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New Quantum Algorithms Finally Crack Nonlinear Equations

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Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what mathematicians call linear differential equations. But in nonlinear systems, interactions can affect themselves: When air streams past a jet’s wings, the air flow alters molecular interactions, which alter the air flow, and so on. This feedback loop breeds chaos, where small changes in initial conditions lead to wildly different behavior later, making predictions nearly impossible — no matter how powerful the computer.

“This is part of why it’s difficult to predict the weather or understand complicated fluid flow,” said Andrew Childs, a quantum information researcher at the University of Maryland. “There are hard computational problems that you could solve, if you could [figure out] these nonlinear dynamics.”

That may soon be possible. In separate studies posted in November, two teams — one led by Childs, the other based at the Massachusetts Institute of Technology — described powerful tools that would allow quantum computers to better model nonlinear dynamics.

Quantum computers take advantage of quantum phenomena to perform certain calculations more efficiently than their classical counterparts. Thanks to these abilities, they can already topple complex linear differential equations exponentially faster than classical machines. Researchers have long hoped they could similarly tame nonlinear problems with clever quantum algorithms.

The new approaches disguise that nonlinearity as a more digestible set of linear approximations, though their exact methods vary considerably. As a result, researchers now have two separate ways of approaching nonlinear problems with quantum computers.

“What is interesting about these two papers is that they found a regime where, given some assumptions, they have an algorithm that is efficient,” said Mária Kieferová, a quantum computing researcher at the University of Technology Sydney who is not affiliated with either study. “This is really exciting, and [both studies] use really nice techniques.”

The Cost of Chaos

Quantum information researchers have tried to use linear equations as a key to unlock nonlinear differential ones for over a decade. One breakthrough came in 2010, when Dominic Berry, now at Macquarie University in Sydney, built the first algorithm for solving linear differential equations exponentially faster on quantum, rather than on classical, computers. Soon, Berry’s own focus shifted to nonlinear differential equations as well.

“We had done some work on that before,” Berry said. “But it was very, very inefficient.”

The problem is, the physics underlying quantum computers is itself fundamentally linear. “It’s like teaching a car to fly,” said Bobak Kiani, a co-author of the MIT study.

So the trick is finding a way to mathematically convert a nonlinear system into a linear one. “We want to have some linear system because that’s what our toolbox has in it,” Childs said. The groups did this in two different ways.

Childs’ team used Carleman linearization, an out-of-fashion mathematical technique from the 1930s, to transform nonlinear problems into an array of linear equations.

Unfortunately, that list of equations is infinite. Researchers have to figure where they can cut off the list to get a good-enough approximation. “Do I stop at equation number 10? Number 20?” said Nuno Loureiro, a plasma physicist at MIT and a co-author of the Maryland study. The team proved that for a particular range of nonlinearity, their method could truncate that infinite list and solve the equations.

The MIT-led paper took a different approach. It modeled any nonlinear problem as a Bose-Einstein condensate. This is a state of matter where interactions within an ultracold group of particles cause each individual particle to behave identically. Since the particles are all interconnected, each particle’s behavior influences the rest, feeding back to that particle in a loop characteristic of nonlinearity.

The MIT algorithm mimics this nonlinear phenomenon on a quantum computer, using Bose-Einstein math to connect nonlinearity and linearity. So by imagining a pseudo Bose-Einstein condensate tailor made for each nonlinear problem, this algorithm deduces a useful linear approximation. “Give me your favorite nonlinear differential equation, then I’ll build you a Bose-Einstein condensate that will simulate it,” said Tobias Osborne, a quantum information scientist at Leibniz University Hannover who was not involved in either study. “This is an idea I really loved.”

Berry thinks both papers are important in different ways (he wasn’t involved with either). “But ultimately the importance of them is showing that it’s possible to take advantage of [these methods] to get the nonlinear behavior,” he said.

Knowing One’s Limits

While these are significant steps, they are still among the first in cracking nonlinear systems. More researchers will likely analyze and refine each method — even before the hardware needed to implement them becomes a reality. “With both of these algorithms, we are really looking in the future,” Kieferová said. Using them to solve practical nonlinear problems requires quantum computers with thousands of qubits to minimize error and noise — far beyond what’s possible today.

