Understanding quantum bit notation

Turns out it’s somewhat intuitive!

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Photo by Mark Garlick on Science Photo Library

Expressing 1 qubit

Expanded notation for 1 qubit

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Expanded notation. (Fig 1)
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Example #1. Note that the |φ₁‘phi one’ (left) is a variable representing the qubit. (Fig 2)
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Example #2. (Fig 3)
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(Fig 4)

Vector notation for 1 qubit

Definition of |0⟩ and |1⟩ in vector notation
Definition of |0⟩ and |1⟩ in vector notation
(Fig 5)
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(Fig 6)
Vector notation
Vector notation
Vector notation. (Fig 7)
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Example #3. This is the vector notation of Example #1. (Fig 8)
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Example #4. This is the vector notation of Example #2. (Fig 9)
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Example #4: |φ₄has a 100% chance of collapsing to |1 when measured, so it is |1. (Fig 10)
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Example #5. (Fig 11)
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Note, it just happens that (1)² = 100% and (0)² = 0%, so it seems the values weren’t squared. (Fig 12)

Expressing 2+ qubits

Expanded notation for 2+ qubits

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1 qubit, 2 states. (Fig 13)
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2 qubits, 4 states. (Fig 14)
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3 qubits, 8 states. (Fig 15)
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Expanded notation of a 4-qubit system. (Fig 16)

Vector notation for 2+ qubits

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Example #6: φ₆ is made of 2 qubits. (Fig 17)
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Example #6. (Fig 18)
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(Fig 19)
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(Fig 20)
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(Fig 21)
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(Fig 22)
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(Fig 23)
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(Fig 24)
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Vector notation for 2 qubits. (Fig 25)
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(Fig 26)
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Notice that there is no |01in the vector representation because it is implied. (Fig 27)
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(Fig 28)
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Remember, the values are squared to find the coefficients. (Fig 29)
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(Fig 30)
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(Fig 31)

What next?

NYC

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