Monthly Archives: July 2020

Quantum technology and quantum computing more specifically has become quite the popular topic in national security circles. The extraordinary level of interest emerges from the potential impacts of quantum computers on information security and general issues of international strategic technological advantage. While academic strength in quantum computing research is globally distributed, U.S. industry maintains substantive international leadership. The most significant technical demonstration of state-of-the-art quantum computing was reported by Google this year, and the first cloud-based quantum-as-a-service offerings are available from IBM and Rigetti, with forthcoming services announced by Amazon Web Services and Microsoft.

With these developments, quantum computing has been identified as a possible target technology for export controls as well as foreign-investment review in emerging tech companies. And the new U.S. National Quantum Initiative is framed around strategic competition and even directly addresses the notion of a technological race with China.

And so now, you Madam, Mister, or Doctor National Security Professional need to understand and speak intelligently about how this technology impacts your portfolio. Where should you begin and how? What are the important lessons to embrace and pitfalls to avoid as you begin your educational journey?

It is easy to find yourself going down the wrong path; there are many new analysts offering expert advice on the technology underlying quantum computing. Many of them merit your skepticism. A combination of technical complexity and competitive media positioning has led to a wide variety of pervasive misconceptions in the field. Watching these flawed and false narratives take off in the national security world that I have worked in for years at DARPA, working with the intelligence community, and now at my own company has been frustrating. And so, as someone with 20 years of experience designing, building, and optimizing quantum computing hardware, I aim to offer friendly advice and insights that arent readily available otherwise.

Learn the Basics

Following many years in which information was found only in specialist technical journals, high-quality educational resources supporting new entrants to the field are finally emerging. I offer some of the better ones below. Turn to them in order to gain proficiency in the underlying technology at either a contextual or technical level, no matter what level of technical expertise you have (or lack).

Q-CTRL the organization I founded and lead has produced an introductory video series for those who have limited background knowledge and are seeking to orient themselves in the field. This is a great place to start if youve encountered various keywords in quantum computing such as qubit, NISQ, or quantum advantage and now want to understand their meaning and context at a high level.

Quantum Computing for the Very Curious is an excellent online e-book introducing quantum computing in an accessible but technical fashion. Its prepared by Michael Nielsen, one of the most recognized textbook authors in the field, and covers material from qubits to universal quantum computing.

The online Qiskit textbook from IBM provides a detailed technical overview of this material, with a focus on programming quantum computers for future quantum developers.

Various supporting tools exist to help build intuition for quantum computing, including BLACK OPAL from my organization, the IBM Quantum Experience, and the Quantum User Interface from the University of Melbourne.

The Massachusetts Institute of Technologys xPRO offers an online course in quantum computing built and taught by actual leading practitioners, such as Peter Shor, Will Oliver, and Isaac Chuang (not consultants, dabblers, or marketers).

Finally, if youd like a broader overview of the intersection between quantum technology and national security, I wrote a primer on quantum technology for national security professionals with Richard Fontaine in these virtual pages.

Start with the History

Many in national security circles became familiar with quantum information and quantum technologies only in the last few years. Understanding the origins of U.S. government activity in the field is essential to evaluating the national security landscape around quantum computing today.

The history of the field is traced back to early intelligence community investments in open university research, following public announcements surrounding the development of Shors algorithm (an algorithm potentially enabling quantum computers to attack public key cryptosystems, named after Peter Shor). Since the late 1990s, the vast majority of participants in the international research field has been supported by competitive programs sponsored by the U.S. Army Research Office and the Intelligence Advanced Research Projects Activity (and its predecessor organizations, the Advanced Research and Development Activity and the Disruptive Technology Office). Ultimately, this targeted, highly competitive funding has been foundational to the development of the international quantum computing research community.. Very broadly, this technical leadership (as measured by recognizable research programs and/or publicly acknowledged funding) has come from the United States, United Kingdom, Germany, Austria, Switzerland, Australia, the Netherlands, and Canada. Much more recently, China has risen independently as it has made quantum information matter of national priority. Singapore and Russia have also made strategic investments in quantum technology.

