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Google and D-Wave Systems say theyve achieved a new milestone in the world of quantum computing.

In a press release, D-Wave says its quantum device has far outpaced a classical computer in a direct competition to complete a difficult computational problem.

The device successfully modeled the behavior of a spinning two-dimensional quantum magnet, and was able to complete the simulation at breakneck speed.

In collaboration with scientists at Google, demonstrating a computational performance advantage, increasing with both simulation size and problem hardness, to over 3 million times that of corresponding classical methods.

Notably, this work was achieved on a practical application with real-world implications, simulating the topological phenomena behind the 2016 Nobel Prize in Physics.

Quantum devices leverage the unique properties of quantum physics to perform certain calculations at revolutionary speeds.

D-Wave says its study proves that quantum computers can more efficiently and effectively tackle tough simulations.

What we see is a huge benefit in absolute terms, with the scaling advantage in temperature and size that we would hope for.

Quantum computing threatens to break the cryptographic algorithms that keep the internet and crypto assets secure. Ripple CTO Davis Schwartz, says he believes developers have about eight years to develop quantum-proof methods to keep digital infrastructures secure.

Featured Image: Shutterstock/Yurchanka Siarhei

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Google Teams With D-Wave in Massive Quantum Computing Leap, Cracking Simulation Problem - The Daily Hodl

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenbergan associate professor in the department of applied mathematics and computer science at the Technical University of Denmarkhad published online, when he discovered their findings had unwittingly given away a solution to a centuries-old graph problem.

Holm, an assistant professor of computer science at the University of Copenhagen, was relieved no one had caught the solution first. It was a real Eureka! moment, he says. It suddenly seemed obvious.

Holm and Rotenberg were trying to find a shortcut for determining whether a graph is planarthat is, if it could be drawn flat on a surface without any of its lines crossing each other (flat drawings of a graph are also called embeddings).

Putting it very bluntly, we formally quantified why something is a terrible drawing.

To mathematicians, a graph often looks different than what most of us are taught in school. A graph in this case is any number of points, called nodes, connected by pairwise relations, called edges. In other words, an edge is a curve that connects two nodes. Under this definition, a graph can represent anything from the complex wiring inside a computer chip to a road map of a city, in which the streets of Manhattan could be represented as edges, and their intersections represented as nodes. The study of such graphs is called graph theory.

Engineers need to find planarity in a graph when, for example, they are designing a computer chip without a crossed wire. But assessing for planarity amid the addition and removal of edges is difficult without drawing the graph yourself and trying not to cross any lines (See The Three Utilities Problem below, which was originally published in an issue of The Strand Magazine in 1913).

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Assessing for planarity becomes even more complicated in larger graphs with lots of nodes and edges, says Rotenberg. This is a real-world issue. Quantum computer chips, for instance, are highly advanced, and finding efficient ways to assess their planarity without wasting time and money is crucial to their development.

These three houses each need access to water, gas, and electricitybut for safety reasons the lines connecting the utilities and houses cannot cross. Grab a sheet of paper, draw out this scenario, and try to connect all three houses to all three utilities without any two lines crossing. Check the solution at the bottom of this page when you think you have the right answer.

In their original 2019 paper published on the preprint server arXivwhere research often first sees the light of day before peer reviewHolm and Rotenberg classified a type of embedding called a balanced or good embedding.

Holm explains that these good embeddings tend to balance the [time] costs of inserting edges so that no possible edge insertion costs too much compared to the rest. This is a concept borrowed for balanced decision trees in computer science, which are designed with evenly dispersed branches for minimized search time. Put another way, good embeddings are easier to add new edges to without violating planarity.

If you were to look at it, Holm says, a good embedding would be simple, unconvoluted. The standard example is the so-called Ladder Graph. A balanced embedding of this graph looks exactly like a ladder. But Holm says: In an unbalanced embedding, it is hardly recognizable.

