Proof-of-work (PoW), or Nakamoto consensus, is a decentralized consensus mechanism that secures a blockchain by requiring nodes to expend energy and compete against each other to solve complex mathematical challenges to add blocks to the chain and receive rewards.

PoW also requires the network nodes to come to a consensus on whether network elements, such as account balances and the order of transactions, are correct. Bitcoin (BTC) is the largest PoW-powered blockchain by market cap in existence.

The mathematical problems Bitcoin network nodes solve require a significant number of computations, and miners often have to deploy application-specific integrated circuit (ASIC) hardware to keep up with the other nodes in a PoW network. Even with ASICs, acquiring majority control of the network and executing a 51% attack to validate invalid transactions would require a substantial amount of computational power.

However, with the introduction of quantum computing technologies, there is a growing concern that the cryptographic underpinnings of blockchain technology, including Bitcoin, could be disrupted. Quantum computers may be able to attack conventional cryptographic methods, such as the ones employed in Bitcoins transaction validation procedure.

In particular, compared to classical computers, quantum computers can tackle complicated mathematical problems like discrete logarithms and integer factorization at an exponentially faster rate. The emergence of quantum computing poses a post-quantum threat to Bitcoins security.

Should a sufficiently potent quantum computer be developed, it might jeopardize the cryptographic integrity of the algorithms that underpin Bitcoin. This could allow malevolent actors to carry out attacks that were previously deemed impossible, such as the capacity to carry out a 51% attack with less computational work than is currently required.

Post-quantum computing refers to the era that would follow the development and deployment of quantum computers that have the potential to solve computational challenges that are presently thought to be beyond the capabilities of classical computers. This covers activities like simulating quantum systems, factoring big numbers and resolving specific optimization issues.

Quantum computing differs fundamentally from classical computing, which relies on bits that can represent either 0 or 1. Instead, quantum bits, or qubits, are used in quantum computing. Due to principles of superposition and entanglement, qubits can represent 0, 1, or both simultaneously.

The implications of quantum computing on PoW are considered one of the greatest incoming threats to the efficacy and effectiveness of blockchains and blockchain cryptography.

In the post-quantum computing era, quantum-resistant cryptographic algorithms will be developed to withstand attacks from quantum computers and ensure the security of sensitive information in a post-quantum world.

Cryptography is a discipline within mathematics focusing on securing communication and data and is fundamental to PoW cryptocurrencies like BTC. The Bitcoin blockchain uses powerful cryptography to ensure its decentralized money transfer model remains trustless, private and secure during peer-to-peer transactions. However, quantum computers may attack it by deploying machines and algorithms powerful enough to break its cryptographic shields.

Bitcoin uses asymmetric encryption (also known as public-key cryptography), which employs two different keys: public and private. The public key is used to encrypt data or, in the case of Bitcoin, to generate a Bitcoin address where funds can be received. However, the private key is used for decryption or signing transactions. The private key proves ownership of the funds and authorizes transactions, allowing them to be securely added to the blockchain.

The most important ways Bitcoin uses cryptography are through digital signatures and hash functions. Both of these, however, are potentially crackable through quantum computing.

The Elliptic Curve Digital Signature Algorithm (ECDSA) for digital signatures allows users to verify who owns a Bitcoin address and approve transactions. If quantum computers become powerful enough, they might be able to defeat ECDSA using techniques such as Shors algorithm, which might theoretically solve the discrete logarithm problem the foundation of ECDSA security in polynomial time.

The powerful superpositioned Schors algorithm could run on a quantum machine and, using a brute force method, determine the private key associated with a public key, hidden with the elliptic curve cryptography (ECC) scheme, invalidating the digital signature.

Cryptographic hash functions, namely SHA-256, are used by Bitcoin in several ways, including the mining process (PoW) and the creation of addresses using public keys. Hash functions are considered more immune to quantum attacks than the public-key cryptography systems today.

However, a sufficiently powerful quantum computer might still present a threat, albeit less immediately concerning than for digital signatures. For instance, Grovers algorithm may theoretically be able to accelerate the search for a pre-image of a hash function. But it only offers a quadratic speed, implying that the threat may be lessened if the hash length is doubled, for example, from 256 to 512 bits.

