📉 Before we begin — why qubits die

A qubit is an extraordinarily fragile object. The superposition and entanglement that make it powerful also make it exquisitely sensitive to the environment. Every stray photon, every vibration, every fluctuating electromagnetic field can destroy the quantum state — a process called decoherence.

Decoherence happens in two ways. T1 relaxation: a qubit in |1⟩ spontaneously drops to |0⟩ by releasing a tiny amount of energy to the environment (like a drop of dye spreading in water). T2 dephasing: a qubit in superposition loses track of its phase — the arrow on the Bloch sphere drifts to a random position on the equator, then the equator itself shrinks to the centre.

These timescales — T1 and T2 — are the fundamental limits on every quantum computation. Every gate must complete within a tiny fraction of T2. Every circuit must finish before the qubits decohere. This is why error correction exists and why quantum hardware is so difficult.

🌀 The numbers that matter

Best superconducting T2 in 2024: ~500 µs. Single-qubit gate time: ~20 ns. This means you can fit about 500,000/20 = 25,000 gates before decoherence ruins the computation. Sounds like a lot — but a useful fault-tolerant quantum circuit might need millions of logical gates, each requiring hundreds of physical gates for error correction. The math is brutal.

📉 Decoherence · Session 5 · Q14

Decoherence Simulator

Watch qubits lose their quantum state in real time. Animate T1 relaxation and T2 dephasing on the Bloch sphere. See why temperature kills coherence — and why 15mK is the magic number.

📉 T1 Relaxation

🌀 T2 Dephasing

🌡️ Temperature

🔊 Noise Channels

🏆 Badge

📉

T1 — Relaxation

Qubit in |1⟩ spontaneously emits energy and drops to |0⟩. Exponential decay with time constant T1. Typically 100–500µs.

🌀

T2 — Dephasing

Phase of superposition randomises. Bloch sphere arrow spirals inward on the equator. T2 ≤ 2×T1 always. The binding constraint for circuit depth.

🌡️

Temperature kills qubits

Thermal photons at room temperature (300K) have enough energy to flip qubits constantly. 15mK suppresses thermal noise by a factor of 20,000.

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Noise channels

Bit-flip, phase-flip, depolarising, amplitude damping. Each models a specific physical mechanism. Error correction must handle all of them.

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Wizzy · Quantum Guide

T1 relaxation: a qubit in |1⟩ spontaneously flips to |0⟩ as it loses energy to the environment. Watch the Bloch sphere arrow decay from the south pole (|1⟩) toward the north pole (|0⟩). The probability of finding |1⟩ decays as e^(-t/T1). Press Start T1 to watch it happen.

T1 Relaxation — Energy Decay

Bloch Sphere (decaying)

P(|1⟩) over time

Press Start to watch the qubit in |1⟩ spontaneously decay to |0⟩. The curve follows P(|1⟩) = e^(-t/T1).

🌀

Wizzy · Quantum Guide

T2 dephasing destroys superposition without flipping the qubit. The phase of (|0⟩+|1⟩)/√2 randomly drifts — the Bloch sphere arrow spirals inward on the equator. After time T2, all phase information is lost. The qubit becomes a classical mixture — 50% |0⟩ or |1⟩ with no quantum coherence. Press Start T2.

T2 Dephasing — Phase Decay

Bloch Sphere (dephasing)

Coherence |⟨ψ|+⟩| over time

Press Start to watch superposition phase decay. The Bloch sphere arrow spirals inward — quantum coherence lost.

🌡️

Wizzy · Quantum Guide

Temperature is the enemy of coherence. At room temperature (300K), thermal photons have 20,000× more energy than at 15mK — enough to constantly flip qubits. Drag the temperature slider from 15mK upward and watch the coherence time plummet from hundreds of microseconds to nanoseconds.

Temperature vs Coherence Time

Temperature: 15 mK

Coherence time (T2)

~500 µs

Superconducting qubit — excellent quantum regime

At 15mK — the base temperature of superconducting quantum processors — coherence times reach hundreds of microseconds. Drag the slider upward and watch coherence time collapse dramatically.

🔊

Wizzy · Quantum Guide

Quantum noise is modelled as specific noise channels — quantum operations applied randomly with some probability. Adjust the sliders to see how each type of noise affects the qubit's Bloch sphere. Understanding noise channels is essential for designing error correction codes.