It seems subjective to say the Ladder Graph is good and its alternatives are bad, but Holm and Rotenberg articulated in their paper why those statements were mathematically true. Putting it very bluntly, we formally quantified why something is a terrible drawing, says Rotenberg, referring to a bad embedding. What the pair didnt realize at the time was that their class of good embeddings played an essential role in speeding up the process of dynamic planarity testing.

When adding a new edge to a planar graph is required, there are two scenarios: There is a safe way to add the edge, possibly after modifying the drawing, or no drawing admitting the edge exists. But in some cases, the embedding of a graph itself might be disguising a way the edge could be inserted in planar fashion. To reveal those alternative paths, mathematicians flip an embedding to change its orientation while keeping it mathematically identical, because the relationship between the connected nodes and edges hasnt changed.

These flips might make it possible to add edges between two newly arranged nodes, edges that would have otherwise violated planarity. Holm and Rotenberg discovered the flips that lead to successful edge insertion and deletion tended to fall into their class of so-called good embeddings. Similarly, these good embeddings require fewer flips overall to successfully add new edges. A win-win.

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The pair have suggested numerous applications for their work, including chip design, surface meshes, and road networks, but Rotenberg has admitted: What attracts us to this problem is its puzzle-like nature. The two are cautious to predict more commercial applications because completing flips in real-world graph designs can be challenging.

However, they say that their approach to assessing dynamic graphs (i.e., graphs that change via insertions and deletions) could impact how mathematicians approach similar problems. Essentially, while their algorithm assesses planarity, it also tracks and calculates changes to the graphs, performing what is called a recourse analysis, says Rotenberg.

But such data gathering isnt superfluous. Rotenberg argues their solution shows that recourse analysis could have algorithmic applications in addition to being interesting in its own right, because here, it led to their efficient planarity test.

Analyzing dynamic mathematical concepts is an open field, she says, but therein lies the potential. The breakthroughs might have already happenedtheyre just hidden in the process.

Solution to the Three Utilities Problem: Its actually impossible in two-dimensional space.

Editor's Note: This story first appears in the March/April 2021 issue of Popular Mechanics magazine.

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The Three Utilities Problem | Graph Theory Breakthrough - Popular Mechanics

Quantum computers could one day replace silicon chips, just like the transistor once replaced the vacuum tube. But for now, the technology required to develop such a quantum computer is beyond our reach. Most research in quantum computing is still very theoretical.

The most advanced quantum computers have not gone beyond manipulating more than 16 qubits, meaning that they are a far cry from practical application. However, the potential remains that quantum computers one day could perform, quickly and easily, calculations that are incredibly time-consuming on conventional computers. Several key advancements have been made in quantum computing in the last few years. Let's look at a few of the quantum computers that have been developed.

Los Alamos and MIT researchers managed to spread a single qubit across three nuclear spins in each molecule of a liquid solution of alanine (an amino acid used to analyze quantum state decay) or trichloroethylene (a chlorinated hydrocarbon used for quantum error correction) molecules. Spreading out the qubit made it harder to corrupt, allowing researchers to use entanglement to study interactions between states as an indirect method for analyzing the quantum information.

In March, scientists at Los Alamos National Laboratory announced the development of a 7-qubit quantum computer within a single drop of liquid. The quantum computer uses nuclear magnetic resonance (NMR) to manipulate particles in the atomic nuclei of molecules of trans-crotonic acid, a simple fluid consisting of molecules made up of six hydrogen and four carbon atoms. The NMR is used to apply electromagnetic pulses, which force the particles to line up. These particles in positions parallel or counter to the magnetic field allow the quantum computer to mimic the information-encoding of bits in digital computers.

Researchers at IBM-Almaden Research Center developed what they claimed was the most advanced quantum computer to date in August. The 5-qubit quantum computer was designed to allow the nuclei of five fluorine atoms to interact with each other as qubits, be programmed by radio frequency pulses and be detected by NMR instruments similar to those used in hospitals (see How Magnetic Resonance Imaging Works for details). Led by Dr. Isaac Chuang, the IBM team was able to solve in one step a mathematical problem that would take conventional computers repeated cycles. The problem, called order-finding, involves finding the period of a particular function, a typical aspect of many mathematical problems involved in cryptography.

