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Quantum Computing 101: Introduction, Evaluation, and Applications

IonQ is building universal quantum computers based on trapped ion technology. This is an easy enough sentence to read, but a much harder one to understand! What are universal quantum computers, anyway? What are trapped ion quantum computers? How can you evaluate ours against others? What will they be used for?

We hope this primer will help you begin to answer some of these basic questions about quantum computers, and leave you better-prepared to understand and further investigate this world-changing technology.

How quantum computers compute

The easiest way to explain quantum computers is to use classical computers — the kind you’re reading this on — as a reference point. First, a potentially-surprising statement: even though classical computing has given us the most spectacular wave of technological innovation in human history, there are certain problems that it will never be able to solve.

It’s not an issue of power, it’s an issue of how classical computers do their calculations in the first place — even if Moore’s Law continues for another thousand years, they will still be no closer to modeling complex chemical interactions, optimizing delivery routes, and a variety of other problems.

Many of these problems have a similar quality: combinatorial explosion, where there are many different variables that all have to be weighed against each other to find an optimal solution. The time (or memory) needed to solve these grow exponentially as the number of variables increase, and this exponential explosion can rapidly overwhelm today's computers, which have to either guess-and-check every possible combination in turn (which could take billions of years), or else resort to imperfect and expensive approximations.

Quantum computers, on the other hand, have access to an entirely different kind of computational system which has the ability to solve these kinds of problems in far fewer steps, without having to try every solution sequentially. That computational system is quantum mechanics, the complex math that describes how atoms and other tiny particles behave and interact.

In a classical computer, we use bits, normally represented by small amounts of electrical current and combined via special gates (normally created with transistors) to perform calculations. Quantum computers have analogues to both of these concepts: classical bits become quantum bits, or qubits for short, and classical logic gates become quantum logic gates, which allow us to take advantage of quantum systems’ most powerful (and unintuitive) properties: superposition and entanglement.

We’ll start with the qubits. In a classical computer, a bit can either be a zero or a one; these are the only two options. Thanks to superposition, qubits can be a zero, a one, or a complex combination of both. You might hear this described as “zero and one at the same time.” This is a useful way to think about what’s going on, but it’s not quite right. It’s also not quite wrong. Superposition just doesn’t have a direct analogue in the non-quantum world; and it’s hard to explain exactly why without a longer explanation about quantum physics — one too long for this primer to cover. The important part is that it makes qubits far more powerful in their ability to store and calculate information than classical bits.

To make many qubits work together to solve a problem, we have to entangle them, using a different kind of quantum logic gate. Once entangled, the two qubits can no longer be described independently; in fact, for every additional qubit you entangle, you need an exponentially-increasing amount of information to completely describe the state of the system. This isn’t the same as saying entanglement allows you to store or process an exponential amount of computationally-useful information; again, it’s a little more complicated than that, and the reason why involves a long trip into the emergent field known as quantum information theory.

What entanglement does allow is the creation of immense computational power — power that dramatically outstrips classical computers — with relatively few qubits. With even 60 or so high-quality qubits, you could run certain algorithms in minutes that would take the world’s largest supercomputer billions of years.

There are many ways to make, control, and entangle a qubit. The most commonly-known of these is the “superconducting” approach, where synthetic qubits are made using solid-state fabrication, similar to classical computer chips, cooled to extremely low temperatures, and controlled via microwave pulses. In recent months, advances using this method from companies like Google, IBM and others have grabbed headlines.

We use a different approach, using actual atoms as qubits. Our atomic qubits are ionized, trapped in 3D space by electromagnetic forces, and manipulated and entangled via lasers. We believe it offers several distinct advantages to solid-state and other less-well-known approaches, such as neutral atoms and spin dot qubits, and has the ability to be the lowest-error, most-powerful quantum computing platform in the market. If you want to go deeper, our hardware explainer page explains trapped ion technology in detail.

Judging the power of quantum computers

By now, you’ve hopefully got a sense of what a quantum computer is, what it does, and how many different ways there are to make one. Because these approaches are so different, comparing the power and ability of these systems can be challenging.

One common method for evaluating the power of quantum computers is to count qubits. Qubits are at the heart of every quantum computer, and so it seems like a reasonable approach, but it’s not actually very effective in giving a complete picture of those qubits’ ability to perform meaningful calculations.

Imagine comparing railroads solely on the number of miles of track they own. There are a number of other factors, such as where the railroad track runs, the freight volume, the level of interconnectedness and how much of the track is in good repair. Depending on the topology, it wouldn’t take many closed bridges in key locations to split the rail system in two, or even bring the whole operation to a standstill.

The same is true with quantum computers. To realistically judge a quantum computer’s power, we have to ask other questions about the qubits and the system as a whole; about quality, connectivity, coherence, and more. The complete list of possible questions is long, but we think these five get at most of the important information:

1. What is the qubits’ coherence time?

Coherence time is a measurement of how long a qubit can maintain its complex quantum state — essentially, a qubit’s lifespan. When a qubit is set up in some quantum mechanical state and left alone, how long before that state decays?

If we were able to keep a qubit perfectly isolated from its surrounding environment, it could theoretically hold its state forever. But, in practice, even the slightest perturbation will collapse this delicate quantum state and ruin the computation entirely. It’s a matter of when, not if, and how long it takes is directly related to how well-isolated the qubit is. In a trapped-ion system, like IonQ’s, coherence time is usually measured in seconds to minutes; in solid state systems, it’s microseconds to milliseconds.

Coherence time matters for quantum computation not only as a way to understand how well-isolated the qubits are, but also as the total budget for computation. You have to complete all of your quantum operations before the qubits decohere and lose their information, so the longer the coherence time, the greater the capacity for long, complex algorithms, and the more valuable the computer is.