What should we take from this history? First, openness, collaboration, and international engagement with allied nations have been central to the success we have seen in building this technological discipline. This success, a global public good, is the result of American international leadership. And it therefore risks being undermined by aggressive actions to curtail international collaboration, especially as so much exploratory science remains to be undertaken. Emerging nationalist sentiment seeking to limit international support for research among allies or to add new export control regimes on immature technologies are regressive. Second, the U.S. defense and intelligence communities have played a critical and irreplaceable role in the field. Todays U.S. National Quantum Initiative is seeking to establish expanded research activity through programs administered by new organizations, including the National Science Foundation and Department of Energy through the national labs. The foundational leadership from within the Department of Defense and the intelligence community places the United States at a strategic advantage in knowledge and internal capability within government. Finally, aside from long-term research and development efforts at industrial organizations such as IBM, large-scale industry-led programs have only emerged since about 2013 at Microsoft, Google, and other tech giants, often grown by acquiring academic research teams. Similarly, the boom in quantum technology startups largely derived from academic programs has been growing for about five years. Notably, all of the relevant industrial research leaders and efforts have had substantial overlap with Army Research Office and IARPA programs. This makes clear both the connectivity of personnel running these programs with research leaders, and demonstrates how these government funding initiatives have been instrumental in seeding todays quantum industry.

True Technical Expertise Is Out There, So Reach Out

Maybe youve been asked to write a memo on something at the intersection of national security and quantum technology. Or maybe youre an international security scholar looking to research and write about the implications of the second quantum revolution. Why not collaborate with, or at least reach out to, someone with technical expertise? Quantum computing is not an easy field to understand, even for sharp minds with a deep understanding of other technical topics. So, look (and ask) before you leap.

Most contemporary leaders in the field have built their entire careers in quantum computing and have come up through advanced Ph.D.-level training programs at major universities around the world. Looking across the growing quantum computing startup ecosystem, almost every chief executive officer, chief technology officer, or other sort of senior executive has come from a senior academic appointment. Similarly, the broad U.S. industrial sector in quantum computing is heavily populated with seasoned experts in the field. Many of us have worked with the U.S. defense and the intelligence communities for years. And this cross-sector collaboration means there are a number of practitioner-experts working in government. Substantive expertise exists within various organizations, including the National Security Agencys Laboratory for Physical Sciences, the Sandia National Laboratories, the Lawrence Berkeley National Laboratory, the National Institute of Standards and Technology (having generated multiple Nobel laureates in quantum physics), the U.S. Army Research Laboratory, and the Army Research Office.

Unfortunately, growth in the field has led to a commensurate growth in the number of consultants and analysts claiming to be experts in quantum computing. Most of these voices are amateur observers, although there are a small number of formally trained experts who have crossed into analytical positions in defense contracting, management consulting, or the like. Third-party business analysts can bring valuable insights into the shape of emerging commercial markets or opportunities for quantum computing to contribute in novel sectors. Use caution when looking to such consultants for expert technical advice on the utility or functionality of quantum computers. As a general matter, beware the LinkedIn profile claiming expertise in quantum computing without evidence!

How to See Through the Hype

The level of true potential for quantum technology in national security and more broadly is profound and fully justifies major investments such as the U.S. National Quantum Initiative. However, this level of promise has inevitably led to hype in the popular media, company press releases, venture-capital newsletters, and (international) government program announcements. It is essential that in making an informed assessment you seek the truth beyond the hype.

The most important leading message is that quantum technology is a deep-tech field and represents a long-term strategic play; the benefits may be enormous in the national security space, but timescales to delivery remain measured in years and decade. We have recently seen an acceleration of commercial and public-sector interest and activity and there is no doubt that this is furthering progress but there has not been an obvious fundamental change in the pace of technological development. Quantum computing has been described erroneously as just engineering at this stage, where all we need to do to realize quantum advantage for useful problems is execute. While there is much room to incorporate lessons from the engineering community, creativity and serendipity remain essential.

Expert leaders in our community feel confident that within five to 10 years we may realize quantum advantage for a problem of general commercial interest. This would certainly be a profound demonstration, but it is supported by the (consistent) rate of progress since the early 2000s and the relatively small scale of machine we believe is needed to achieve this goal. By contrast, codebreaking using Shors algorithm remains a multi-decadal play because the scale of the system required is likely to be gigantic (thousands of high-performing logical qubits, each capable of performing billions of operations).