Noise Channels — Adjustable Probability

Bit-flip (X) channel

Randomly flips |0⟩↔|1⟩ with probability p

p = 0%

Phase-flip (Z) channel

Randomly applies Z gate — flips phase of superposition

p = 0%

Depolarising channel

Applies X, Y, or Z with equal prob p/3 — worst-case noise

p = 0%

Remaining coherence (Bloch vector length)

100%

Adjust the noise sliders to see how each channel shrinks the Bloch vector — reducing quantum coherence. Error correction (Q15) learns to counteract these effects.

📉

Wizzy · Quantum Guide

🎊 You now understand the physical challenge at the heart of quantum computing! Decoherence is the reason quantum computers need to be colder than outer space, why circuits must be short, and why error correction is not optional — it's the only path to large-scale quantum computation.

🧠 What you actually learned today

T1 relaxation: a qubit in |1⟩ spontaneously decays to |0⟩ with time constant T1 (~100–500µs for superconducting qubits). Limits how long you can store a qubit.
T2 dephasing: superposition phase randomises with time constant T2 ≤ 2T1. This is the binding constraint on circuit depth — all gates must complete within T2.
Temperature: at 300K, thermal energy destroys superposition in nanoseconds. At 15mK, thermal excitations become exponentially suppressed — coherence can last hundreds of microseconds.
Noise channels: bit-flip (X), phase-flip (Z), and depolarising noise each model different physical error mechanisms. Error correction codes target specific channels.
The key ratio: (T2) / (gate time) = maximum circuit depth before decoherence. Best superconducting: ~500µs / 20ns = 25,000 gates. Error correction extends this effectively.

📉

Decoherence Expert Badge!

You understand why quantum computers need to be colder than outer space!

Optional. Stays on this device only — not sent to WhizzStep.

📉 WhizzStep Quantum Lab

Activity completion card for

Student Name

has explored Quantum Decoherence — T1, T2, Temperature & Noise Channels

This records completion of a browser activity only. It is not an accredited certificate or proof of mastery.

Decoherence Expert

T1 & T2

Noise Channels

📖 Quantum Vocabulary

Decoherence KEY

The process by which a quantum system loses its quantum properties (superposition, entanglement) due to interaction with its environment. The central challenge in building quantum computers.

T1 time KEY

Energy relaxation time — how long a qubit in |1⟩ stays in |1⟩ before decaying to |0⟩. Follows P(|1⟩) = e^(-t/T1). Superconducting: 100–500µs.

T2 time KEY

Phase coherence time — how long superposition phase survives before randomising. Always T2 ≤ 2T1. The binding circuit depth limit.

Noise channel NEW

A mathematical model of an error — a quantum operation applied randomly with some probability. Types: bit-flip (X), phase-flip (Z), depolarising, amplitude damping.

NISQ

Noisy Intermediate-Scale Quantum — today's quantum computers. 50–4000 physical qubits, significant error rates, no full error correction. The era we're currently in.

Fault-tolerant QC

Quantum computation with full error correction — logical qubits encoded in many physical qubits, capable of arbitrary-length computation. Still years away from realisation.

Key Concepts from Q14

T1 vs T2

📉 Two ways to die

T1 kills the qubit's energy state. T2 kills the qubit's phase. T2 is always the tighter constraint — it's the wall every quantum circuit runs into first.

Temperature

🌡️ 15mK matters

The Boltzmann factor e^(-ℏω/kT) controls thermal excitation rate. Dropping from 300K to 15mK suppresses thermal noise by a factor of ~10 trillion — enabling coherence times a million times longer.

Circuit depth

📏 T2 / gate time

The ratio (T2) / (gate time) is the maximum number of gates before decoherence. Best 2024: ~500µs / 20ns ≈ 25,000. Error correction effectively multiplies this by 100–1000×.

Error correction

🛡️ The solution (Q15)

Error correction encodes logical qubits in many physical qubits, detecting and fixing errors faster than they accumulate. It's the only known path to fault-tolerant quantum computing.

About this lab

Q-14 Real-System Constraints Classes 8-12 15 min Applied

Learning objective: Explore how simplified noise models affect a qubit state. Cooling requirements vary by hardware platform.

What this simplifies: This is a local browser simulation, not access to real quantum hardware.

Privacy: No learner input leaves the device.

Teacher prompt: Ask the class why this simulation might mislead someone who takes it too literally.

Reflect: What is one thing this activity showed you that you did not expect?

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