And both algorithms can realistically handle only mildly nonlinear problems. The Maryland study quantifies exactly how much nonlinearity it can handle with a new parameter, R, which represents the ratio of a problem’s nonlinearity to its linearity — its tendency toward chaos versus the friction keeping the system on the rails.

“[Childs’ study is] mathematically rigorous. He gives very clear statements of when it will work and when it won’t work,” Osborne said. “I think that’s really, really interesting. That’s the core contribution.”

The MIT-led study doesn’t rigorously prove any theorems to bound its algorithm, according to Kiani. But the team plans to learn more about the algorithm’s limitations by running small-scale tests on a quantum computer before moving to more challenging problems.

The most significant caveat for both techniques is that quantum solutions fundamentally differ from classical ones. Quantum states correspond to probabilities rather than to  absolute values, so instead of visualizing air flow around every segment of a jet’s fuselage, for example, you extract average velocities or detect pockets of stagnant air. “This fact that the output is quantum mechanical means that you still have to do a lot of stuff afterwards to analyze that state,” Kiani said.

It’s vital to not overpromise what quantum computers can do, Osborne said. But researchers are bound to test many successful quantum algorithms like these on practical problems in the next five to 10 years. “We’re going to try all kinds of things,” he said. “And if we think about the limitations, that might limit our creativity.”

Source: https://www.quantamagazine.org/new-quantum-algorithms-finally-crack-nonlinear-equations-20210105/

Blockchain

Altcoins rally while Bitcoin bulls are thwarted by resistance at $34K

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Bitcoin’s (BTC) tumble below $30,000 was short-lived as the top cryptocurrency found a new wave of support, including a $10 million ‘buy the dip’ moment from MicroStrategy. 

Data from Cointelegraph Markets and TradingView shows the strong inflows have helped lift BTC 4.92% to a daily high at $33,866.

As the prospect of the Biden administration passing massive stimulus packages to help get the United States economy going again, conversations about Bitcoin becoming a reserve currency are beginning to pop up again.

Although Bitcoin’s recent volatility has some analysts saying BTC is a cyclical asset rather than a hedge, the price recent movements have caught the eye of retail investors who have shown a renewed interest in cryptocurrencies in general.

Daily cryptocurrency market performance. Source: Coin360

Even the Bank of International Settlements has acknowledged that digital currencies may have use and the organization has outlined plans to roll out a variety of central bank digital currency trials this year.

Now that the Bitcoin fear index has flipped from “Extreme Greed” to “Fear,” some investors appear to be taking Warren Buffet’s advice of “buying when there is blood on the streets”.

Institutional investors are wary of future regulation

According to Chad Steinglass, head of trading at CrossTower, Bitcoin’s correction may have initially been triggered by critical comments fromU.S. Treasury Secretary Janet Yellen.

Prior to Yellen’s comments, Bitcoin was experiencing a “post-correction consolidation” and was “rangebound between $34,000 and $38,000” with traders “waiting to see which side of the range would be challenged or broken.”

BTC/USDT 4-hour chart. Source: TradingView

Steinglass further explaind that Bitcoin’s next steps will be determined by the actions of institutional investors. He said:

“$31,000 was a pocket of strong support, so at least not everyone is selling. We’ll have to wait and see if that wall remains, or if institutions continue to accumulate. If they do, it’s likely that the trend will re-establish itself and continue. If they move to the sidelines waiting for more regulatory guidance, then their lack of buy flows will be acutely felt.”

Altcoins bounce back

Many of the top altcoins also recovered nicely from this week’s correction. Polkadot (DOT) rallied 7.09% to a daily high at $18, while Chainlink (LINK) posted a double-digit gain and topped out at $22.31. Tezos (XTZ) has also seen a surge in interest which boosted the altcoin by 15% to $3.36.

The overall cryptocurrency market cap now stands at $949.8 billion and Bitcoin’s dominance rate is 64.4%.

