What is Quantum Computing

Everything here is runnable on your own circuit. Try it in the console

Most explanations of quantum computing begin with physics. This one begins with the real thing. The board below is our Live lab, the latest jobs from our own test account, each one a real quantum program run on a CPU, an NVIDIA GPU, a Google TPU or a real quantum processor. The rings of the orbit run from CPU on the inside to QPU on the outside, and every dot is a job. Open the full board with View the live lab and keep it in mind as you read, because every idea in this guide is somewhere on it.

What is quantum computing?

Quantum computing is a way of processing information that uses the laws of quantum mechanics, the physics that governs atoms, electrons and particles of light. The computer in your phone or laptop stores everything as bits, and every bit is either 0 or 1. A quantum computer uses quantum bits, called qubits. A qubit can be in a superposition of 0 and 1, and several qubits can be entangled so that they no longer behave independently. A quantum algorithm choreographs those effects so that when the qubits are finally measured, the answer you are looking for is the outcome you are most likely to see.

The reason anyone cares is scale. Describing n qubits exactly takes 2ⁿ numbers. Ten qubits need 1,024 of them, which a browser tab handles in an instant. Thirty need about a billion, or 16 GiB of memory. Fifty need 16 PiB, more memory than the largest supercomputers have. A quantum computer never writes that list down. Its qubits are the state, which is why problems ruled by quantum physics, molecules and materials above all, are its natural home.

Quantum computers will not make everything faster. Email, video and spreadsheets gain nothing from qubits, and for most everyday work a classical chip stays quicker and far cheaper. The advantage is confined to particular kinds of problem, and finding and proving those is much of what the field is working on. Our guide to CPU vs GPU vs TPU vs QPU shows where each kind of chip fits.

A short history of quantum computing

In 1981 the physicist Richard Feynman argued that nature is quantum, so simulating it properly needs a computer that is quantum too. In 1994 Peter Shor showed that a quantum computer could factor large numbers vastly faster than the best known classical method, which put much of today's encryption on notice. Two years later Lov Grover found a quantum speedup for searching unsorted data. The first machines with a handful of qubits followed in the late 1990s, and since the mid 2010s real quantum processors have been reachable over the cloud. That is the model this site runs on, known as quantum computing as a service, or QCaaS.

How does quantum computing work?

Four ideas carry almost all of it, and a fifth turns them into a program.

Qubits and superposition

A bit is a switch, on or off. A qubit is closer to a direction. Picture an arrow inside a sphere, the Bloch sphere, with 0 at the north pole and 1 at the south. The arrow can point anywhere on the surface, and every direction between the poles is a superposition. Each state carries two amplitudes, one for 0 and one for 1, and when you measure the qubit it lands on 0 or 1 with probabilities set by those amplitudes. Physically a qubit can be a tiny superconducting circuit, a single trapped ion, a neutral atom or a photon.

Entanglement

Entangle two qubits and they share one state between them. In a Bell state each qubit on its own is a coin flip, yet the two always agree when measured, however far apart they are. Einstein called it spooky action at a distance. Entanglement is what lets the information in a quantum computer grow as 2ⁿ, and the GHZ and Bell state tutorial builds one you can run.

Interference

Amplitudes behave like waves. They can be positive or negative, so when two paths lead to the same outcome they can add up or cancel out. A quantum algorithm is a recipe that arranges this on purpose, so the paths to wrong answers cancel and the paths to the right one reinforce. Grover's search algorithm is the classic example. It finds a marked item among N in about √N steps, where a classical search needs about N.

Measurement and shots

Reading a qubit ends its superposition. You get a plain 0 or 1, and the amplitudes are gone. So a quantum program is run many times, and each run is called a shot. A job of 1,000 shots returns a histogram of the bitstrings that came out, and the answer is read from that distribution. That is why quantum results are statistical, and why the error bound further down this page matters so much.

Gates and circuits

A quantum program is usually written as a circuit, a set of wires for the qubits with gates placed along them. The Hadamard gate puts a qubit into an equal superposition, the CNOT gate entangles two, and rotation gates tune amplitudes by any angle. Circuits are written in languages like OpenQASM or built with SDKs such as Qiskit and PennyLane, and you can build one by dragging gates onto wires in our free online quantum circuit simulator, with no account and nothing to install.

