Quantum Annealing Time-to-Solution Calculator

Introduction: why quantum annealing time-to-solution planning matters

In quantum annealing, the question is not only whether a single run can find a good answer, but how long it takes to reach a target confidence after repeating that run. This calculator turns that planning problem into two numbers you can test: per-run success probability and elapsed wall-clock time.

The useful part of the page is the connection between probability and runtime. A faster schedule is not automatically better if it lowers the chance of success, and a higher target confidence can push the required number of repetitions upward very quickly. By keeping the inputs visible, the calculator makes that tradeoff easier to inspect.

The sections below show how to choose the fields, how the result is computed, and what assumptions matter when you compare quantum annealing scenarios.

What quantum annealing problem does this calculator solve?

This calculator answers a common quantum annealing planning question: how many repeated anneals are needed to reach a chosen cumulative success probability, and how much total runtime will those repeats consume once overhead is included?

That is helpful when you are comparing candidate schedules, estimating whether a hardware job fits a deadline, or deciding whether a small improvement in per-run success rate is worth the extra setup time. The output is meant to support what-if analysis, not to replace measurements from the machine itself.

Before you start, phrase the decision in one sentence, for example whether a 99% target is realistic, whether a slower anneal buys enough reliability, or whether a lower overhead setting changes the total enough to matter. When the question is clear, the input fields are easier to use correctly.

How to use this quantum annealing time-to-solution calculator

1. Enter Anneal time per run (ms) with the unit shown beside the field.
2. Enter Success probability per run (0-1) with the unit shown beside the field.
3. Enter Target cumulative success probability (0-1) with the unit shown beside the field.
4. Enter Overhead per run (ms) with the unit shown beside the field.
5. Click Calculate Time to Solution to recompute the required run count and total runtime.
6. Review the runs, milliseconds, and seconds in the result before you compare a second scenario.

If you want to compare two setups, keep the inputs beside you and rerun the calculator with only one change at a time. That makes it much easier to see whether the difference comes from the schedule itself or from the probability assumption.

Quantum annealing inputs: how to pick good values

The fields here map directly to the quantum annealing time-to-solution model. Many mistakes come from mixing units or from using a probability that does not match the same hardware settings as the timing data. Use the following checklist as you enter values:

• Units: the form expects milliseconds, so convert seconds, minutes, or microseconds before entering anneal time or overhead.
• Ranges: if an input has a minimum or maximum, treat that range as a guardrail for the model rather than a suggestion.
• Defaults: any prefilled numbers are just starting points; replace them with values from your own machine or benchmark before you trust the output.
• Consistency: if the success probability came from repeated trials, make sure it reflects the same problem instance, schedule, and post-processing approach as the timing inputs.

The four fields in this calculator represent the pieces of the runtime model:

• Anneal time per run (ms): the duration of one annealing attempt on the schedule you want to test.
• Success probability per run (0-1): the chance that one anneal reaches the outcome you want.
• Target cumulative success probability (0-1): the confidence level you want after repeated runs.
• Overhead per run (ms): setup, readout, reset, or orchestration time that happens every time you repeat the anneal.

If you only know a rough success rate, start with the estimate you trust least and then test a second scenario that is a little better or a little worse. The gap between those scenarios often tells you more than any single point estimate.

Formulas: how quantum annealing inputs become a time-to-solution estimate

For quantum annealing, the calculator uses the standard repeated-trial model: if a single run succeeds with probability p, then k independent runs reach cumulative success 1-(1-p)^k. The page rounds k up to the next whole run and multiplies that count by the time spent on each run.

In symbols, the required run count is:

The total elapsed time is then:

Here, t_a is the anneal time per run and t_o is the overhead per run. If overhead dominates, the total runtime will track overhead more than anneal duration; if success probability is the main bottleneck, the run count will dominate the estimate. Because the result is rounded to whole runs, a small change in probability or target can add an extra attempt.

Worked example: 20 ms anneals at 10% success probability

This example uses the page's default-style inputs to show how the quantum annealing calculation unfolds.

• Anneal time per run (ms): 20
• Success probability per run (0-1): 0.1
• Target cumulative success probability (0-1): 0.99
• Overhead per run (ms): 5

Step 1: solve for the number of runs needed. With a 99% target and a 10% success rate per run, the calculator gives k = ⌈ln(1 - 0.99) / ln(1 - 0.1)⌉ = ⌈43.7...⌉ = 44.

Step 2: add the per-run timing components. Each attempt takes 20 + 5 = 25 ms, so the total runtime is 44 × 25 ms = 1,100 ms, or 1.100 s.

Step 3: verify that the cumulative success probability for 44 independent attempts is just above the target. That makes the result a practical planning estimate rather than a single-run prediction.

Comparison table: quantum annealing runtime sensitivity to per-run success probability

The table below keeps the anneal schedule and overhead fixed so you can see how sensitive total runtime is to the per-run success rate.

The nonlinearity matters because the output changes in whole runs, so a small improvement in probability may remove an entire 25 ms block, while a small drop can add one. That is why it helps to compare more than one scenario before choosing a schedule.

How to interpret the quantum annealing time-to-solution result

In this calculator, the results panel reports the minimum whole number of runs needed and the total wall-clock time after adding overhead. Check three things: the run count is whole and plausible, the time units are milliseconds and seconds, and the direction matches your expectation. Higher per-run success probability or a lower target should reduce the run count, while more overhead should increase total time.

The page keeps the comparison in the browser, so if you want a record, copy the inputs and the displayed result into your notes before you move on to the next scenario. That is usually enough to recreate the estimate later without relying on an export feature that is not present here.

If the output looks right on all three checks, you can treat it as a useful planning estimate for the current schedule and probability assumption.

Limitations and assumptions for quantum annealing time-to-solution estimates

This calculator is deliberately simple: it estimates quantum annealing time to solution by assuming independent repeated runs with a fixed success probability and fixed overhead. That makes it useful for planning, but it also means a few real-world effects are left out.

• Independence: each anneal is treated as independent; correlations between attempts are ignored.
• Stable probability: the success rate is assumed not to drift across runs or as operating conditions change.
• Constant overhead: overhead is added to every run, even if a real workflow batches or reuses setup steps.
• Whole-run rounding: the calculator rounds up to whole runs, so the estimate can jump when inputs change slightly.
• No queueing or external delays: waiting time for lab access, cloud scheduling, transfer, or post-processing is not included.

If your workflow uses adaptive parameters, extra post-processing, or hardware-specific retries, treat the result as a planning baseline rather than a final prediction. The calculator is most useful when the inputs come from the same device and problem class you intend to run.