This highlights another essential piece of advice for quantum novices: caveat emptor. Question the messenger when reading media reports about technological breakthroughs. In many cases commercial and nationalist motives have clouded the landscape of media reporting on the true state of progress in the field. This is especially true at the intersection of quantum computing and national security for obvious reasons. For instance, in their excellent report, Elsa B. Kania and John Costello explain that quantum technology has clearly become a matter of national priority in China, but that it has become difficult to discern real progress from strategic hyperbole in state media. Unfortunately, the same can be true for corporate media releases closer to home. Many journalists have repeated press-release pronouncements without applying the skepticism the topic demands. National security professionals might then use such articles as a source, leaving an important debate ill-served. It is therefore important that such professionals seek validation of claims via primary-source information. This is of utmost importance in understanding the intersection between national security and quantum technology, as misunderstandings of the capabilities of the underlying technology can completely change the associated security implications.

As an example of such a negative impact on national security assessments, the combination of a rise in corporate and nationalist marketing and credulous media reporting has led to many misleading lay descriptions of how quantum technology operates in the security space. The research area perhaps most subject to misrepresentation is quantum communications, which has become an area of major Chinese investment and clear technical leadership. Quantum communications uses concepts of quantum physics (such as the destructive nature of measurement) in order to offer information security. In particular, these systems are theoretically provably secure a term that has a specific quantitative technical definition relating to the probability of eavesdropping in a nominally successful round of communication. This suggestive nomenclature has led to the broad use of popular terms such as unhackable communications or unbreakable quantum security. But these claims are specious. People have translated a technical definition (provably secure) into an accessible but incorrect lay term (unhackable or unbreakable) when, in fact, there is an entire subfield dedicated to cryptographic attacks on quantum communications systems. None of this means that advances in quantum communications wouldnt be enormously valuable, but it does reveal the shallow nature of some aspects of the popular narrative.

On a final and lighter note, its my pleasure to inform you that quantum radar is not likely to be an imminent threat to stealth technology as is sometimes claimed by Chinese media. There is global research interest in the application of quantum illumination to suppress certain kinds of technical noise in radar systems. It is possible that China has built functional prototypes and could in principle be far ahead of the United States and its allies, but there is no evidence that this has made Chinas radars able to detect stealthy or low-observable aircraft in ways they could not before. Public-domain, state-of-the art research from a Canadian team also publicly claiming they hope to defeat stealth technology does not support such claims. Demonstrated benefits show approximately two times improvement in imaging quality using quantum illumination at one-meter imaging distance in a laboratory. This is far from field-deployable, and a factor of two times improvement in imaging even if it did carry over to realistic distances and conditions does not necessarily render low-observable aircraft vulnerable. Nonetheless, media reporting on this topic has been breathless, even within national security publications. Unfortunately, the primary source material which could be used to raise doubts about claims surrounding quantum radar is highly technical and inaccessible to most analysts. While highly specific, this example illustrates how a lack of understanding of the technical material coupled with nationalistic media releases and credulous journalists can produce deleterious strategic assessments.

The advice I offer here is broad and aims to help national security professionals seeking to build a knowledge base in quantum technology. This is an essential undertaking for anyone seeking to engage meaningfully with this emerging and high-impact field.

Michael J. Biercuk is a professor of quantum physics and quantum technology at the University of Sydney and a chief investigator in the ARC Centre of Excellence for Engineered Quantum Systems. In 2017, he founded Q-CTRL, a quantum technology company for which he serves as CEO.

Image: Department of Defense (Photo by Nancy Wong, University of Chicago)

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Read Before Pontificating on Quantum Technology - War on the Rocks

The smallest conceivable length of time might be no larger than a millionth of a billionth of a billionth of a billionth of a second. That's according to a new theory describing the implications of the universe having a fundamental clock-like property whose ticks would interact with our best atomic timepieces.

Such an idea could help scientists get closer to doing experiments that would illuminate a theory of everything, an overarching framework that would reconcile the two pillars of 20th-century physics quantum mechanics, which looks at the smallest objects in existence, and Albert Einstein's relativity, which describes the most massive ones.

Related: The 18 biggest unsolved mysteries in physics

Most of us have some sense of time's passage. But what exactly is time?

"We don't know," Martin Bojowald, a physicist at Pennsylvania State University in University Park, told Live Science. "We know that things change, and we describe that change in terms of time."

