Quantum 6, 649 (2022).

https://doi.org/10.22331/q-2022-02-10-649

The characterization of open quantum systems is a central and recurring problem for the development of quantum technologies. For time-independent systems, an (often unique) steady state describes the average physics once all the transient processes have faded out, but interesting quantum properties can emerge at intermediate timescales. Given a Lindblad master equation, these properties are encoded in the spectrum of the Liouvillian whose diagonalization, however, is a challenge even for small-size quantum systems. Here, we propose a new method to efficiently provide the Liouvillian spectral decomposition. We call this method an Arnoldi-Lindblad time evolution, because it exploits the algebraic properties of the Liouvillian superoperator to efficiently construct a basis for the Arnoldi iteration problem. The advantage of our method is double: (i) It provides a faster-than-the-clock method to efficiently obtain the steady state, meaning that it produces the steady state through time evolution shorter than needed for the system to reach stationarity. (ii) It retrieves the low-lying spectral properties of the Liouvillian with a minimal overhead, allowing to determine both which quantum properties emerge and for how long they can be observed in a system. This method is $textit{general and model-independent}$, and lends itself to the study of large systems where the determination of the Liouvillian spectrum can be numerically demanding but the time evolution of the density matrix is still doable. Our results can be extended to time evolution with a time-dependent Liouvillian. In particular, our method works for Floquet (i.e., periodically driven) systems, where it allows not only to construct the Floquet map for the slow-decaying processes, but also to retrieve the stroboscopic steady state and the eigenspectrum of the Floquet map. Although the method can be applied to any Lindbladian evolution (spin, fermions, bosons, …), for the sake of simplicity we demonstrate the efficiency of our method on several examples of coupled bosonic resonators (as a particular example). Our method outperforms other diagonalization techniques and retrieves the Liouvillian low-lying spectrum even for system sizes for which it would be impossible to perform exact diagonalization.

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OnJuno, the crypto app helping Americans receive their paycheck in crypto, has announced an integration with ZenGo, a multichain crypto wallet app with keyless recovery and 24/7 in-app customer support. This integration provides OnJuno users with a secure, accessible way to get paid in digital assets without fear.

ZenGo supports all current OnJuno assets, Bitcoin, Ethereum, and USDC, while storing a slew of other cryptocurrencies as well, such as DOGE, LUNA, and UST. 

Setting up a ZenGo wallet is easy, and the two companies are offering a $50 ETH or BTC bonus when users receive their first direct deposit of $250 or more. Users can start by creating an OnJuno account with the referral code ZENGO before receiving their banking numbers and deciding what percentage of their paycheck to convert to crypto. Finally, users can choose the ZenGo wallet during the sign-up process and set up a direct deposit straight to it.

“OnJuno sits at the sweet spot between crypto & banking. We believe that in order to reach a future where transactions are primarily in crypto, we need to first bridge the gap between TradFi & DeFi. Hence, we are striving to enable as many crypto native users to easily use their crypto for their day-to-day transactions and keep more & more of their total wealth in crypto. We are excited to announce this partnership with ZenGo, which is the first step towards achieving that goal. We are already in the works to announce many more partnerships with wallets across the DeFi space,” said Jack Knutson, Head of Partnerships at OnJuno.

"Getting paid in Bitcoin and Ethereum is now easier than ever. Thanks to ZenGo's integration with OnJuno, Americans can finally get an unparalleled way to get simply paid in crypto and invest, control, and recover their funds like never before,” said ZenGo CEO Ouriel Ohayon.

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About ZenGo

ZenGo is the multichain crypto wallet for everyone. Buy, trade, and earn up to 8% interest on Bitcoin, Ethereum, and 70+ other crypto assets with unbelievable simplicity and bulletproof security. ZenGo is known for its legendary, 24/7 in-app customer support and its keyless MPC technology that gives you full control over your crypto, but is always recoverable. More on ZenGo here: https://zengo.com

 

About OnJuno

OnJuno has an ambitious vision to power the next wave of billion crypto users by helping them invest, earn and save cryptocurrencies right from the safety of an FDIC-insured checking account. OnJuno's core feature, “get paid in crypto”, is currently backed by Sequoia, Polychain, Consensys and #Hashed. The team built the Nuo protocol, one of the earliest lending platforms in DeFi. Nuo was the first to introduce contract wallets and meta transactions to simplify the user experience. Nuo had processed over $100 million in margin loans and was one of the top five protocols on DeFi pulse in early 2019. Today, the same team is passionately building OnJuno - an app used and loved by employees from Apple, Google, Amazon, and crypto natives alike. By seamlessly converting paycheck to crypto and enabling crypto spending in the real world, OnJuno gives its members the financial freedom they deserve. More on OnJuno here: https://onjuno.com

OnJuno Team Contact

[email protected]

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