Securing PoW against quantum threats and developing post-quantum blockchain security have become essential. The blockchains quantum computing challenge is to develop solutions that can protect it from a quantum computer powerful enough to break all of its current cryptographic security measures.

Quantum-proof cryptocurrency and quantum resistance in blockchains may be possible with techniques like lattices, isogenies and codes.

A lattice-based cryptography is based on the mathematical concept of a lattice. A lattice is a grid of evenly spaced points that extend infinitely in every direction. This type of cryptography uses the complexity of lattices as the basis for encrypting or decrypting messages.

Lattice-based cryptography uses operations on lattice points to carry out encryption, decryption and other cryptographic functions. An attacker would find it challenging to decipher the original message or decryption key without knowing the precise structure of the lattice utilized in the encryption process due to the complexity and intractability of problems on lattices, which serve as the foundation for security.

Isogeny-based cryptography is an evolution of ECC and focuses on securely passing secret messages using the mathematical properties of elliptic curves. However, it introduces a new layer of complexity by using isogenies rather than the points on the curves directly, as in traditional ECC.

Isogeny-based cryptography is similar to two parties coming up with a secret handshake in public, with every move being observed, but no one can replicate it. Like lattice-based cryptography, its complexity offers possible defense against quantum computer attacks, making isogeny-based cryptography a viable option for post-quantum cryptography.

Code-based cryptography is based on challenging-to-decode general linear code. It is based on creating puzzles with error-correcting code, which is a set of mathematical tools used to detect and correct errors in data transmission. For example, if a message sent over the internet gets corrupted before it reaches its target, an error-correcting code would be used to recover it accurately.

In code-based cryptography, it should be straightforward for anyone with the right key to decode a message but challenging for anyone else. Code-based cryptography is considered to have quantum resistance potential because decoding random linear code the basis of code-based cryptography is not known to be efficiently solvable by quantum computers based on current algorithms, including Shors and Grovers.

In 2022, the United States Department of Commerces National Institute of Standards and Technology (NIST) announced it had chosen the first set of encryption tools designed to withstand attacks by quantum machines. The four selected algorithms will become a part of NISTs post-quantum cryptographic standard, which is set to be finalized in 2024. They are:

The future of PoW cryptocurrencies in the quantum era is a topic of significant interest and concern within the cryptographic and blockchain communities. Scientists from the University of Sussex estimate that a quantum system capable of utilizing 13 million qubits could break the cryptographic algorithms (that secure the Bitcoin blockchain) within 24 hours.

The mining component of PoW may be impacted by quantum computing. Although quantum techniques, like Grovers algorithm, can accelerate mining through a quadratic speedup in the search for a nonce that meets the PoW criterion, the potential disruption to cryptographic security outweighs this benefit. Nonetheless, the processing capacity required to significantly influence PoW mining is not yet available.

To protect PoW blockchains from future quantum attacks, the blockchain community is actively investigating and creating cryptographic algorithms resistant to quantum attacks. For instance, QuEra, a startup founded by former researchers from Harvard University and Massachusetts Institute of Technology, has released an incredibly ambitious roadmap for a Quantum machine set to be released soon.

The company plans on releasing a quantum computer with 100 logical qubits and 10,000 physical Qubits by 2026. It has been claimed that the machine will demonstrate a practical quantum advantage, meaning this computer will be able to perform tasks that todays bit-based computers cannot.

Quantum computers are still unable to crack cryptographic algorithms like those used in Bitcoin due to their small size or lack of fidelity. The field is progressing, though many technical obstacles, such as qubit coherence durations, error rates and others, have yet to be solved.

Written by Aditya Das

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An overview of post-quantum threats to proof-of-work cryptocurrencies - Cointelegraph

Quantum computing promises to solve problems that are impossible for todays computers, including key problems in cryptography, drug discovery, finance, and data analysis. By leveraging the quantum properties of individual atoms and elementary particles, these computers can store and manipulate information in a fundamentally different way from classical computers, opening the door to new algorithms and new solutions.