Source: https://cointelegraph.com/news/altcoins-rally-while-bitcoin-bulls-are-thwarted-by-resistance-at-34k

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DeFi surge, rising TVL and new partnerships underpin Ren’s 100% rally

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Interoperability between blockchains is rapidly becoming one of the buzz phrases being thrown around when discussing decentralized finance and the coins most likely to rally during an altcoin bull run. 

The rapid growth of DeFi, its ever expanding total value locked and soaring ETH gas fees further highlight the sector’s need for a layer 2 option that also supports the ability to transact value across different networks.

REN’s open protocol is designed specifically to fill this need by providing interoperability and liquidity between the top blockchains including Bitcoin, Ethereum and Zcash.

Over the past three weeks the price of REN has increased by more than 200%, going from $0.251 on Dec. 27 to a new all-time high of $0.778 on Jan. 20 driven by a record $369 million in 24-hour volume.

REN/USDT 4-hour chart. Source: TradingView

Three reasons for the recent price surge in the price of REN include the announcement of a collaboration with Google, the continued increase in total value locked on the platform and the ability to earn passive income in multiple cryptocurrencies through the operation of a darknode.

Google software pivot boosts sentiment, addresses RENvm scaling issues

On Jan.19 the REN team tweeted:

Ren has been researching & building on @Asylodev, an open and flexible framework by @Google. @GCPCloud confidential computing relaxes RenVM’s economic constraints, allowing for an unbounded scaling solution. #RenVM.”

Not long after the tweet, REN price began to rally to a new all-time high. As mentioned in the tweet, Asylo is an open and flexible framework from Google designed to help build portable applications that run on Secure Enclave hardware.

The secure enclave hardware allows users to run general-purpose applications in a secure environment where both the data, and the application itself, cannot be compromised by anyone, including the user. This makes for a more secure experience for all parties involved and helps protect against malicious code and backdoor attacks.

Asylo also makes it possible to port an application from one type of hardware to the next, meaning that developers can support multiple implementations with relative ease, including Intel implementations, AMD implementations, and any others that appear in the future. The diversity of choice this allows is an important feature to ensure decentralization on the network.

Total value locked soars to a new high

Community engagement and added value are key factors when it comes to the long-term success of a blockchain project.

Since the release of the Ren virtual machine mainnet (RenVM) in May 2020, engagement on the platform has steadily increased as Bitcoin holders now had another way to bring their BTC to Ethereum and the growing DeFi space.

As seen in the chart below, the total value locked on the Ren platform reached a new all-time high of $653.6 million on Jan. 20 and a total of 14,670 BTC are locked on the platform to create renBTC.

Total value locked in RenVM. Source: DeFi Pulse

The list of assets that RenVM supports continues to grow with BTC, Bitcoin Cash (BCH), Zcash (ZEC), Filecoin (FIL), Terra (LUNA), Dogecoin (DOGE) and Digibyte (DGB) currently available to transact on the Ethereum and Binance blockchains.

Development is currently underway to make it possible to interact on the Polkadot (DOT), Solana (SOL) and Cosmos (ATOM) networks as well, which would further enhance the interoperability provided.

Darknodes, passive income and a decreasing supply

The third driving force behind the recent price appreciation of REN relates to the Ren token use case and how it can help users earn passive income. RenVM is a network of virtual computers that make up a virtual machine, which are also referred to as Darknodes.

REN token holders who wish to operate a darknode need to lock up 100,000 REN which wiil enable them to process transactions on the network and earn a fee in the form of the token transacted. Thus, a darknode operator has the opportunity to earn passive income in the form of multiple different cryptocurrencies from one location.

Ren Darknode Statistics. Source: Renproject

As can be seen in the above graphic, 17.13% of REN’s total supply is currently bonded on the platform and supports the operation of darknodes.

During the most recently completed cycle, the network as a whole earned $839,128 in fees in the form of BTC, ZEC, FIL and BCH. The total network fees collected since the launch of the RenVM equals $2.975 million.

The continued addition of new tokens and interoperability with new blockchains will likely see increased usage of the network and an increase in the amount of fees earned. At the current price of $0.6157 it costs $61,570 to operate a darknode.

RenVM total users over time. Source: Dune Analytics

As activity on the network increases, the amount of fees generated will also increase, making it even more lucrative for token holders to operate a darknode. This has the potential to lead to further price appreciation from REN as every new darknode results in a direct decrease in its circulating supply.

