Classical-quantum alliances (uneasy truces)¶

Hybrid quantum-classical systems are what you get when two fundamentally incompatible approaches to computation are forced to work together by researchers who’ve spent too much grant money to back out now. It’s a partnership built on necessity rather than mutual respect, like the Watch cooperating with the Thieves’ Guild, or Vetinari tolerating the existence of the Alchemists. Both sides are convinced they’re doing the heavy lifting while the other takes undeserved credit.

The classical computer handles everything that requires reliability, speed, and operating at temperatures above absolute zero. The quantum computer gets called in for the one specific task that might benefit from quantum effects, performs it with great ceremony and uncertain accuracy, then hands back results that need extensive interpretation. Together they form a computational odd couple that occasionally produces something useful, more frequently produces expensive confusion, and always requires careful management to prevent the quantum bit from collapsing into uselessness.

Classical preprocessing or the sensible bit¶

Before any quantum computation happens, classical computers do the actual work of turning your problem into something a quantum system might conceivably handle. This involves data cleaning, feature extraction, dimensionality reduction, and the sort of prosaic engineering that doesn’t make it into breathless press releases about quantum supremacy.

Your raw data arrives in whatever chaotic format the real world has vomited up. Classical algorithms clean it, normalise it, and reduce it to a manageable size because quantum computers have approximately seventeen qubits available and your dataset has three million features. Classical optimisation determines what parameters to try. Classical software translates your problem into quantum gate sequences. Classical hardware controls the quantum system and reads out its results.

This is the equivalent of the Night Watch doing three weeks of careful investigative work, knocking on doors, interviewing witnesses, and gathering evidence, before calling in a wizard to cast one very specific spell that might, possibly, reveal a crucial clue. The wizard then takes credit for solving the case while the Watch goes back to doing actual police work.

The preprocessing must also account for the quantum computer’s many limitations and preferences. Your data needs encoding into quantum states, which means mapping classical information onto the delicate quantum properties of particles that would rather be left alone. Different encoding schemes exist, each with tradeoffs that classical computers must evaluate. Too much data and you overwhelm the few available qubits. Too little and you’re not using the quantum computer’s full capacity, assuming it has any.

None of this appears in the papers with titles like “Quantum supremacy in machine learning.” The preprocessing is mentioned in a brief methods section, described in the passive voice, and attributed to “standard techniques” as though it handled itself while researchers were busy doing quantum things.

Quantum computation or the exciting and terrifying bit¶

Here’s where the actual quantum computation happens, assuming the qubits haven’t already decohered from exposure to passing thoughts about measurement. The quantum computer receives the carefully preprocessed, extensively optimised parameters from its classical handler and attempts to do something quantum with them.

In VQE, the quantum system prepares a trial quantum state and measures its energy. In QAOA, it alternates between problem-specific operations and mixing operations for a predetermined number of layers. In quantum sampling, it attempts to generate samples from some probability distribution that’s too complicated for classical methods. In all cases, it does this while simultaneously fighting against decoherence, gate errors, and the fundamental hostility of the universe toward maintaining quantum effects in anything larger than a few dozen qubits.

The quantum computation typically takes microseconds to milliseconds, during which the qubits must remain isolated from everything that might constitute measurement or environmental noise. Any stray electromagnetic field, thermal fluctuation, or cosmic ray passing through can collapse the quantum state and ruin the calculation. It’s performing precision choreography while the entire world tries to trip you up.

When it works, you get measurement results: classical bits extracted from quantum states through a process that irreversibly destroys the quantum information. When it doesn’t work, you get measurement results that look superficially identical but are actually garbage, and determining which you’ve got requires careful analysis that happens in the next stage.

The quantum computer completes its task and returns to idle, having contributed anywhere from one percent to maybe fifteen percent of the total computational effort, but accounting for ninety-five percent of the technical difficulty, cost, and publicity material.

Classical post-processing or translating quantum gibberish¶

The quantum computer has spoken. It has produced measurement results in the form of bit strings, probability distributions, or energy estimates. These results are precisely as useful as a drunk oracle’s pronouncements, requiring extensive interpretation before anyone can extract meaning.

Classical computers take the quantum outputs and do the actual analysis. They aggregate multiple measurement results because single quantum measurements are useless due to quantum randomness. They apply error mitigation techniques to account for all the gate errors and decoherence that definitely occurred. They perform statistical analysis to determine whether the results are meaningful or just expensive noise. They feed the results into classical optimisation algorithms that decide what parameters to try next.

In hybrid variational algorithms, this post-processing includes running classical optimisation to adjust the quantum circuit parameters. The quantum computer provides gradient information or energy landscapes, and classical algorithms use this to search for better solutions. Back and forth they go, quantum evaluation and classical optimisation, like a particularly awkward country dance where one partner is refrigerated and the other isn’t sure if this is working.