Although modern quantum computers are still small and error-prone, they have come a long way in the past decade, and continued investment, both from governments and the private sector, promises further breakthroughs. In the past year, there have been important developments, including a thousand-fold increase in the length of time that information persists, large improvements in algorithmic performance and error correction, and the first quantum computer with more than 1000 quantum bits. Once only a theoretical possibility, this emerging form of computing continues to move closer to being a practical reality.

In this weeks episode of the TechTank Podcast, co-host Darrell West delves into the future and capabilities of powerful quantum computers. To aid in comprehending these revolutionary machines, Darrell West is joined by Joseph Keller, a visiting fellow in the Foreign Policy programs Strobe Talbott Center for Security, Strategy, and Technology at Brookings.

You can listen to this episode and subscribe to the TechTank Podcast on Apple, Spotify, or Acast.

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The future of quantum computing | The TechTank Podcast | Brookings - Brookings Institution

In a thought experiment that would be inadvisable to put into practice, Erwin Schrdinger argued that if a cat were placed in a sealed box with a mechanism that may or may not trigger the release of poison to kill the animal, it would be both dead and alive at the same time. Besides inadvertently raising the blood pressure of cat lovers a demographic thatshouldn't be messed with he was trying to demonstrate the idea of quantum superposition, the theory behind qubits and quantum computing.

Conventional computers as well as phones, tablets and everything else with a computing element rely on bits, the smallest possible units of information. Each of them can only hold a single value at a time traditionally represented as a one or zero. Anything stored or processed in a computer is, deep under the surface, converted by programming languages to ones and zeros the lowercase letter "a," for example goes by "1100001." A single GB of data, about the volume of streaming Netflix for an hour, represents over 8.5 billion bits, meaning ones or zeros. Printed out, that would be almost 3 million pages (don't try this at home.)

That slightly abstract piece of information gets much more complicated when it comes to quantum computing. Quantum bits, or qubits, can flicker between the two states a little like a tossed coin except with differing probabilities. Crucially, qubits can also be entangled to always land on the same result, which means a single string can store multiple pieces of information simultaneously.

Quantum in the cloud

As a result, quantum computers are said to have the potential to store and process more information than even the most advanced supercomputers relying on conventional bits. Scientists expect they will lend themselves particularly well to tasks that require the analysis of different combinations of factors, such as discovering new materials, battery chemistries orplanning traffic.

Still, these use cases are not here yet. The quantum computers available today cannot do anything conventional computers can't and there are some significant quirks that still need to be overcome. Crucially,the number of qubitsinside a quantum computer will need to increase, and the technology's susceptibility toerrors caused by environmental noisehas yet to be fully resolved.

None of this has prevented companies, including many telcos, from hopping aboard the bandwagon. For example, Deutsche Telekom's T-Systems, which providesdigital and IT solutions to businesses, already offers cloud access to quantum computers.

It has teamed up with several companies producing quantum computers, giving customers access to different types of the technology, with each company creating qubits in a different way. For now, the platform includes computers from market heavyweight IBM, alongside IQM and AQT.

T-Systems has also partnered with European platform PlanQK, which is developing a quantum computing ecosystem. As a result, customers have access to ready-made quantum algorithms andapplications. While these do not currently outperform conventional computers,PlanQKsays the idea behind the project is to allow developers to gain knowledge about specific hardware platforms and build the skills required.

In future, more telcos could venture in a similar direction. Andrew Lord, the senior manager of optical networks and quantum research atBT, told Light Reading during an interview that the company would consider selling access to cloud computers in future, perhaps as part of a broader computing platform.

The issue, Lord says, is that quantum computers alone will not be able to solve many of the problems put to them. The goal, then, is to provide a more generic service with quantum as one of the elements included.

"The challenge is, how can you orchestrate between that? So how do you take a problem from a customer and say, the best way of solving this problem is in this combination of compute, whether it's high performance computing, quantum computing, other types, and how do you orchestrate between all of that." The result would be a holistic computing and networking environment, where a customer only pays for the computing time they need. "So that that then becomes a resource scheduling kind of problem, which we're good at," said Lord.