Physics presents two conflicting views of time, he added. One, which stems from quantum mechanics, speaks of time as a parameter that never stops flowing at a steady pace. The other, derived from relativity, tells scientists that time can contract and expand for two observers moving at different speeds, who will disagree about the span between events.

In most cases, this discrepancy isn't terribly important. The separate realms described by quantum mechanics and relativity hardly overlap. But certain objects like black holes, which condense enormous mass into an inconceivably tiny space can't be fully described without a theory of everything known as quantum gravity.

In some versions of quantum gravity, time itself would be quantized, meaning it would be made from discrete units, which would be the fundamental period of time. It would be as if the universe contained an underlying field that sets the minimum tick rate for everything inside of it, sort of like the famous Higgs field that gives rise to the Higgs boson particle which lends other particles mass. But for this universal clock, "instead of providing mass, it provides time," said Bojowald.

By modeling such a universal clock, he and his colleagues were able to show that it would have implications for human-built atomic clocks, which use the pendulum-like oscillation of certain atoms to provide our best measurements of time. According to this model, atomic clocks' ticks would sometimes be out of sync with the universal clock's ticks.

This would limit the precision of an individual atomic clock's time measurements, meaning two different atomic clocks might eventually disagree about how long a span of time has passed. Given that our best atomic clocks agree with one another and can measure ticks as small as 10^(minus19) seconds, or a tenth of a billionth of a billionth of a second, the fundamental unit of time can be no larger than 10^(minus 33)seconds, according to the team's paper, which appeared June 19 in the journal Physical Review Letters.

"What I like the most about the paper is the neatness of the model," Esteban Castro-Ruiz, a quantum physicist at the Universit Libre de Bruxelles in Belgium who was not involved in the work, told Live Science. "They get an actual bound that you can in principle measure, and I find this amazing."

Research of this type tends to be extremely abstract, he added, so it was nice to see a concrete result with observational consequences for quantum gravity, meaning the theory could one day be tested.

While verifying that such a fundamental unit of time exists is beyond our current technological capabilities, it is more accessible than previous proposals, such as the Planck time, the researchers said in their paper. Derived from fundamental constants, the Planck time would set the tiniest measureable ticks at 10^(minus 44) seconds, or a ten-thousandth of a billionth of a billionth of a billionth of a billionth of a billionth of a second, according to Universe Today.

Whether or not there is some length of time smaller than the Planck time is up for debate, since neither quantum mechanics nor relativity can explain what happens below that scale. "It makes no sense to talk about time beyond these units, at least in our current theories," said Castro-Ruiz.

Because the universe itself began as a massive object in a tiny space that then rapidly expanded, Bojowald said that cosmological observations, such as careful measurements of the cosmic microwave background, a relic from the Big Bang, might help constrain the fundamental period of time to an even smaller level.

Originally published on Live Science.

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The universe's clock might have bigger ticks than we imagine - Livescience.com

Albert Einstein is often held up as the epitome of the scientist. Hes the poster child for genius. Yet he was not perfect. He was human and subject to many of the same foibles as the rest of us. His personal life was complicated, featuring divorce and extramarital affairs.

Though most of us would sell our in-laws to achieve a tenth of what he did, his science wasnt perfect either: while he was a founder of what came to be called Quantum Mechanics, he disagreed with other scientists about what it all meant, and he once thought he had proved that gravitational waves could not exist (an anonymous reviewer of his paper found his mistake and set him straight). Yet Einstein did create one thing that, as far as we can tell, is as correct as anything can be in science. That is his theory of gravity, called General Relativity.

He presented the theory to the world over four consecutive Wednesdays in November 1915 in lectures at the Prussian Academy of Sciences. Einstein was by then well respected in European physics circles, and one can imagine more than one person in the audience that November thinking that hed gone bonkers. Einsteins theory purported to replace the hugely successful 1687 gravity theory of Isaac Newton, which posited gravity as an attractive force between masses, with one where gravity was a result of the curving and warping of space and time by massive objects. And the evidence for this new theory? It managed to account for a tiny discrepancy of 120 kilometers per year in the spot where Mercury makes its closest approach to the Sun. The concepts behind this new theory were so radical and unfamiliar that it was said that only three people in the world understood it.

