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Quantum

intermediate · Interactive lab

Quantum Advantage

A quantum computer is not a faster computer. For two kinds of problem the advantage is enormous, for one it is quadratic and usually swallowed by overhead, for most there is none at all — and for some, nobody knows yet.

By the end: Read a workload as a scaling question: how the classical cost grows, how the quantum cost grows, and what the overhead does to the difference.

Your challenge

Start here. This lab opens with every workload marked as a decisive quantum win, which is the wrong starting point and roughly the content of a bad conference talk. Two of these have no known advantage at all, one is quadratic and loses to its own overhead, and two have no settled answer in either direction — their rows show no arithmetic, because there is none to show. Marking everything unsettled is the other wrong answer, and it is graded as one. Read each row and answer.

See it happen

Two growth rates and an overhead

Advantage: not shown here
Slowed down so you can follow
THE WORKLOAD|+⟩and a coin in a boxGROWTH RATESOVERHEADZ BASISanswers 0 and 1ORDERS OF MAGNITUDETHE QUBITTHE COIN
A workload arrives with a size. The classical cost and the quantum cost are computed from how each one grows, the error-correction overhead is added to the quantum side, and the tally shows both as orders of magnitude, here and at ten times the size.
  1. The workload → Growth rates
  2. Growth rates → Overhead
  3. Overhead → Orders of magnitude
STEP 1 / 6

Not a faster computer

The workload arrives with a size, and the bench does one piece of arithmetic: how the classical cost grows, how the quantum cost grows, and what the Overhead does to the difference. Watch the two pairs of bars.

Configure

Your answer for each workload

For each workload, say what a fault-tolerant quantum computer would do for it. The numbers on each row are computed from growth rates and overhead — read them before answering.

What would a fault-tolerant quantum computer do for this workload?
A decisive advantage
· Orders of magnitude, even with overhead counted.
A quadratic gain, eaten by overhead
· Real, and not a business case at these sizes.
No known advantage
· A quantum algorithm exists and is not better: the question is closed.
Genuinely unsettled
· No growth rate on either side, so the bench shows nothing. Not the same as no advantage.
  1. W-901 — Recover a private key from a 2048-bit public key

    The workload an attacker runs, and the reason migrations have dates.

    The work
    At size 2,048: classical about 10^35 operations, quantum about 10^16 including overhead
    Ten times bigger
    classical about 10^91, quantum about 10^19
    Where a quantum machine would win
    Already at this size; it starts paying from about size 1,000
  2. W-902 — Search a million unindexed customer records

    The example every introduction uses for Grover's algorithm.

    The work
    At size 1,000,000: classical about 10^6 operations, quantum about 10^9 including overhead
    Ten times bigger
    classical about 10^7, quantum about 10^10
    Where a quantum machine would win
    At no size in this range, once the overhead is counted
  3. W-903 — Join two fifty-million-row tables in the nightly load

    The workload that actually costs money in most enterprises.

    The work
    At size 50,000,000: classical about 10^8 operations
    Ten times bigger
    classical about 10^9
    Where a quantum machine would win
    Nowhere known: no quantum algorithm beats the classical one here
  4. W-904 — Simulate the electronic structure of a 60-orbital catalyst

    Simulating quantum mechanics is the thing classical machines cannot scale to.

    The work
    At size 60: classical about 10^18 operations for an exact method, quantum about 10^13 including overhead
    Ten times bigger
    classical about 10^181, quantum about 10^16
    Where a quantum machine would win
    Already at this size; it starts paying from about size 60
    What the classical figure is
    The cost of an exact method. Approximate classical methods do better on many systems, and by how much is itself unsettled
  5. W-905 — Train the fraud-detection model on tabular data

    The claim that appears in most quantum machine-learning decks.

    The work
    Nothing to compute: no settled growth rate on either side
    Ten times bigger
    Still nothing — a bigger problem does not settle an open question
    Where a quantum machine would win
    Not settled either way, which is not the same as no advantage
  6. W-906 — Optimise delivery routes for five hundred vehicles

    The combinatorial-optimisation pitch, and the one most often piloted.

    The work
    Nothing to compute: no settled growth rate on either side
    Ten times bigger
    Still nothing — a bigger problem does not settle an open question
    Where a quantum machine would win
    Not settled either way, which is not the same as no advantage
  7. W-907 — Speed up the nightly file load between two systems

    An I/O-bound workload, dressed as a compute problem.

    The work
    At size 10,000,000: classical about 10^7 operations
    Ten times bigger
    classical about 10^8
    Where a quantum machine would win
    Nowhere known: no quantum algorithm beats the classical one here

Four answers, and one of them is that nobody knows. A row with numbers on it is a row the bench can settle; a row with none is the one that is genuinely open. Read the classical growth, the quantum growth and the overhead before choosing.

Learn more

Why this pattern exists

The question that reaches an architect is never "what is a qubit?" — it is "should this workload be on the roadmap?". Answering it needs two numbers and a habit. The numbers are how the best known classical algorithm grows with the size of the problem, and how the best known quantum one grows, with the overhead of error correction counted in. The habit is refusing to answer when the answer is not known. Factoring is the famous case: the classical cost of breaking a 2048-bit key is around 10^35 operations by the best known method and the quantum cost is around 10^16 even after overhead, which is why post-quantum cryptography has a deadline. Searching an unindexed table is the famous disappointment: the quantum route really is quadratically better, and a million rows still costs 10^9 operations against 10^6 classically, because the overhead is larger than the gain. And for two of the seven workloads here the bench computes nothing at all, because nobody has a growth rate to give it. That is a finding, not a gap.

Seven workloads an enterprise might actually put on a roadmap. For each one the bench computes the orders of magnitude of work the best known classical algorithm needs, what the best known quantum algorithm would need with error-correction overhead counted, and the size at which the quantum route would start to pay — or shows nothing at all, for the two where no growth rate is settled on either side. No device, vendor or year appears anywhere.

  • Read a workload as a scaling question: how the classical cost grows, how the quantum cost grows, and what the overhead does to the difference.
  • Tell a decisive advantage from a quadratic one, and a quadratic one from no advantage at all.
  • Say "not known" where it is not known — and answer where the arithmetic does settle it, because refusing every question costs a roadmap the decisions it could have made.

The rule this lesson applies: Quantum computers are not faster processors; they are machines on which a few specific algorithms have a different shape. Where an algorithm like Shor's exists, the advantage is decisive and the consequence is a migration deadline rather than a performance project. Where the only route is a Grover-type search, the gain is the square root of the classical work — real, and in practice swallowed by an error-correction overhead of several orders of magnitude, so the crossover size is far beyond any table an enterprise actually has. For most enterprise workloads the bottleneck is not arithmetic at all: joining two fifty-million-row tables, or moving a night's worth of files, is dominated by getting data in and out, and loading classical data into a quantum machine is itself an unsolved cost. Simulating quantum systems is the one place where the scaling argument is not in dispute — and even there, read what the classical number is: this bench costs an exact method, while the classical work is done with approximations that do far better on many systems, so which molecules are reachable in practice remains an engineering question rather than a settled one. And some questions — most machine-learning and combinatorial-optimisation claims — have no settled growth rate on either side: the honest answer is that nobody knows, and this bench computes nothing for them rather than printing a number it cannot defend. The grading treats certainty in either direction as the error, and it treats the opposite as an error too: answering "nobody knows" where the arithmetic is on the row is not calibration. This model uses growth rates and an overhead exponent only; it names no device, no vendor and no date, and it is not a prediction about when anything will be built.