Quantum computers vs classical computers

The fairest summary is that quantum computers are specialists. They will sit beside classical machines rather than replace them, the way GPUs sit beside CPUs today, and most real workflows are hybrid, with a classical computer steering a quantum one through many short runs.

Types of quantum computers

Nobody yet knows which way of building a qubit will win, so several are being built in parallel.

• Superconducting qubits are tiny electrical circuits cooled to about a hundredth of a degree above absolute zero, colder than outer space, inside a dilution refrigerator. They switch fast and are made with chip fabrication methods. Rigetti and IQM build them, and that cold is the zero Kelvin in our own name, the Zero Kelvin Simulation Foundry
• Trapped ions are single charged atoms held in a vacuum by electric fields and controlled with lasers. Every ion of a kind is identical by nature, they hold their state for a long time, and every ion in a chain can interact with every other. IonQ and AQT build them, and transmon vs trapped ion compares the two approaches
• Neutral atoms are uncharged atoms arranged in a grid by laser beams called optical tweezers and excited to Rydberg states so that they interact. QuEra's Aquila is programmed in analog, with laser pulses that evolve the whole register at once instead of gates. More in neutral atom quantum computing
• Photonic machines encode information in single particles of light, sent through an optical circuit of beamsplitters and phase shifters. We ran Quandela's Belenos three times, for about a euro each, and its photons showed Hong-Ou-Mandel interference with a visibility of 95.4%, 97.0% and 97.7%. We measured a photonic quantum computer has the full runs
• Quantum annealers are a specialised design for optimisation, which settle a system of qubits into its lowest energy state

Real quantum computers you can use today

Every processor below takes real jobs on ZKSF today, from the web console, the Python SDK and the Android app. Each card shows what the machine is, what its maker aims it at, its price per task and per shot, and what it returned when we ran it ourselves.

That is six quantum processors from five manufacturers, Rigetti, IQM, IonQ, AQT and QuEra, across three kinds of hardware. Prices are the providers' list prices with no markup. Several of these machines accept work only in scheduled windows, and the Engines now panel in the Live lab above shows which are open, as does our live engine status page.

Quantum simulators, the other half of quantum computing

Not every quantum job needs a quantum computer. A quantum simulator runs the same circuit on classical hardware and calculates what an ideal machine would return. Exact simulation keeps every amplitude, so the doubling memory caps it at a few dozen qubits, a limit our article on the 34 qubit wall measures. Approximate methods go much further on the right circuits. Tensor networks handle thousands of qubits when entanglement stays modest, and Clifford circuits, the kind error correction is built from, run at thousands of qubits too.

Simulators matter for three reasons. They give the ideal answer to compare hardware against. They let you develop and debug for a fraction of a cent before paying for real shots. And for many circuits that matter today they are simply the cheapest way to the answer. We run 22 engines in all, CPUs, NVIDIA GPUs and Google TPU v5e and v6e chips beside the quantum processors, and an automatic router picks the cheapest engine that fits each job. What is quantum circuit simulation goes deeper.

Common quantum computing acronyms

Quantum computing has a vocabulary of its own. These are the acronyms you will meet first.

Many more terms, from Bloch sphere to wave function, are explained in plain English in our quantum computing dictionary.

What is quantum computing used for?

Quantum computing applications cluster around problems where the number of possibilities explodes. These are the areas the field expects it to matter most, and each link leads to a published benchmark where we ran a real instance on CPUs, GPUs, TPUs and quantum processors and recorded the result and the bill.

• Chemistry and drug discovery. Molecules are quantum systems, so simulating them is the original use case. See chemicals and pharma
• Finance. Portfolio optimisation, risk and pricing. See finance and trading
• Artificial intelligence. Quantum machine learning, generative models and neural network quantum states. See AI quantum computing
• Logistics and transport. Vehicle routing and delivery planning. See logistics and transport
• Manufacturing. Job shop scheduling on the factory floor. See manufacturing
• Scheduling and allocation. Rostering and frequency allocation as independent sets, native to neutral atom hardware. See scheduling and allocation
• Space and satellites. Choosing which observations a satellite makes on each pass. See space and satellites
• Traffic and smart cities. Routing vehicles to keep congestion down. See traffic and smart cities
• Cryptography. Shor's algorithm, and the move to encryption that survives it. See cryptography

Here are two of those runs exactly as they were measured, results, certificates and costs included.