Scientists from IBM and Stanford University successfully demonstrated Shor's Algorithm on a quantum computer. Shor's Algorithm is a method for finding the prime factors of numbers (which plays an intrinsic role in cryptography). They used a 7-qubit computer to find the factors of 15. The computer correctly deduced that the prime factors were 3 and 5.

The Institute of Quantum Optics and Quantum Information at the University of Innsbruck announced that scientists had created the first qubyte, or series of 8 qubits, using ion traps.

Scientists in Waterloo and Massachusetts devised methods for quantum control on a 12-qubit system. Quantum control becomes more complex as systems employ more qubits.

Canadian startup company D-Wave demonstrated a 16-qubit quantum computer. The computer solved a sudoku puzzle and other pattern matching problems. The company claims it will produce practical systems by 2008. Skeptics believe practical quantum computers are still decades away, that the system D-Wave has created isn't scaleable, and that many of the claims on D-Wave's Web site are simply impossible (or at least impossible to know for certain given our understanding of quantum mechanics).

If functional quantum computers can be built, they will be valuable in factoring large numbers, and therefore extremely useful for decoding and encoding secret information. If one were to be built today, no information on the Internet would be safe. Our current methods of encryption are simple compared to the complicated methods possible in quantum computers. Quantum computers could also be used to search large databases in a fraction of the time that it would take a conventional computer. Other applications could include using quantum computers to study quantum mechanics, or even to design other quantum computers.

But quantum computing is still in its early stages of development, and many computer scientists believe the technology needed to create a practical quantum computer is years away. Quantum computers must have at least several dozen qubits to be able to solve real-world problems, and thus serve as a viable computing method.

For more information on quantum computers and related topics, check out the links below.

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Today's Quantum Computers - Computer | HowStuffWorks

This result is the first experimental challenge against the extended Church-Turing thesis, which states that classical computers can efficiently implement any reasonable model of computation. With the first quantum computation that cannot reasonably be emulated on a classical computer, we have opened up a new realm of computing to be explored.

The Sycamore ProcessorThe quantum supremacy experiment was run on a fully programmable 54-qubit processor named Sycamore. Its comprised of a two-dimensional grid where each qubit is connected to four other qubits. As a consequence, the chip has enough connectivity that the qubit states quickly interact throughout the entire processor, making the overall state impossible to emulate efficiently with a classical computer.

The success of the quantum supremacy experiment was due to our improved two-qubit gates with enhanced parallelism that reliably achieve record performance, even when operating many gates simultaneously. We achieved this performance using a new type of control knob that is able to turn off interactions between neighboring qubits. This greatly reduces the errors in such a multi-connected qubit system. We made further performance gains by optimizing the chip design to lower crosstalk, and by developing new control calibrations that avoid qubit defects.

We designed the circuit in a two-dimensional square grid, with each qubit connected to four other qubits. This architecture is also forward compatible for the implementation of quantum error-correction. We see our 54-qubit Sycamore processor as the first in a series of ever more powerful quantum processors.

ApplicationsThe Sycamore quantum computer is fully programmable and can run general-purpose quantum algorithms. Since achieving quantum supremacy results last spring, our team has already been working on near-term applications, including quantum physics simulation and quantum chemistry, as well as new applications in generative machine learning, among other areas.

We also now have the first widely useful quantum algorithm for computer science applications: certifiable quantum randomness. Randomness is an important resource in computer science, and quantum randomness is the gold standard, especially if the numbers can be self-checked (certified) to come from a quantum computer. Testing of this algorithm is ongoing, and in the coming months we plan to implement it in a prototype that can provide certifiable random numbers.

Whats Next?Our team has two main objectives going forward, both towards finding valuable applications in quantum computing. First, in the future we will make our supremacy-class processors available to collaborators and academic researchers, as well as companies that are interested in developing algorithms and searching for applications for todays NISQ processors. Creative researchers are the most important resource for innovation now that we have a new computational resource, we hope more researchers will enter the field motivated by trying to invent something useful.

