ke saath, roughly ~1000 physical qubits sirf ek logical qubit encode kar sakte hain via Quantum Error Correction; physical aur logical counts orders of magnitude se differ karte hain.

Why questions

Gate operations unitary kyun hone chahiye, koi bhi invertible matrix kyun nahi?

Sirf unitary maps norm

∣ α ∣^{2} + ∣ β ∣^{2} = 1

preserve karte hain; ek general invertible matrix total probability ko drift karne deta, jo physically forbidden hai. Dekho Unitary Operators and Reversible Computing.

Independent decoherence rates add kyun hote hain, multiply kyun nahi?

Independent decays har ek exponential factor dete hain, aur

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

; survivals multiply karne ka matlab rates add karna hai.

Relaxation (

T_{1}

) dephasing mein sirf

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

contribute kyun karta hai,

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

kyun nahi?

Coherence off-diagonal density-matrix element mein rehti hai, jo amplitude ke saath scale hoti hai population ke saath nahi; amplitude population rate ke aadhe par decay karta hai, isliye factor

\frac{1}{2}

aata hai.

State ko

cos θ

ki jagah

cos \frac{θ}{2}

se kyun likhte hain?

Taaki

θ \in [0, π]

poore Bloch Sphere ko north pole (

∣0 ⟩

) se south pole (

∣1 ⟩

) tak sweep kare, orthogonal states ko opposite poles par rakh sake.

T_{2}

akele se

T_{2} / t_{g}

ek better figure of merit kyun hai?

Yeh count karta hai ki coherence khatam hone se pehle kitne gates run ho sakte hain; ek lamba

T_{2}

slow gates ke saath, ek chhote

T_{2}

fast gates ke saath se kam operations allow kar sakta hai.

Hum measurement aasan karne ke liye qubit clone kyun nahi kar sakte?

No-cloning theorem ek unknown quantum state ko copy karna forbid karta hai — linearity/unitarity ka consequence — isliye tum baar baar padhne ke liye backup copies nahi bana sakte.

Entanglement computation ke liye kyun matter karta hai, sirf correlation ke liye nahi?

Yeh bahut saare qubits ke amplitudes ko jointly interfere karne deta hai taaki galat answers poore register mein cancel ho jaayein; product (unentangled) states woh global interference produce nahi kar sakti.

Edge cases

Exactly

θ = 0

par, phase

ϕ

kya karta hai?

Kuch bhi observable nahi — north pole par

sin \frac{θ}{2} = 0

, toh

∣ ψ ⟩ = ∣0 ⟩

regardless of

ϕ

; poles Bloch Sphere ke coordinate singularities hain.

Jab

T \to 0

P_{1} / P_{0} = e^{- Δ E / k_{B} T}

ka kya hota hai?

Yeh

\to 0

ho jaata hai, toh qubit perfectly

∣0 ⟩

mein initialized ho jaata hai; yeh ideal limit hai jo finite cold dilution fridges sirf approximate kar paati hain.

Jab

T \to \infty

(ya room temperature),

P_{1} / P_{0}

kya hoga?

Yeh

\to 1

ho jaata hai — dono levels equally populated, qubit fully scrambled aur useless, isliye GHz-scale gaps ke liye room-temperature operation fail karta hai.

Agar

T_{ϕ} \to \infty

(koi pure dephasing nahi), toh

T_{2}

kya hoga?

Phir

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

, toh

T_{2} = 2 T_{1}

— best possible coherence, purely relaxation se limited.

α ∣0 ⟩ + β ∣1 ⟩

ko measure karne ke baad agar outcome 0 aaye toh state kya hogi?

Yeh exactly

∣0 ⟩

mein collapse ho jaati hai; superposition aur saari phase information gone, toh dobara measure karne par hamesha 0 milega.

Ek classical bit ki state describe karne ke liye kitne real parameters chahiye, qubit ke liye kitne?

Ek classical bit mein ek discrete parameter hota hai (0 ya 1); ek pure qubit mein do continuous real parameters hote hain

(θ, ϕ)

— quantum power ka source hai, lekin directly payoff nahi. Dekho Classical Bits vs Qubits.

Agar ek gate

T_{2}

se zyada time leta hai, toh kya computation salvageable hai?

Nahi — coherence gate khatam hone se pehle

1/ e

past decay ho chuki hai, toh uska output essentially random phase carry karta hai; gates

t_{g} ≪ T_{2}

satisfy karni chahiye.

Recall Ek-line self-test

Upar saare answers cover karo, list top to bottom chalao, aur har ek ke liye apna verdict aur uska reason zor se bolo. Jis bhi item mein reason dabb jaaye woh tumhara agla study target hai — inme se zyatar sirf chaar facts par trace back hote hain: amplitudes (probabilities nahi) interfere karte hain, global phase invisible hai, $T_{2} \leq 2 T_{1}$ , aur $P_{1} / P_{0} = e^{- Δ E / k_{B} T}$ .