Quantum radio

Yet another area of quantum relevant to telcos is quantum sensing. It uses quantum physics to create what Lord calls ridiculously sensitive sensors that can "pinpoint the location of something down to millimeters," pick up on the vibration of a fiber to deduce that a car has driven on a road above it, or provide alerts about leaking pipes.

Such functionalities could help telcos, which often run extensive fiber optic networks, to better utilize those assets. Because of quantum sensors' higher sensitivity, which can increase communication ranges, the technology could also yield better radios. In the long run, quantum radio could improve mapping and cell phone communications indoors, underwater, underground and in urban canyons.

In 2022, BT trialled quantum antenna technology that relies on excited atomic states, increasing sensitivity compared with traditional technologies. Its atomic radio frequency receiver can pick up weaker signals, and it could be placed inside passive optical receivers in hard-to-reach areas to improve mobile coverage. According to the company, the technology is still in its early stages, but it could eventually make smart cities, IoT and smart agriculture cheaper to implement.

The demonstration used digital modulation within one of EE's main commercial 5G frequency ranges. And earlier this year, the company used a quantum optical radio receiver to make a three-way Microsoft Teams call between three UK locations using EE's 4G spectrum. While a lot of quantum technology might still be far from deployment, BT reckons this particular technology could be deployed in three to five years' time, reportedTelcoTitans.

Although quantum computing and sensing have clearly caught the eye of the telecom industry, it's impossible to tell when these technologies may be ready for prime time, especially in the case of quantum computing. But unlike Schrdinger's unlucky cat, we at least know they are alive and kicking.

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Telcos jostle for position ahead of quantum leap - Light Reading

PARIS, Jan. 23, 2024 Alice & Bob, a leading hardware developer in the race to fault tolerant quantum computers, in collaboration with the research institute Inria, today announced a new quantum error correction architecture low-density parity-check (LDPC) codes on cat qubits to reduce hardware requirements for useful quantum computers.

The theoretical work, available on arXiv, advances previous research on LDPC codes by enabling the implementation of gates as well as the use of short-range connectivity on quantum chips. The resulting reduction in overhead required for quantum error correction will allow the operation of 100 high-fidelity logical qubits (with an error rate of 10-8) with as little as 1,500 physical cat qubits.

Over 90% of quantum computing value depends on strong error correction, which is currently many years away from meaningful computations, said Jean-Franois Bobier, Partner and Director at the Boston Consulting Group. By improving correction by an order of magnitude, Alice & Bobs combined innovations could deliver industry-relevant logical qubits on hardware technology that is mature today.

This new architecture using LDPC codes and cat qubits could run Shors algorithm with less than 100,000 physical qubits, a 200-fold improvement over competing approaches 20 million qubit requirement. said Thau Peronnin, CEO of Alice & Bob. Our approach makes quantum computers more realistic in terms of time, cost and energy consumption, demonstrating our continued commitment to advancing the path to impactful quantum computing with error corrected, logical qubits.

Cat qubits alone already enable logical qubit designs that require significantly fewer qubits, thanks to their inherent protection from bit flip errors. In a previous paper by Alice & Bob and CEA, researchers demonstrated how it would be possible to run Shors algorithm with 350,000 cat qubits, a 60-fold improvement over the state-of-the art.

LDPC codes are a class of efficient error correction codes that reduce hardware requirements to correct errors occurring in information transfer and storing. By using LDPC codes on a cat-qubit architecture, this latest work not only shows how the qubit footprint of a fault tolerant quantum computer could be further reduced but overcomes two key challenges for the implementation of quantum LDPC (qLDPC) codes.

Alice & Bob recently announced the tape out of a chip that would encode their first logical qubit prototype, known as Helium 1. When logical qubits with a sufficiently low error rate are implemented and using the cat qubit LDPC code technique, Alice & Bob would be capable of harnessing the computing power of 100 logical qubits with as little as 1,500 physical qubits, to run fault-tolerant algorithms.

As leading superconducting quantum computing manufacturers like IBM offer up to 1,121 physical qubits, outperforming classical computers in the simulation of quantum systems (quantum supremacy) is a milestone that would become attainable within current hardware capabilities using Alice & Bob new architecture.