2. What is the qubits’ connectivity?

Connectivity in this case means the qubits’ ability to “talk” to each other via an entangling gate. In trapped ion systems, we have what’s called “complete” connectivity: any pair of qubits can make a gate in a single operation. In other technologies, such as superconducting quantum computers, only physically adjacent qubits can do so without using other qubits as intermediaries, introducing error and overhead that can reduce accuracy and computational power.

3. How identical are your qubits?

Qubits must be as identical as possible. When scaling a quantum computer past a trivial number of qubits, building reliable interactions between them becomes enormously difficult if they aren’t. If their resonant frequencies (or anything else!) are even slightly different, the calibration and tuning of each qubit and the way it interacts with every other qubit in the system quickly becomes a nightmare. In solid-state systems, even the slightest error in manufacturing one of their synthetic atoms can create immense issues. The trapped ion approach, however, uses actual atoms, making them inherently perfect and perfectly identical.

4. What is the gate fidelity?

Gate fidelity determines how many gates you can run in the first place, and that determines the size of the algorithms you can run. Like classical computers, logic gates are the basic building blocks of an algorithm. But unlike classical computers, quantum gates aren’t perfect yet, and the errors add up fast.

You’ll sometimes see these errors reported directly, as gate error rate, or you may see a metric called fidelity, which is the inverse of the error rate — a 1% gate error rate equals 99% fidelity, 0.5% error means 99.5% fidelity, and so-on. They answer the same question: when you perform a gate, how close is the end state to your desired state?

Error Rate

2 x 2

2 x 2 x 2 x 2 x 2 x 2 x 2





4 +- .004

512 +- 4


4 +- .20

512 +- 172


4 +- .80

512 +- 426

Critically, these errors compound as the size of the algorithm grows and more gates are performed (as seen above). As error rate increases, the depth of calculation becomes limited, and it’s not long before you have a nearly useless answer. It’s great to have lots of qubits, but if they have poor gate fidelity, your quantum computer isn’t very powerful. As you add qubits, you must improve gate fidelity to make it useful.

You might have heard about an error corrected qubit or logical qubit. These zero-error qubits are created by combining a number of physical qubits into a single "logical" qubit — how many depends on the fidelity of these physical qubits, so fidelity is still important — using complex error-correction algorithms. While these are likely the future of quantum computation, no one has been able to create one in hardware yet. Many great minds in academia, industry, and within IonQ itself are working on achieving this next great milestone.

5. How many qubits are there?

Finally, we can count qubits. Only when qubits are identical, with good coherence times and gate fidelities, does adding qubits make a quantum computer more powerful. In fact, it exponentially increases the computational power — every time you add a qubit, the computational system doubles in size. This allows us, in a sense, to extend Moore’s Law by adding only a single qubit a year. At IonQ, our goal is to double the number of qubits every year, producing a doubly-exponential growth in computing power.

Put together, this leads to a Quantum Goldilocks Rule:

  • A large number of qubits isn’t useful if the qubits are of low fidelity (and limited gate depth).

  • A small number of qubits with high fidelity isn’t useful either.

  • A quantum computer that has a sufficient fidelity to allow at least n x n gates (where n is the number of qubits) is just right.

Game-changing use cases

Once you’ve evaluated those five factors to judge the power of a quantum computer, it’s time to begin to explore the applications that make the most sense to run on it.

The reality is, few systems are powerful enough to address real-world user applications in a way that offers a quantum speedup at all, let alone a commercially meaningful one. But, hardware is progressing fast, and this won’t be true for much longer. The time to find the game-changing applications is now, and many companies have already begun. In 2019, numerous leading companies across a variety of industries began examining highly-complex real-world problems that might be solved with quantum computers. With the availability of quantum computing on the cloud, we believe this number — and the applications they find — will skyrocket.

As quantum computers become more accessible and more powerful, there will be a cultural shift as companies start to envision tackling even more ambitious sets of problems:

  • Pharmaceutical companies will seek to discover new kinds of drugs, and be able to speed up early-stage development by being able to simulate much more complex compounds, therapies, and interactions.

  • The agriculture industry could save massive amounts of money—and reduce impact on the climate—by re-tooling the process used to create fertilizer.

  • Governments could better address climate change by figuring out more efficient ways to capture and remove carbon and other greenhouse gases from the atmosphere.

  • The fintech industry will leverage quantum technology to develop valuable portfolios based on vast collections of assets with interconnected dependencies. It could also be used to better detect fraud.

  • Logistics companies will be able to save tremendous amounts of money by optimizing the routes their drivers take. The average driver makes 120 deliveries a day, meaning the total possible combinations he or she takes is a number with 199 digits--larger than how old the Earth is in nanoseconds. It’s estimated the company could save $30 million by figuring out how a single driver can cover one less mile a day. Multiply that across its entire network, and the savings could be staggering.

  • Quantum hardware companies will even turn the technology inward, using quantum computers to look for better qubits and more efficient quantum algorithms.

We don’t know for certain if quantum computers will be able to handle all of these applications. But the potential is there—if not for these exact problems, then ones like them. And ones we cannot even begin to conceptualize.

Nor do we know precisely when these computers will deliver on their immense promise. But we know they’re going to have a huge impact, and we suspect it’ll be sooner than you might think. Quantum is the natural evolution of computing, and will allow us to address problems we’ve long had to ignore because we didn’t have the power.

Quantum computing is going to give companies new superpowers. It will be a true game changer for entire industries. Sure, we don’t exactly know what those superpowers will be, but even so, would you turn down the opportunity to find out?