Which error correction runs can you compare?
Match the round counts before comparing final logical-memory failures.
The question
A fictional quantum memory test checks the final readout against a known state once for each completed block. Its table labels both sets as 10 rounds per block.
| Blocks | Failed | |
|---|---|---|
| Configuration A | 2000 | 36 |
| Configuration B | 2000 | 20 |
These are counts of failed blocks, not counts of failures in individual rounds.
“What does this record support about the two configurations?”
Not saved by this site. Your browser may restore text when you navigate back.
A strong answer, step by step
Open each step in turn. This is one strong answer, not the only one.
Step 1: What is the measured unit?
What would you do here? Open the move you’d make.
Read the failure count as errors in each round
Tempting, but it misses something. There is no failure count by round.
Compare final failures per completed block
The strong move. The table gives one scored result per block.
Treat the result as hardware gate fidelity
Tempting, but it misses something. This is a known-state memory readout check, with a different outcome.
See how a strong candidate says it
“The outcome is a failed block. Each completed block contributes one final readout check.”
Why it works: The table contains no record of which round a failure occurred in.
Step 2: What is the reported gap?
What would you do here? Open the move you’d make.
A reports 1.8% and B reports 1.0%, pending a match check
The strong move. The counts give the rates. The comparison depends on the shared exposure.
B is proven to reduce errors by 0.8 points per round
Tempting, but it misses something. The reported fractions count failed blocks and do not establish a per-round effect.
The rates are equal because the block counts match
Tempting, but it misses something. The denominators match but the failure counts differ.
See how a strong candidate says it
“A reports 36/2,000 = 1.8% failed blocks. B reports 20/2,000 = 1.0%, a gap of 0.8 percentage points if the block lengths match.”
Why it works: These are observed fractions. Check the round count in the run records before comparing.
Step 3: What does the matched comparison show?
The run record shows B’s original row used 5 rounds per block. A separate B run with the same 10 rounds and scoring as A recorded 30 failures in 2,000 blocks.
What would you do here? Open the move you’d make.
Keep 1.8% to 1.0% as the matched comparison
Tempting, but it misses something. The 1.0% row has only five rounds per block.
Divide the short B row’s rate by five to estimate a per-round rate
Tempting, but it misses something. A final block failure is not a count of independent failures in each round.
Compare 1.8% to 1.5% across the 10-round blocks
The strong move. These rows score the same length of block with the same check.
See how a strong candidate says it
“Use the 10-round rows. A recorded 36/2,000 = 1.8%. B recorded 30/2,000 = 1.5%. The observed difference is 0.3 percentage points. That is one-sixth of A’s observed rate.”
Why it works: The earlier B result used fewer rounds. The new B row matches A’s exposure and scoring.
Step 4: What claim can you make?
What would you do here? Open the move you’d make.
Claim a fault-tolerance threshold from the two matched rows
Tempting, but it misses something. The test compares two observed fractions at one block length.
State the observed difference and ask for repeats
The strong move. The claim stays within the measured block counts and conditions.
Report the better short-run number and omit the round count
Tempting, but it misses something. The different exposure is necessary to interpret that number.
See how a strong candidate says it
“B recorded six fewer failed blocks among 2,000 in the matched setting. I’d give the counts and ask for repeat evidence and uncertainty before claiming error suppression.”
Why it works: The matched comparison supports the observed difference at this exposure. It does not show a threshold or repeatability.
The answer, in short
- Decision
- Compare A at 1.8% with B at 1.5% across the matched 10-round blocks.
- Because
- The five-round B row answers a different measurement question.
- What would change it
- Ask for repeats and other matched exposures before making a broader claim.
Common traps
- Comparing different round counts as the same experiment
- Interpreting failures per block as a per-round rate
Check your answer
- What is counted once per block?
- Do the round counts match?
- What is the observed matched difference?
- What evidence would support a stronger claim?
Last reviewed Nov 11, 2026