In previously proposed qLDPC codes implementation, most notably IBMs last years paper, long-range qubit connectivity and high-weight stabilizers were required, which represent a daunting technical challenge. In contrast, Alice & Bobs combined approach of cat qubits with classical LDPC codes allows the use of short-range, local qubit interactions and low-weight stabilizers.

This simpler architecture enables for the first time the implementation of a fault-tolerant set of parallelizable logical gates without additional hardware complexity. Allowing for logical gates is a necessary step for the implementation of quantum algorithms and practical quantum computing altogether.

About Alice & Bob

Alice & Bob is a start-up based in Paris and Boston whose goal is to realize the first universal, fault-tolerant quantum computer. Founded in 2020, Alice & Bob has already raised 30M in funding, hired over 80 employees, and demonstrated experimental results surpassing those of technological giants like Google or IBM. Alice & Bob specializes in cat qubits, a technology pioneered by the companys founders and later adopted by Amazon. Demonstrating the power of its cat architecture, Alice & Bob recently showed it could reduce hardware requirements to build a large-scale useful quantum computer by up to 200 times compared to competing approaches.

Source: Alice & Bob

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Alice & Bob Advance Quantum Computing with Fewer Qubits Needed for Error Correction - HPCwire

Klea Dhimitri

Applications Engineer, Hamamatsu Corporation

What image pops into your head when you hear the words quantum technology?

What about quantum computer?

There is a very good chance you are thinking of the gold chandelier often found in a large dilution refrigerator that quantum computing players like IBM and Google use to cool and operate a superconducting qubit. However, there is one core technology that is often overlooked when we talk about quantum computers And thats photonics. Dr. Bob Sutor who spent more than two decades at IBM Research in New York working and leading IBMs efforts in quantum computing knows the large cyrostats very well. Currently Dr. Sutor is the vice president and chief quantum advocate at Infleqtion where at an event he stated:

Photonics is huge. Photonics is at the core of the future quantum infrastructure and without good growth of photonics industry driving down the cost and size into for example photonics integrated circuits none of this stuff is going to work beyond toy size machines that are disconnected from each other [1].

This article aims to shed light on how photonics is currently enabling multiple areas in emerging quantum fields like quantum computing, quantum communication & networking and quantum sensing, as well as touch on the challenges and opportunities that lie ahead.

The quantum technology landscape can be partitioned in a variety of ways, but in this article we will split the field into four pillars 1) Quantum Computation & Simulation 2) Quantum Communication & Networking 3) Quantum Metrology & Sensing and 4) Fundamental Research. The subsections within each pillar that utilizes photonics are highlighted in yellow in figure 1. The figure illustrates that over 2/3rd of the field utilizes photonics and photonics plays a major role in the quantum technology landscape.

Figure 1: Overview of quantum technology pillars where the use of photonics is highlighted in yellow.

Photonics role in quantum computation & simulation

Scientists are investigating a variety of qubit modalities to realize a universal fault tolerant quantum computer, but for several qubit modalities photonics is at the core of their toolbox. Photonics have a wide range of capabilities such as the ability to apply gate operations, confine atoms in an array and detect qubit states (either 0 or 1) through low light fluorescence or lack thereof from trapped ions or neutral atoms. Qubit modalities such as photonic quantum computing use the photon to the max. by utilizing a property of the photon to construct a qubit. The vision for photonic quantum computing is the entire optical table, from light sources to the optics to the photon detectors on a chip [2].

Scaling and fidelity are the main drivers for photonic component development in qubit modalities, such as trapped ions, neutral atoms and photonic qubits.

Trapped ions current infrastructure needed to operate a small chain of tens of ions typically takes up two optical tables [4]. Developing photonic components like photonic integrated circuit (PICs) are of interest to trapped ion developers, for example, because it could help make the modality more scalable. Bringing together more ions while each ion is being controlled precisely could help scale the processor without a large cumbersome infrastructure to scale along with it [7].

