A toy quantum table separates constant from balanced functions. This is a toy exact table; real quantum algorithms also use complex amplitudes and interference. The one-query test decides constant versus balanced; it does not read both function values.
Quantum Gates
Example
A toy quantum table separates constant from balanced functions. This is a toy exact table; real quantum algorithms also use complex amplitudes and interference. The one-query test decides constant versus balanced; it does not read both function values.
highlighted = computed this step
Build the concrete table
Compute the highlighted logic-table value.
f(0)=0 f(1)=0 after query pair=(0,0) \begin{array}{c|c}\text{f(0)=0 f(1)=0}&\hlmath{\text{after query pair=(0,0)}}\end{array} f(0)=0 f(1)=0 after query pair=(0,0)
Build the concrete table
Compute the highlighted logic-table value.
f(0)=0 f(1)=0 after query pair=(0,0) constant zero final measure=0 \begin{array}{c|c}\text{f(0)=0 f(1)=0}&\text{after query pair=(0,0)}\\\text{constant zero}&\hlmath{\text{final measure=0}}\end{array} f(0)=0 f(1)=0 constant zero after query pair=(0,0) final measure=0
Build the concrete table
Compute the highlighted logic-table value.
f(0)=0 f(1)=0 after query pair=(0,0) constant zero final measure=0 f(0)=1 f(1)=1 after query pair=(1,1) \begin{array}{c|c}\text{f(0)=0 f(1)=0}&\text{after query pair=(0,0)}\\\text{constant zero}&\text{final measure=0}\\\text{f(0)=1 f(1)=1}&\hlmath{\text{after query pair=(1,1)}}\end{array} f(0)=0 f(1)=0 constant zero f(0)=1 f(1)=1 after query pair=(0,0) final measure=0 after query pair=(1,1)
Build the concrete table
Compute the highlighted logic-table value.
f(0)=0 f(1)=0 after query pair=(0,0) constant zero final measure=0 f(0)=1 f(1)=1 after query pair=(1,1) constant one final measure=0 \begin{array}{c|c}\text{f(0)=0 f(1)=0}&\text{after query pair=(0,0)}\\\text{constant zero}&\text{final measure=0}\\\text{f(0)=1 f(1)=1}&\text{after query pair=(1,1)}\\\text{constant one}&\hlmath{\text{final measure=0}}\end{array} f(0)=0 f(1)=0 constant zero f(0)=1 f(1)=1 constant one after query pair=(0,0) final measure=0 after query pair=(1,1) final measure=0
Build the concrete table
Compute the highlighted logic-table value.
f(0)=0 f(1)=0 after query pair=(0,0) constant zero final measure=0 f(0)=1 f(1)=1 after query pair=(1,1) constant one final measure=0 f(0)=0 f(1)=1 after query pair=(0,1) \begin{array}{c|c}\text{f(0)=0 f(1)=0}&\text{after query pair=(0,0)}\\\text{constant zero}&\text{final measure=0}\\\text{f(0)=1 f(1)=1}&\text{after query pair=(1,1)}\\\text{constant one}&\text{final measure=0}\\\text{f(0)=0 f(1)=1}&\hlmath{\text{after query pair=(0,1)}}\end{array} f(0)=0 f(1)=0 constant zero f(0)=1 f(1)=1 constant one f(0)=0 f(1)=1 after query pair=(0,0) final measure=0 after query pair=(1,1) final measure=0 after query pair=(0,1)
Build the concrete table
Compute the highlighted logic-table value.
f(0)=0 f(1)=0 after query pair=(0,0) constant zero final measure=0 f(0)=1 f(1)=1 after query pair=(1,1) constant one final measure=0 f(0)=0 f(1)=1 after query pair=(0,1) balanced identity final measure=1 \begin{array}{c|c}\text{f(0)=0 f(1)=0}&\text{after query pair=(0,0)}\\\text{constant zero}&\text{final measure=0}\\\text{f(0)=1 f(1)=1}&\text{after query pair=(1,1)}\\\text{constant one}&\text{final measure=0}\\\text{f(0)=0 f(1)=1}&\text{after query pair=(0,1)}\\\text{balanced identity}&\hlmath{\text{final measure=1}}\end{array} f(0)=0 f(1)=0 constant zero f(0)=1 f(1)=1 constant one f(0)=0 f(1)=1 balanced identity after query pair=(0,0) final measure=0 after query pair=(1,1) final measure=0 after query pair=(0,1) final measure=1
Build the concrete table
Compute the highlighted logic-table value.