The views and opinions expressed here are solely those of the author and do not necessarily reflect the views of Cointelegraph.com. Every investment and trading move involves risk, you should conduct your own research when making a decision.

Source: https://cointelegraph.com/news/defi-surge-rising-tvl-and-new-partnerships-underpin-ren-s-100-rally

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Denarius Announces Beta of Kronos Wallet and Private Decentralized Chat

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Kronos, a new application beta from the developers of Denarius (D), provides people a way to socialize and transact without a central authority. This new proof of concept takes decentralization, blockchain and privacy to the next level.

“Blockchains like Bitcoin and Ethereum have paved the way of innovation for cryptocurrencies and new applications like Denarius (D): Kronos, to bridge the gap for a faster and cheaper way to transact and utilize cryptocurrency.” — James R. (Cryptocurrency User)

Kronos, a new application beta from the developers of Denarius (D), provides people a way to socialize and transact without a central authority. This new proof of concept takes decentralization, blockchain, and privacy to the next level. “Users” are able to freely join the Kronos Chat platform, as it is redundantly available due to it using peer-to-peer technology. Kronos has no downtime or possible banning of the platform. Examples of this in current history include, Amazon Web Services (AWS) taking down the Parler app’s platform hosting [1]. Google Play Store and Apple App Store removing the Parler application [2]. Signal App going offline [3]. Whatsapp invasion of privacy [4]…the list goes on.

Kronos is a secure cryptocurrency wallet but also chat reinvented. With the Kronos Chat you can chat and send cryptocurrency across the world in seconds. End-to-end encrypted messages and no storage of your chats, anywhere. Kronos Chat is powered by YOU by leveraging the latest peer-to-peer technologies. Censorship is everywhere and increasing daily. Kronos Wallet allows you to be truly free, with “self-moderation” you finally have the power to choose your own censorship while you socialize. Kronos stores only required data securely and locally, not on an unknown centralized server in the cloud. Kronos supports optional Two Factor Authentication (2FA) and One-time Password (OTP) Yubikey authentication and uses BIP39 technology for your cryptocurrency wallet with the most advanced and leading encryption technologies available today.

Bitcoin was the first cryptocurrency to solve the Byzantine Generals Problem, but transactions are slow. Ethereum created a smart contract platform, but transaction fees are expensive. Denarius stayed true to its roots by forking the original Bitcoin Satoshi code and modified the coin to become a faster and cheaper alternative to Bitcoin. Now Denarius with Kronos changes things. BTC, ETH, and D coins can be sent using the Kronos Wallet with more cryptocurrencies and tokens being added soon, possibly USDC, USDT, Namecoin (NMC), Devault (DVT), Primecoin (XPM), etc. Interplanetary File System (IPFS) integration and file uploading directly inside of the Kronos Chat also allows the user to upload files such as documents, images, and media directly inside of Kronos, ready to be shared via the plethora of IPFS public gateways available.

Cryptocurrency Credits
Bitcoin (BTC) created by Satoshi Nakamoto
Ethereum (ETH) created by Vitalik Buterin
Denarius (D) created by Carsen Klock

For more information
Kronos Wallet: https://kronoswallet.com
Denarius (D): https://denarius.io

BlockForums.org: https://blockforums.org
Bitcoin (BTC): https://bitcoin.org
Ethereum (ETH): https://ethereum.org
IPFS: https://ipfs.io

Sources
1.) https://www.theverge.com/2021/1/11/22223335/parler-amazon-terminates-web-hosting-aws-google-apple-capitol
2.) https://techcrunch.com/2021/01/08/parler-removed-from-google-play-store-as-apple-app-store-suspension-reportedly-looms
3.) https://www.cnet.com/news/signal-operational-again-after-daylong-outage/
4.) https://www.poynter.org/tech-tools/2019/whatsapps-breach-is-proof-that-online-privacy-takes-a-little-work/

Press Contact
marketing@denarius.io

Source: https://themerkle.com/denarius-announces-beta-of-kronos-wallet-and-private-decentralized-chat/

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