The post-processing must also account for systematic biases in the quantum hardware. Certain qubits are noisier than others. Certain gate operations accumulate more errors. The measurement apparatus has its own biases and imperfections. Classical algorithms correct for all of this using calibration data and error models that themselves required extensive classical computation to produce.

What emerges is an answer to your original question, possibly correct, certainly expensive, and heavily dependent on how much you trust the quantum hardware to have done its job properly. The classical post-processing presents this with appropriate confidence intervals, caveats, and suggestions for further validation, most of which involve more classical computation.

Where the bottlenecks actually are¶

Everywhere. The bottlenecks are everywhere.

Classical preprocessing is bottlenecked by the quantum computer’s limited qubit count and connectivity. You can’t just throw your full dataset at the quantum system because it has maybe fifty usable qubits and they’re not all connected to each other. Reducing your problem to fit requires classical algorithms that may take longer than just solving the whole thing classically in the first place.

Quantum computation is bottlenecked by decoherence, gate errors, limited qubit count, poor connectivity, slow gate operations, and the fundamental difficulty of keeping quantum states coherent for more than a few microseconds. Current quantum computers can perform maybe a few thousand gate operations before errors accumulate to the point of uselessness. Many quantum algorithms require millions or billions of gates to show advantage over classical methods.

Classical post-processing is bottlenecked by the noisy, ambiguous nature of quantum measurement results. You need many repeated measurements to build up statistics, and even then you’re extracting information from a system that’s been fighting against decoherence the entire time. Error mitigation adds overhead. Validation adds overhead. Interpreting results adds overhead.

The communication between classical and quantum systems is bottlenecked by the need to repeatedly shuttle information back and forth. Each round trip involves classical optimisation, quantum state preparation, quantum computation, quantum measurement, and classical analysis. The quantum bit might be fast, but the total latency is dominated by everything else.

Meanwhile, purely classical approaches don’t have any of these problems. They run on hardware that’s been optimised for decades. They don’t require dilution refrigerators. They scale to billions of parameters. They’re reliable, debuggable, and fast. The quantum advantage needs to be enormous to overcome these practical differences, and for most problems, it isn’t.

Why most quantum ML is ninety-five percent classical with quantum garnish¶

Here’s the secret that vendors quietly acknowledge after the journalists leave: most “quantum machine learning” is overwhelmingly classical computation with a small quantum subroutine buried somewhere in the middle. The quantum bit might be theoretically interesting, possibly advantageous in specific circumstances, but in terms of actual computational work, it’s garnish on a classical meal.

Take quantum kernel methods, where you use a quantum computer to calculate kernel functions for classical support vector machines. The data preprocessing is classical. The SVM training is classical. The quantum computer calculates one specific similarity measure between data points, and even that gets called thousands of times, with each call requiring classical control and post-processing. The final model is classical, the predictions are classical, and the quantum contribution is a small component in the middle that could plausibly be replaced with classical approximations for most applications.

Variational quantum algorithms are similar. Classical optimisation drives the entire process. The quantum computer evaluates proposed solutions, but that evaluation is wrapped in layers of classical processing, error mitigation, and interpretation. The iterative loop continues until classical convergence criteria are met, producing a solution that classical algorithms interpret and validate.

Even quantum sampling, which at least does something genuinely quantum, requires classical verification, analysis, and application to whatever problem you’re actually trying to solve. The samples themselves are just numbers until classical algorithms turn them into insights, models, or decisions.

This isn’t necessarily a problem. Hybrid approaches are a reasonable way to extract whatever advantage quantum systems offer while letting classical computers handle everything they’re good at. But it does mean that calling these systems “quantum machine learning” is rather like calling a shepherd’s pie “beef and gravy pie” while ignoring the potatoes, vegetables, and the fact that the dish is mostly potatoes anyway.

The quantum component attracts funding, generates papers, and sounds impressive in grant applications. The classical components do the actual work, quietly and without recognition, like the Watch solving crimes while wizards take credit. When the hybrid system produces results, press releases emphasise the quantum innovation. When it fails, technical explanations mention calibration issues, systematic errors, and the inherent challenges of quantum hardware, which are all euphemisms for “the classical bits worked fine but the quantum bit didn’t.”

The path forward likely involves more of this: classical-quantum systems where each component does what it’s actually good at, with increasingly sophisticated integration and error handling. Quantum computers may never dominate machine learning, but they might contribute useful subroutines while classical systems provide the infrastructure, reliability, and bulk computational power. It’s not as exciting as pure quantum supremacy, but it has the considerable advantage of possibly working.