Figure 2: Trapped ion setup from the Blatt Lab

Photonics role in quantum communication & networking

The photon is a tried and tested carrier of sending information over long distances as seen in classical optical communication networks. The attraction of the photon in quantum communication and quantum networking is that a qubit can travel over long distances [6] as well as notify the users when an eavesdropper is listening in. Devices such as quantum random number generators (QRNG) that produce truly random keys used in quantum communication protocols could be realized with in utilizing light sources and detectors as well [5].

Quantum key distribution and quantum network hardware also rely on photonics, such as excitation or pump lasers for photon sources to emit photons in optical fibers, for example, and detectors from single photon detectors to photodiodes to detect them on the receiving end of the fiber.

Land quantum networks are distance limited due to optical fiber losses and lack of quantum repeaters. Space and satellite networks are aperture and diffraction loss limited. Main driver for photonic component development for quantum communication is to preserve photons over long distances.

Figure 3: Different types of quantum networks

Photonics role in quantum metrology & sensing

The field of quantum metrology and sensing is focused on accurate probing of the environment in terms of measurement such as electric, magnetic and gravitational fields, as well as timing and positioning. Information that quantum sensors measure could be communicated via fluorescence. In the case of a nitrogen vacancy- (NV) based magnetometer, different fluorescence intensities relate to the strength of the magnetic fields present. The main drivers for photonic component development of quantum sensing are size, weight, power & cost (SWaP-C) for field deployable applications.

Market opportunity for photonics

The market for quantum systems is currently not high, but the market for photonic components is high and promising. Over half of the bill of materials (BOM) cost for quantum systems goes to lasers while the rest is split among detectors, modulators and other components. Currently, the largest market for photonic components is in research at an estimated $171 million for lasers and $33 million for photonic components that include detectors, modulators, and other components. Its predicted that from 2025 and beyond that photonic components for quantum products manufactured by OEMs will be larger than photonic components used in research [8].

Challenges of photonics in quantum technologies

One of the photonic challenges for quantum technologies is the construction of single photon sources that contain all the desired features for applications like quantum key distribution and some forms of photonic quantum computing [9]. Photonic integrated circuits (PICs) are seen as the holy grail for quantum technology. However, PICs still present a few challenges such as bringing all optical components including lasers and detectors on chip as well as the cost of a PIC production line. These production lines need high volume to keep cost manageable and unclear if quantum applications will scale and if so when [10]

Ongoing advancements of photonic components will be instrumental in realizing quantum systems and building them for the quantum 2.0 era.

References

[1] YouTube Video of Bob Sutor. https://www.youtube.com/watch?v=sRAZ8PJzzLY 6:28 to 6:56

[2] Masuda, A. (2019). https://www.news.ucsb.edu/2019/019679/pushing-quantum-photonics

[3] Choi, C.Q. (2021). https://spectrum.ieee.org/race-to-hundreds-of-photonic-qubits-xanadu-scalable-photon

[4] Jurcevic,P.,Mandelbaum,R. (2021). Heres How Ion Trap Quantum Computers Work. The Quantum Aviary. https://thequantumaviary.blogspot.com/2021/03/heres-how-ion-trap-quantum-computers.html [5] Jennifer Aldama, Samael Sarmiento, Ignacio H. Lpez Grande, Stefano Signorini, Luis Trigo Vidarte, and Valerio Pruneri, Integrated QKD and QRNG Photonic Technologies, J. Lightwave Technol. 40, 7498-7517 (2022)

[6] Awschalom, D.D., et.al. https://doi.org/10.2172/1900586

[7] Niffenegger, R.J., Stuart, J., Sorace-Agaskar, C.et al.Integrated multi-wavelength control of an ion qubit.Nature586, 538542 (2020). https://doi.org/10.1038/s41586-020-2811-x

[8] Tematys Photonics@Quantum: Technologies for Quantum Systems Report (April 2022)

[9] OIDA, OIDA Quantum Photonics Roadmap: Every Photon Counts, Optica Industry Report, 3 (2020)

[10] Davis.S et al. Piercing the Fog off Quantum-Enabling Laser Technology (QELT) A report based on a QED-C Enabling Technology Workshop. QED-C. (2018).

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TQI Exclusive: Photonics Illuminating Quantum Technology: Trends, Challenges and Opportunities - The Quantum Insider