Second, were investing in our team and technology to build a fault-tolerant quantum computer as quickly as possible. Such a device promises a number of valuable applications. For example, we can envision quantum computing helping to design new materials lightweight batteries for cars and airplanes, new catalysts that can produce fertilizer more efficiently (a process that today produces over 2% of the worlds carbon emissions), and more effective medicines. Achieving the necessary computational capabilities will still require years of hard engineering and scientific work. But we see a path clearly now, and were eager to move ahead.

AcknowledgementsWed like to thank our collaborators and contributors University of California Santa Barbara, NASA Ames Research Center, Oak Ridge National Laboratory, Forschungszentrum Jlich, and many others who helped along the way.

Today we published the results of this quantum supremacy experiment in the Nature article, Quantum Supremacy Using a Programmable Superconducting Processor. We developed a new 54-qubit processor, named Sycamore, that is comprised of fast, high-fidelity quantum logic gates, in order to perform the benchmark testing. Our machine performed the target computation in 200 seconds, and from measurements in our experiment we determined that it would take the worlds fastest supercomputer 10,000 years to produce a similar output.

Each run of a random quantum circuit on a quantum computer produces a bitstring, for example 0000101. Owing to quantum interference, some bitstrings are much more likely to occur than others when we repeat the experiment many times. However, finding the most likely bitstrings for a random quantum circuit on a classical computer becomes exponentially more difficult as the number of qubits (width) and number of gate cycles (depth) grow.

The Sycamore ProcessorThe quantum supremacy experiment was run on a fully programmable 54-qubit processor named Sycamore. Its comprised of a two-dimensional grid where each qubit is connected to four other qubits. As a consequence, the chip has enough connectivity that the qubit states quickly interact throughout the entire processor, making the overall state impossible to emulate efficiently with a classical computer.

The success of the quantum supremacy experiment was due to our improved two-qubit gates with enhanced parallelism that reliably achieve record performance, even when operating many gates simultaneously. We achieved this performance using a new type of control knob that is able to turn off interactions between neighboring qubits. This greatly reduces the errors in such a multi-connected qubit system. We made further performance gains by optimizing the chip design to lower crosstalk, and by developing new control calibrations that avoid qubit defects.

We designed the circuit in a two-dimensional square grid, with each qubit connected to four other qubits. This architecture is also forward compatible for the implementation of quantum error-correction. We see our 54-qubit Sycamore processor as the first in a series of ever more powerful quantum processors.

ApplicationsThe Sycamore quantum computer is fully programmable and can run general-purpose quantum algorithms. Since achieving quantum supremacy results last spring, our team has already been working on near-term applications, including quantum physics simulation and quantum chemistry, as well as new applications in generative machine learning, among other areas.

We also now have the first widely useful quantum algorithm for computer science applications: certifiable quantum randomness. Randomness is an important resource in computer science, and quantum randomness is the gold standard, especially if the numbers can be self-checked (certified) to come from a quantum computer. Testing of this algorithm is ongoing, and in the coming months we plan to implement it in a prototype that can provide certifiable random numbers.

Whats Next?Our team has two main objectives going forward, both towards finding valuable applications in quantum computing. First, in the future we will make our supremacy-class processors available to collaborators and academic researchers, as well as companies that are interested in developing algorithms and searching for applications for todays NISQ processors. Creative researchers are the most important resource for innovation now that we have a new computational resource, we hope more researchers will enter the field motivated by trying to invent something useful.

Second, were investing in our team and technology to build a fault-tolerant quantum computer as quickly as possible. Such a device promises a number of valuable applications. For example, we can envision quantum computing helping to design new materials lightweight batteries for cars and airplanes, new catalysts that can produce fertilizer more efficiently (a process that today produces over 2% of the worlds carbon emissions), and more effective medicines. Achieving the necessary computational capabilities will still require years of hard engineering and scientific work. But we see a path clearly now, and were eager to move ahead.