Yet a few people, like David Hilbert in Germany, Willem de Sitter in the Netherlands, and Arthur Eddington in England grasped the startling implications of this theory. Within four years, Eddington would propel Einstein to science superstardom with the announcement that his team of astronomers had detected the bending of starlight by the Suns gravity and had found that it agreed with Einsteins prediction, not Newtons. Newspapers around the world proclaimed, Einstein theory triumphs.

And that was pretty much it for General Relativity for the next 40 years. Because it was perceived as predicting only tiny corrections to Newtonian gravity, and as being virtually incomprehensible, the subject receded into the background of physics and astronomy. Einsteins theory was quickly superseded by other areas, such as nuclear, atomic and solid-state physics, which were viewed as of both fundamental and practical importance.

Yet in the 1960s, a remarkable renaissance began for Einsteins theory, fueled by discoveries such as quasars, spinning neutron stars (pulsars), the background radiation left over from the big bang, and the first black holes. Precise new techniques, exploiting lasers, atomic clocks, ultralow temperatures, and spacecraft, made it possible to put General Relativity to the test of experiment as never before. During the subsequent decades, researchers performed literally hundreds of new experiments and observations to check Einsteins theory. Some of these were improved versions of Einsteins original tests involving Mercury and the motion of light. Others were entirely new tests, probing aspects of gravity that Einstein himself had never conceived of. Many were centered in the solar system using planets and spacecraft, or in sophisticated laboratories on Earth. Others exploited systems called binary pulsars, consisting of two neutron stars revolving around each other. More recently we have witnessed numerous gravitational wave observations by the LIGO-Virgo instruments, the study of stars orbiting the supermassive black hole at the center of the Milky Way, and the stunning image of the black hole shadow in the galaxy M87.

In this vast and diverse array of measurements, scientists have not found a single deviation from the predictions of general relativity. When you consider that the theory we are using today is the same as the one revealed in November 1915, this string of successes is rather astounding. After more than 100 years, it seems Einstein is still right.

Will this perfect record hold up? We do know, for example, that the expansion of the universe is speeding up, not slowing down, as standard general relativity predicts. Will this require a radical new theory of gravity, or can we make do with a minimal tweak of general relativity? As we make better observations of black holes, neutron stars and gravitational waves, will the theory still pass the test? Time will tell.

Featured Image Credit: by Roman Mager via Unsplash

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Testing Einstein's theory of relativity | OUPblog - OUPblog

The smallest conceivable length of time might be no larger than a millionth of a billionth of a billionth of a billionth of a second. Thats according to a new theory describing the implications of the universe having a fundamental clock-like property whose ticks would interact with our best atomic timepieces.

In physics, time is typically thought of as a fourth dimension. But some physicists have speculated that time may be the result of a physical process, like the ticking of a built-in clock.

If the universe does have a fundamental clock, it must tick faster than a billion trillion trillion times per second, according to a theoretical study published June 19 in Physical Review Letters.

In particle physics, tiny fundamental particles can attain properties by interactions with other particles or fields. Particles acquire mass, for example, by interacting with the Higgs field, a sort of molasses that pervades all of space (SN: 7/4/12). Perhaps particles could experience time by interacting with a similar type of field, says physicist Martin Bojowald of Penn State. That field could oscillate, with each cycle serving as a regular tick. Its really just like what we do with our clocks, says Bojowald, a coauthor of the study.

Time is a puzzling concept in physics: Two key physics theories clash on how they define it. In quantum mechanics, which describes tiny atoms and particles, time is just there. Its fixed. Its a background, says physicist Flaminia Giacomini of the Perimeter Institute in Waterloo, Canada. But in the general theory of relativity, which describes gravity, time shifts in bizarre ways. A clock on the surface of the Earth ticks more slowly than one aboard an orbiting satellite, for example.

In attempts to combine these two theories into one theory of quantum gravity, the problem of time is actually quite important, says Giacomini, who was not involved with the research. Studying different mechanisms for time, including fundamental clocks, could help physicists formulate that new theory.

The researchers considered the effect that a fundamental clock would have on the behavior of atomic clocks, the most precise clocks ever made (SN: 10/5/17). If the fundamental clock ticked too slowly, these atomic clocks would be unreliable because they would get out of sync with the fundamental clock. As a result, the atomic clocks would tick at irregular intervals, like a metronome that cant keep a steady beat. But so far, atomic clocks have been highly reliable, allowing Bojowald and colleagues to constrain how fast that fundamental clock must tick, if it exists.