f(0)=0 f(1)=0 after query pair=(0,0) constant zero final measure=0 f(0)=1 f(1)=1 after query pair=(1,1) constant one final measure=0 f(0)=0 f(1)=1 after query pair=(0,1) balanced identity final measure=1 f(0)=1 f(1)=0 after query pair=(1,0) \begin{array}{c|c}\text{f(0)=0 f(1)=0}&\text{after query pair=(0,0)}\\\text{constant zero}&\text{final measure=0}\\\text{f(0)=1 f(1)=1}&\text{after query pair=(1,1)}\\\text{constant one}&\text{final measure=0}\\\text{f(0)=0 f(1)=1}&\text{after query pair=(0,1)}\\\text{balanced identity}&\text{final measure=1}\\\text{f(0)=1 f(1)=0}&\hlmath{\text{after query pair=(1,0)}}\end{array} f(0)=0 f(1)=0 constant zero f(0)=1 f(1)=1 constant one f(0)=0 f(1)=1 balanced identity f(0)=1 f(1)=0 after query pair=(0,0) final measure=0 after query pair=(1,1) final measure=0 after query pair=(0,1) final measure=1 after query pair=(1,0)
Build the concrete table
Compute the highlighted logic-table value.
f(0)=0 f(1)=0 after query pair=(0,0) constant zero final measure=0 f(0)=1 f(1)=1 after query pair=(1,1) constant one final measure=0 f(0)=0 f(1)=1 after query pair=(0,1) balanced identity final measure=1 f(0)=1 f(1)=0 after query pair=(1,0) balanced not final measure=1 \begin{array}{c|c}\text{f(0)=0 f(1)=0}&\text{after query pair=(0,0)}\\\text{constant zero}&\text{final measure=0}\\\text{f(0)=1 f(1)=1}&\text{after query pair=(1,1)}\\\text{constant one}&\text{final measure=0}\\\text{f(0)=0 f(1)=1}&\text{after query pair=(0,1)}\\\text{balanced identity}&\text{final measure=1}\\\text{f(0)=1 f(1)=0}&\text{after query pair=(1,0)}\\\text{balanced not}&\hlmath{\text{final measure=1}}\end{array} f(0)=0 f(1)=0 constant zero f(0)=1 f(1)=1 constant one f(0)=0 f(1)=1 balanced identity f(0)=1 f(1)=0 balanced not after query pair=(0,0) final measure=0 after query pair=(1,1) final measure=0 after query pair=(0,1) final measure=1 after query pair=(1,0) final measure=1
Read the table verdict
Compute the highlighted logic-table value.
f(0)=0 f(1)=0 after query pair=(0,0) constant zero final measure=0 f(0)=1 f(1)=1 after query pair=(1,1) constant one final measure=0 f(0)=0 f(1)=1 after query pair=(0,1) balanced identity final measure=1 f(0)=1 f(1)=0 after query pair=(1,0) balanced not final measure=1 verdict interference: measure 0 means constant, 1 means balanced \begin{array}{c|c}\text{f(0)=0 f(1)=0}&\text{after query pair=(0,0)}\\\text{constant zero}&\text{final measure=0}\\\text{f(0)=1 f(1)=1}&\text{after query pair=(1,1)}\\\text{constant one}&\text{final measure=0}\\\text{f(0)=0 f(1)=1}&\text{after query pair=(0,1)}\\\text{balanced identity}&\text{final measure=1}\\\text{f(0)=1 f(1)=0}&\text{after query pair=(1,0)}\\\text{balanced not}&\text{final measure=1}\\\text{verdict}&\hlmath{\text{interference: measure 0 means constant, 1 means balanced}}\end{array} f(0)=0 f(1)=0 constant zero f(0)=1 f(1)=1 constant one f(0)=0 f(1)=1 balanced identity f(0)=1 f(1)=0 balanced not verdict after query pair=(0,0) final measure=0 after query pair=(1,1) final measure=0 after query pair=(0,1) final measure=1 after query pair=(1,0) final measure=1 interference: measure 0 means constant, 1 means balanced
logic-computation
Every row is intentionally ordered and pinned to the lesson specification.