AcknowledgementsWed like to thank our collaborators and contributors University of California Santa Barbara, NASA Ames Research Center, Oak Ridge National Laboratory, Forschungszentrum Jlich, and many others who helped along the way.

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Google AI Blog: Quantum Supremacy Using a Programmable ...

If there's anemoji that perfectly encapsulates quantum computing, it's the exploding head.

Consider, for example, thatthe temperature of most quantum processing chips must be kept as close to absolute zero (roughly -460 degrees Fahrenheit) as possible. Or that some physiciststhinkquantum computing isthe first technology that allows useful tasks to be performed in collaboration between parallel universes.Or that a quantum computer recently made history go backward. True, it was only a simulation, but still brain blowing stuff.

Before we get carried away, though, lets consider the foundational basics. Classical computers operate using binary bits, storing data and running processes using ones and zeroes. Quantum machines, however, runon multi-state components called qubits, which can reach the superposition of essentially being both one and zero while also entanglingincombined states. In lay terms, that means quantum computerscan do lots of things typical computers can't, including crunching massive amounts of complex information faster than an over-caffeinated cheetah in a time-lapse video.

At this point, imagining those applications is a bit like daydreaming about Christmas in May:there's plenty of anticipation and even wonder, butthe big day itself remains a long way off. That's becauseso far, no one approach to quantum computing has proven ideal. Also, the key work of stabilizing those qubits is arduous and expensive.As theoretical computer scientist Scott Aaronson told Gizmodo, actually building a useful quantum computer is a massive technological undertaking.

Even so, an increasing number of companies including well-funded startups andseveralmajor players(think Google, IBM, Microsoft)that have partnered with research institutions to pool wallets and brain power are trying to close the gap between present and future. When quantum computing is perfected, they know, it will transform a host of industries:medicine, fusion energy, plasma science, climate change, electric vehicles, finance, artificial intelligence and (in rather scary ways) information security.

Which companywill lay claim to the first big quantum-computing breakthrough? Check out these 20 leading contenders.

Location: Austin, Texas

What it does: With apologies to poetic pioneer Peter Shor, the biggest personality in quantum computing is probably William Hurley, aka Whurley, the Austin serial entrepreneur who heads up Strangeworks. The impressively bearded founder is well-known for headline-grabbing stunts, like the time he zapped an intern with a Taser-strapped drone. But hes a serious quantum evangelist whose company completed a $4 million seed round last year, while eyeing a near-term goal of launching quantum-application subscription services for the aerospace, energy, pharmaceutical and finance industries. Fun fact: Hes also the coauthor of Quantum Computing for Babies.

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Location: Cambridge, Mass.

What it does: Quantum Circuits isnt the only Ivy League quantum spinoff. Using proprietary technology and exclusive algorithms developed at Harvard University, Zapata Computing not unlike QC Ware is building quantum software platforms with big-fish enterprise companies in mind. (A recent round of $21 million VC money will help the cause.) According to Forbes, Zapata is making virtual chemistry, machine learning and optimization its first-wave QC focal points.

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Location: Boulder, Colo.

What it does:While you cant exactly hit up TaskRabbit when your quantum computer needs help, service and product support are must-haves for developers. ColdQuanta manufactures various quantum components like vacuum systems and processors to keep atoms brutally cold, which aids the all-important work of cutting down qubit motion and noise. The startup recently brought on D-Wave veteran Bo Ewald as president and CEO.

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Location: Berkeley, Calif.

What it does: When XPRIZE founder Peter Diamandis listed what he believes to be the three major players in the push toward quantum supremacy in America, he named two titans (Google and IBM) and one startup: Rigetti Computing. Rigetti recently announced the public beta of its Quantum Cloud Services platform, which the company calls the first cloud service powered by quantum computing.

Location: College Park, Md.