Live run, the hydrogen molecule

Chemistry is quantum computing's home ground. The smallest molecule, H2, fits on two qubits, which means it fits every processor we offer, so it is the one problem we have run on all four kinds of compute. The circuit prepares the molecule's ground state with VQE, the variational quantum eigensolver, and measures ZZ, a correlation between the two qubits whose ideal value is exactly -1.

Run on our engines

The H2 molecule at its equilibrium bond length, whose exact electronic ground state is -1.857275 Ha. Two qubits, so it fits every device we offer. Submitted to each kind of compute we offer, on 16 September 2026. Every figure below is a real job on the service, priced as any customer would be priced.

Device	Engine	Kind	Qubits	Result	Cost
	exact.cpu	CPU	2	ZZ = -1.0000, the ideal value certificate	$0.0001
NVIDIA	exact.gpu	GPU	2	ZZ = -1.0000, the ideal value certificate	$0.0001
IQM	qpu.iqm.garnet	QPU	2	ZZ = -0.9326, superconducting, 4,096 shots certificate	$6.239
Rigetti	qpu.rigetti	QPU	2	ZZ = -0.5420, superconducting, 4,096 shots * certificate	$2.041
Rigetti	qpu.rigetti	QPU	2	ZZ = -0.5107, the same circuit re-run * certificate	$2.041
AQT	qpu.aqt.ibex	QPU	2	ZZ = -0.9200, trapped ion, 100 shots certificate	$2.650
	neural.cpu	CPU	2	-1.116981 Ha total, 0.0203 Ha above exact certificate	$0.0001
Google	neural.tpu	TPU	2	-1.116981 Ha total, 0.0203 Ha above exact certificate	$0.074

* The two Rigetti rows are one circuit run twice, an internal reproduction of the published benchmark notebook. A depolarizing noise model puts both versions at about -0.99, so the shortfall is not the circuit shape, but the identical program has not yet run on both devices. The steps are in the docs.

A note on the hardware certificates: they state Hellinger fidelity against the exact distribution. For an optimisation circuit that distribution is spread across many outcomes rather than concentrated on one, so the figure is low by construction and is not a measure of whether the device found a good answer. The result column above is.

The same problem is yours to run: every instance here is seeded, so it rebuilds exactly. Open the console and a cost estimate is free before anything executes.

The simulators return the ideal value. IQM Garnet and AQT IBEX Q1, a superconducting chip and a trapped ion machine, land within 0.08 of it, and that shortfall is real hardware noise. Rigetti Cepheus came back near -0.5 twice on the same circuit, and the note under the table records what we know so far. Every row with a certificate links to it, so you can check the result yourself. The method is on chemicals and pharma, and the VQE tutorial walks through the circuit.

Live run, choosing a portfolio

Finance is full of choices that multiply. This instance asks for the best 4 holdings out of 12 assets, which is 495 possible portfolios, few enough that the provably best one is known. It was posed as an optimisation problem and solved with QAOA, the quantum approximate optimisation algorithm.

Run on our engines

A 12-asset portfolio choosing exactly 4 holdings, seed 20260902, whose provable optimum is 0.199796. On 25 September the same instance ran on exact.tpu, a Google TPU, which found that optimum. Submitted to each kind of compute we offer, on 16 and 25 September 2026 at 500 shots. Every figure below is a real job on the service, priced as any customer would be priced.

