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📊 Organizing Quantum Memory

Understanding how quantum computers organize and manage qubits in registers

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🎯 What is a Quantum Register?

A quantum register is a collection of qubits organized to work together as a computational unit. Just as classical computers use registers to store binary data, quantum computers use quantum registers to maintain quantum states across multiple qubits.

⚡ Exponential Scaling

An n-qubit register can represent 2ⁿ computational basis states simultaneously through superposition. A 3-qubit register holds 8 states (|000⟩ to |111⟩), while a classical 3-bit register holds only one.

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State Representation

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Entanglement

Qubits in a register can become entangled, creating correlations impossible classically

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Qubit Addressing

Individual qubits are indexed (q₀, q₁, ..., qₙ₋₁) for targeted operations

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Information Density

A 50-qubit register requires 18 petabytes to simulate classically

📝 Register Notation

|000⟩All qubits in |0⟩ state (ground state)

|101⟩Mixed computational basis state

|ψ⟩ = Σ αᵢ|i⟩General superposition of all basis states

|Φ⁺⟩ = (|00⟩+|11⟩)/√2Bell state (maximally entangled)

💡 Key Insight

The exponential scaling of quantum registers is fundamental to quantum computational advantage. While a classical register grows linearly, quantum registers grow exponentially in their information capacity.