What it does: Its tempting to reduce quantum computing to a simple numbers game, namely number of total qubits. The truth is, you have to consider qubit qualityrather than mere quantity. Still, when IonQ last year bested the qubit counts of IBM (50)and Google(72) with its 160-qubit processor, jaws dropped. Whereas most QC companies employ superconductors, IonQ which recently welcomed famed Amazon Prime boss Peter Chapman as CEO is pioneering the trapped-ion method through which ions are isolated in a vacuum chamber and subatomic particles are cooled via lasers, eliminating the need for the gigantic copper-looking contraptionsthat are common to quantum computers.

Location: Palo Alto, Calif.

What it does: A developer ofenterprise software for quantum computers, QC Ware counts Citi and Goldman Sachs among its investors. It has alsoteamed with a number of other outfits, includingD-Wave, IBM and, perhaps most notably, Google, whose open-source quantum interface Cirq was recently integrated into QC Wares cloud service.

Location: Armonk, N.Y.

What it does: Most quantum computing developers are pursuing the universal gate model, rather than, say, annealers (more on those later). The gate model puts qubits into circuits, not unlike traditional ones-and-zeros bits, via superconducting. Tech mainstay IBM is a leader in this lane, having developed at least eight gate-model prototypes, one as high as 50 qubits. (Thats a lot.) Earlier this year, IBM unveiled the Q System One, a step forward for stability and commercial research. It also recently partnered with Exxon Mobil to work on a network that, both parties hope, could lead to innovations in predictive climate models and electric grid management.

Location: Burnaby, B.C.

What it does: About that annealing. In the simplest terms, the quantum annealing process aims to return the lowest possible energy solutions by focusing mostly on questions of optimization. D-Wave Systems which recently announced their least noisy entry, the Pegasus is most synonymous with this approach. But is it actually quantum? Not really, some critics say. It doesnt operate on the gate model, which means Pegasus ultra-high qubit rate isnt really all that comparable to almost all of D-Waves contemporaries. Still, its hybrid software developments could very well help advance QC's thorny question of scalability.

Location: Washington, D.C.

What it does: Quantum computing is poised to revolutionize fintech, where its supercomputing prowess will simplify risk management, credit scoring, portfolio optimization and just about every other facet of finance. (You wont be surprised to learn that Goldman Sachs invests in D-Wave Systems.) Data analytics company and IBM partner QxBranch is building quantum computing software rather than hardware that could prove a boon in this context. Another predictive bona fide: its poised to out-predict NateSilver, creating gobsmackingly sophisticated election forecasting models.

Location: New Haven, Conn.

What it does: Founded in 2015 by three veterans of Yales applied physics department, Quantum Circuits unveiled its testing facility this past January. The cofounders are considered trailblazers in quantum computing with superconducting circuits (hence the name), and the company is illustrative of the science-meeting-tech, academia-meeting-big-business cross-pollination that marks the quest for quantum supremacy.

Location: Berkeley, Calif.

What it does: The exponential boost in data-processing power that quantum computing holds over classical computing opens the door for a, well, quantum leap in pharmaceutical research. Bleximo which raised $1.5 million in seed funding and was named to the Cyclotron Road fellowship last year has singled out QC-enabled medical development as its first practical goal. To that end, the company is trying to develop what it calls quantum accelerator, essentially quantum-based computational systems designed for a single, specific application, its narrower use being a tradeoff for greater performance.

Location: Vancouver, B.C.

What it does: On the topic of pharma research, 1QBit made waves when it partnered with two major players: tech consultants Accenture and biotech multinational Biogen. The ultimate goal is to use quantum computing to create a molecular modeling application, which in turn couldlead to breakthroughs in drug development to treat neurodegenerative conditionslike dementia. The early-entry quantum company, founded in 2012 and described by Forbes as the worlds first dedicated quantum computing focused commercial business, also teamed with Dow Chemical Company in 2017 to explore how nature-simulating QC might propel materials science.