Device	Engine	Kind	Qubits	Result	Cost
	mps.quimb.cpu	CPU	12	0.199796, the optimum certificate•best outcome	$0.0001
	exact.cpu	CPU	12	0.247259, beats 97.6% certificate	$0.0001
NVIDIA	exact.gpu	GPU	12	0.251747, beats 96.4% certificate	$0.0001
Rigetti	qpu.rigetti	QPU	12	0.247730, beats 97.4% * certificate	$0.5125
IQM	qpu.iqm.garnet	QPU	12	0.221427, beats 99.2% certificate	$1.025
IQM	qpu.iqm.emerald	QPU	12	0.245130, beats 98.0% certificate	$1.100
Google	exact.tpu	TPU	12	0.199796, the optimum certificate	$0.0776
Google	neural.tpu	TPU	—	the penalised QUBO is diagonal, which is not the shape a neural ansatz is for	—

* The Rigetti row is a separate sample of ours on this same instance, with the QAOA angles re-optimised for it. The steps are in the docs.

A note on the hardware certificates: they state Hellinger fidelity against the exact distribution. For an optimisation circuit that distribution is spread across many outcomes rather than concentrated on one, so the figure is low by construction and is not a measure of whether the device found a good answer. The result column above is.

The same problem is yours to run: every instance here is seeded, so it rebuilds exactly. Open the console and a cost estimate is free before anything executes.

A tensor network on a CPU and a Google TPU both found the optimum. Every quantum processor returned a portfolio better than at least 97% of the 495, with IQM Garnet ahead of 99.2% of them, from one 500 shot run each, costing between $0.5125 and $1.100. The CPU and GPU rows cost $0.0001 each. That is quantum computing in 2026 in miniature, real hardware doing real work, with classical methods still the ones to beat. The instance is on finance and trading.

Can quantum computers break encryption?

This is the application that worries governments. On a large enough machine, Shor's algorithm breaks RSA and the elliptic curve cryptography behind Bitcoin and Ethereum. We ran it against real elliptic curves and recovered private keys up to 7 bits long on 21 qubits, with the 7 bit key recovered on a GPU in 66 seconds. A 256 bit Bitcoin key needs roughly 2,304 logical qubits, which current estimates put at somewhere between 10,000 and 500,000 physical qubits depending on the error rate. Nobody has that machine yet, which is why the world is already moving to post quantum cryptography. The numbers are on cryptography and in quantum computing and Bitcoin.

All sixteen of our applications, with their circuits, shot counts and costs, are on applications, and our survey of the top quantum computing use cases puts all nine sectors on one page.

Quantum algorithms worth knowing

The hardware matters because of the algorithms that run on it. These are the ones every introduction to quantum computing arrives at sooner or later.

• Shor's algorithm factors large numbers and solves discrete logarithms, the problems most public key encryption relies on
• Grover's algorithm searches unsorted data in about √N steps instead of N
• VQE finds the lowest energy of a molecule or material, in a loop between a quantum and a classical computer
• QAOA tackles optimisation problems such as routing, scheduling and portfolios
• Quantum simulation evolves a quantum system directly, the use Feynman had in mind
• The quantum Fourier transform is the engine inside Shor's algorithm and many others

Our quantum algorithm examples page runs eight of them for real, GHZ, Grover, QAOA, VQE, Bernstein-Vazirani, teleportation, a Rydberg atom chain and a 1001 qubit error correcting code, and each one links to the certificate from that exact run.

Why every quantum result needs an error bound

Here is the part most introductions leave out. Today's quantum computers are noisy. Qubits lose their state to the slightest disturbance, a process called decoherence, and every gate adds a little error. The field calls this the NISQ era, for noisy intermediate scale quantum. Simulators have their own version of the problem, since the approximate methods that reach thousands of qubits work by discarding information.

So a number from a quantum computer, or from a simulator approximating one, always comes with an uncertainty. Without it you cannot tell a real result from noise, compare two machines fairly or stake a decision on the answer. A result without an error bound is a guess with decimal places.

That is why every finished job on ZKSF can be exported as a public, verifiable certificate.

• ZCC-v0.1 states the accuracy of an approximate simulation, as a convergence check or as a bound measured inside the run itself
• ZHF-v0.1 states the fidelity of a run on real quantum hardware, comparing the measured counts against the exact answer for the same circuit
• ZQEC-v0.1 states the logical error rate of a quantum error correction run, with a 95% confidence interval

Anyone can check a certificate with an open source tool, without an account and without calling our service. The certification page has the full specification, and quantum error bars explains the thinking behind it.