Physicists suspect that theres an ultimate limit to how finely seconds can be divided. Quantum physics prohibits any slice of time smaller than about 10-43 seconds, a period known as the Planck time. If a fundamental clock exists, the Planck time might be a reasonable pace for it to tick.

To test that idea, scientists would need to increase their current limit on the clocks ticking rate that billion trillion trillion times per second number by a factor of about 20 billion. That seems like a huge gap, but to some physicists, its unexpectedly close. This is already surprisingly near to the Planck regime, says Perimeter physicist Bianca Dittrich, who was not involved with the research. Usually the Planck regime is really far away from what we do.

However, Dittrich thinks that theres probably not one fundamental clock in the universe, but rather there are likely a variety of processes that could be used to measure time.

Still, the new result edges closer to the Planck regime than experiments at the worlds largest particle accelerator, the Large Hadron Collider, Bojowald says. In the future, even more precise atomic clocks could provide further information about what makes the universe tick.

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Scientists Say This Is the Smallest Unit of Time That Could Exist - lintelligencer

A trio of theorists has modeled time as a universal quantum oscillator and found an upper bound of 1033 seconds for the oscillators period. This value lies well below the shortest ticks of todays best atomic clocks, making it unmeasurable. But the researchers say that atomic clocks could be used to indirectly confirm their models predictions.

Physics has a time problem: In quantum mechanics, time is universal and absolute, continuously ticking forward as interactions occur between particles. But in general relativity (the theory that describes classical gravity), time is malleableclocks located at different places in a gravitational field tick at different rates. Theorists developing a quantum theory of gravity must reconcile these two descriptions of time. Many agree that the solution requires that time be defined not as a continuous coordinate, but instead as the ticking of some physical clock, says Flaminia Giacomini, a quantum theorist at Canadas Perimeter Institute for Theoretical Physics (PITP).

Such a fundamental clock would permeate the Universe, somewhat like the Higgs field from particle physics. Similar to the Higgs field, the clock could interact with matter, and it could potentially modify physical phenomena, says Martin Bojowald of Pennsylvania State University in University Park.

But researchers have yet to develop a theory for such a clock, and they still dont understand the fundamental nature of time. Aiming to gain insights into both problems, Bojowald and his colleagues imagined the universal clock as an oscillator and set out to derive its period. Their hope was that doing so might offer ideas for how to probe times fundamental properties.

In the model, the team considers two quantum oscillators, which act like quantum pendulums oscillating at different rates. The faster oscillator represents the universal, fundamental clock, and the slower one represents a measurable system in the lab, such as the atom of an atomic clock. The team couples the oscillators to allow them to interact. The nature of this coupling is different from classical oscillators, which are coupled through a common force. Instead, the coupling is imposed by requiring that the net energy of the oscillators remains constant in timea condition derived directly from general relativity.

The team finds that this interaction causes the two oscillators to slowly desynchronize. The desynching means that it would be impossible for any physical clock to indefinitely maintain ticks of a constant period, placing a fundamental limit on the precision of clocks. As a result, the ticks of two identically built atomic clocks, for example, would never completely agree, if measured at this precision limit. Observing this behavior would allow researchers to confirm that time has a fundamental period, Bojowald says.

Bojowald and his colleagues used the desynchronization property to derive an upper limit of 1033 seconds for the period of their fundamental oscillating clock. This limit is 1015 times shorter than the tick of todays best atomic clocks and 1010 times longer than the Planck time, a proposed length for the shortest measurable unit of time.

Resolving a unit of Planck time is far beyond current technologies. But the new model potentially allows researchers to get much closer than before, says Bianca Dittrich, who studies quantum gravity at PITP. Bojowald agrees. Using the timescale of the desynchronization between clocks to make time measurements, rather than the clocks themselves, could allow for measurements on much shorter timescales, he says.

Another bonus of choosing an oscillating quantum system as the model for a fundamental clock is that such a system closely resembles clocks used in the lab, says Esteban Castro-Ruiz, of the Universit Libre de Bruxelles, who studies problems involving quantum clocks and gravity. The resemblance is key, says Castro-Ruiz, because it brings the question of a fundamental period of time to a more concrete setting, where one can actually start thinking about measurable consequences.

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Study: The Period of the Universe's Clock - lintelligencer