Location: Toronto

What it does: This well-financed Toronto startup is notable for exploring photonic quantum computing, which uses the quantum properties of light particles to run. Last year it released free, open-source software that basically lets anyone run commands on publicly accessible, cloud-based quantum computers, like the IBM Q Experience or the University of Bristols Quantum in the Cloud part of a wider push to familiarize enthusiasts with QC operational basics. More recently, Xanadu announced a whopping $32 million in early stage financing.

Location: Santa Clara, Calif.

What it does: Venerable processor-makerIntel has been seriously exploring quantum computing since at least 2015, when it partnered with leading Dutch research group QuTech. Among its most recent contributions to the cause: a first-of-kind QC testing device, dubbeda cryoprober. The tool purportedly can (relatively) quickly measure qubit characteristics even at the hundreds-below-zero temperatures often required for qubit stabilization, speeding up a process that once took days just to gather small amounts of data. As for the long term, according to its director of quantum hardware,Intel is eyeing nothing less than a million-qubit system the number at which truly transformational power will occur.

Location: Waterloo, Ont.

What it does: RSA security encryption relies on prime numbers to secure your information. More specifically, it relies on the fact that prime factorization of large numbers is prohibitively time-consuming for would-be hackers. But if a quantum computer powerful enough to run Shors factorization algorithm ever came along, all that security essentially vanishes. This looming threat has birthed an entire sub-industry dedicated to patching potentially huge vulnerabilities. Isara has emerged as an early frontrunner, working to develop security systems that essentially allow communication between classical and quantum algorithms.

Location: Mountain View, Calif.

What it does: The as-yet still-theoretical concept of quantum supremacy is easily explained (the power ofquantum computers to perform tasks that classical computers can't) and extremely difficult to achieve. Some developers claim its arrival is imminent; others say its several years away. Googles Research wing, which has partnered with NASA to win the great quantum supremacy races, appears to be in the former camp. Hartmut Neven, director of the tech giants Quantum Artificial Intelligence lab, recently told Quanta that quantum computers are growing doubly exponentialwhere it looks like nothing is happening, nothing is happening, and then whoops, suddenly youre in a different world.

Location: Redmond, Wash.

What it does: While most quantum-computing research hitches its qubits to the superconductor/solid-state wagon or, to a lesser degree, trapped ions, Microsoft rolls along a third route: topological qubits. These qubits would sidestep so many pesky stability requisites (those mind-bogglingly cold temps, no physical vibrations) by splitting an electron essentially, double anti-interference protection and exhibiting two ground states (a.k.a. ground state degeneracy). We say would, however, because the process still remains strictly theoretical.

Location: Charlotte, N.C.

What it does: Despite years of gestation, this many-tentacled conglomerate only recently peeled back the lab curtains on its quantum efforts. Somewhat surprisingly, Honeywell is going the less-traveled trapped-ion route, similar to IonQ. Honeywell runs its trap system with ytterbium atoms, which it claims has a leg up over solid-state competitors. Because each of these atoms is identical, defined in nature by its atomic structure, our system can be uniformly formed and controlled more easily and quickly compared to alternative systems that do not directly use atoms, says president Tony Uttley, a former operations manager at NASA. It was apparently enough to convince the Canadian Space Agency, which recently inked a multi-million deal with Honeywell to run a satellite mission to test quantum encryption.

Location: Berkely, Calif.

What it does: As its names hints, Atom Computing uses qubits made from neutral atoms, described by Science as a dark horse candidate in the quantum-computing sweepstakes. Backed by at least $5 million in venture capital and founded by Benjamin Bloom, a former senior quantum engineer at Rigetti and member of the team that smashed the atomic clock record, Atom hopes its novel approach will lead to scalable beyond-super computers that advance pharmaceutical research, computational chemistry and more.

Location: Toronto

What it does: North of the border, the Creative Destruction Lab non-profit has incubated several notable quantum alumni, including Xanadu, D-Wave partners Solid State AI and this forward-thinking biotech startup. A Rigetti partner, ProteinQure uses quantum computing and machine learning to computer-simulate designs for protein-based drugs.

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20 Quantum Computing Companies You Need To Know | Built In