Quantum error correction, logical qubits and ZQEC

The long term fix for noise is quantum error correction. It spreads one logical qubit across many physical qubits, measures checks called syndromes without disturbing the stored information, and a decoder works out which errors happened so they can be undone. Below a threshold error rate, adding qubits makes the logical qubit more reliable, which is the road to fault tolerant quantum computing. Our guide to logical qubits vs physical qubits explains the trade.

Measuring how well a code works is a challenge of its own. A logical error rate is a proportion counted over a finite number of shots, so a run with no failures reads exactly zero, and no finite experiment proves a code never fails. A ZQEC-v0.1 certificate therefore carries a Wilson score interval, which stays honest at zero, and names the decoder beside the result, because the decoder is part of the claim. See ZQEC on the certification page and simulating quantum error correction.

What does quantum computing cost?

Less than most people expect. On ZKSF you pay per job, with no subscription. Simulator jobs start at $0.0001, a hundredth of a cent. A quantum processor charges a flat $0.30 per task plus a per shot rate set by its provider, so a 500 shot run is $0.5125 on Rigetti Cepheus and 1,000 shots on QuEra Aquila is $10.30. Every job shows its price before it runs.

The quantum computing cost calculator turns any budget into shots on every machine, side by side. What it costs to rent a quantum computer works through when real hardware is worth it and when a simulator returns the exact answer for a fraction of a cent, and quantum computing cost in 2026 breaks down how quantum computing is priced.

How to start with quantum computing today

You do not need a physics degree or a lab. Pick the step that suits you.

• Try it free in your browser. The online quantum circuit simulator runs circuits of up to 10 qubits exactly in the page, with no account and nothing to install
• Learn the language. The quantum computing dictionary explains the terms, and the algorithm examples show working circuits with their certificates
• Run on real hardware. Sign up to the web console, add credit and send a circuit to a quantum processor. Your account comes with its own Orbit, the same board as the Live lab at the top of this page, which fills with your jobs as you run them
• Write code. pip install qsim-sdk and every engine is one function call away, with Qiskit and PennyLane plugins for the code you already have
• Use your phone. Our quantum computing mobile app for Android brings the same engines and quantum processors to your pocket. It is getting a backend upgrade with new features right now, and its Google Play page has the latest

Quantum computing questions, answered

What is quantum computing in simple terms?

It is computing with qubits instead of bits. Qubits follow the rules of quantum physics, so they can hold superpositions and become entangled, and quantum algorithms use those effects to solve certain problems far faster than an ordinary computer could.

What is a qubit?

A qubit, or quantum bit, is the basic unit of quantum information. A bit is always 0 or 1, while a qubit can be in a superposition of both until it is measured, when it gives a 0 or a 1 with probabilities set by its state.

Is quantum computing real?

Yes. Real quantum computers exist and run real jobs every day, including the ones in the Live lab at the top of this page. They are still small and noisy, so for now they complement classical computers on particular problems.

Can I use a quantum computer today?

Yes. Through quantum computing as a service you can run a circuit on a real quantum processor from a browser, an SDK or a phone. On ZKSF that means six processors from Rigetti, IQM, IonQ, AQT and QuEra, priced per task and per shot.

What is quantum computing used for?

Simulating molecules and materials for chemistry and drug discovery, optimisation in finance, logistics and manufacturing, quantum machine learning, and cryptography, where it threatens today's public key encryption. Our applications pages publish measured runs for sixteen of them.

Will quantum computers replace classical computers?

No. They are specialists for particular problems and will work alongside classical computers, which stay faster and cheaper for almost everything else.

How much does it cost to use a quantum computer?

From $0.0001 a job on a simulator and from just over $0.30 a task on real hardware, depending on the processor and the number of shots. The cost calculator prices any budget.

Do I need to know physics to start?

No. You can build and run circuits in the browser simulator without any maths, and the dictionary, tutorials and algorithm examples fill in the theory as you go.

Everything here is runnable on your own circuit. Try it in the console