journey to quantum

Reality Is Not What It Seems: The Journey to Quantum Gravity

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“The man who makes physics sexy . . . the scientist they’re calling the next Stephen Hawking.” — The Times Magazine From the  New York Times –bestselling author of  Seven Brief Lessons on Physics ,  The Order of Time , and the forthcoming Helgoland , a closer look at the mind-bending nature of the universe. What are the elementary ingredients of the world? Do time and space exist? And what exactly is reality? In elegant and accessible prose, theoretical physicist Carlo Rovelli leads us on a wondrous journey from Democritus to Einstein, from Michael Faraday to gravitational waves, and from classical physics to his own work in quantum gravity. As he shows us how the idea of reality has evolved over time, Rovelli offers deeper explanations of the theories he introduced so concisely in  Seven Brief Lessons on Physics . Rovelli invites us to imagine a marvelous world where space breaks up into tiny grains, time disappears at the smallest scales, and black holes are waiting to explode—a vast universe still largely undiscovered.

About the Author

Carlo Rovelli is a theoretical physicist who has made significant contributions to the physics of space and time. He has worked in Italy and the United States and currently directs the quantum gravity research group of the Centre de Physique Théorique in Marseille, France. His books, including Seven Brief Lessons on Physics , The Order of Time , and Helgoland , are international bestsellers that have been translated into more than fifty languages.

Praise for Reality Is Not What It Seems: The Journey to Quantum Gravity

“Some physicists, mind you, not many of them, are physicist-poets. They see the world or, more adequately, physical reality, as a lyrical narrative written in some hidden code that the human mind can decipher. Carlo Rovelli, the Italian physicist and author, is one of them…Rovelli's book is a gem. It's a pleasure to read, full of wonderful analogies and imagery and, last but not least, a celebration of the human spirit.” —NPR Cosmos & Culture   “If your desire to be awestruck by the universe we inhabit needs refreshing, theoretical physicist Carlo Rovelli…is up to the task.” — Elle “[ Reality Is Not What It Seems ] is simultaneously aimed at the curious layperson while also useful to the modern scientist… Rovelli lets us nibble or gorge ourselves, depending on our appetites, on several scrumptious equations. He doesn’t expect everyone to be a master of the equations or even possess much mathematical acumen, but the equations serve as appetizers for those inclined to get their fill, so to speak.” —Raleigh News & Observer “With its warm, enthusiastic language and tone, [ Seven Brief Lessons on Physics ] is also deeply humanistic in approach, using words like  elegant  and  beauty  about a subject…that can seem impenetrably dense and abstract… Reality Is Not What It Seems  takes much the same approach.” — New York Magazine “Rovelli writes beautiful prose while walking the reader through the history and concept of 'reality' and what it all means for the yet to be discovered universe and thus our own lives.” —Pasadena Star-News “Rovelli writes with elegance, clarity and charm. . . . A joy to read, as well as being an intellectual feast.” —New Statesman “Rovelli offers vast, complex ideas beyond most of our imagining—‘quanta,’ ‘grains of space,’ ‘time and the heat of black holes’—and condenses them into spare, beautiful words that render them newly explicable and moving.” — On Being with Krista Tippett “Rovelli’s lyrical language, clarity of thought, and passion for science and its history make the title a pleasure to read (albeit slowly), and his diagrams and footnotes will allow readers to understand the material better and tackle a more expert level of insight.” —Booklist “Rovelli smoothly conveys the differences between belief and proof. . . his excitement is contagious and he delights in the possibilities of human understanding.”— Publishers Weekly “Science buffs will admire Rovelli's lucid writing…Cutting-edge theoretical physics for a popular audience that obeys the rules (little math, plenty of drawings), but it's not for the faint of heart.”— Kirkus Reviews “A fascinating adventure into the outer limits of space and into the smallest atom…Rovelli manages to break down complex, proven ideas into smaller, easily assimilated concepts so those with little to no scientific background can understand the fundamental ideas…Rovelli's infectious enthusiasm and excitement for his subject help carry readers over the more difficult aspects, allowing one to let the imagination soar…An exciting description of the evolution of physics takes readers to the edge of human knowledge of the universe.” —Shelf Awareness “Rovelli draws deep physics into the light with rather greater success... He wears a broad erudition lightly, casually and clearly explaining.” —Read It Forward

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In photos: Journey to the center of a quantum computer

By Charlotte Hu

Posted on Sep 7, 2022 9:30 AM EDT

The beating heart of IBM’s quantum computer is a chip no bigger than a quarter. These extravagant machines promise to solve difficult problems that stump today’s best classical computers. The chip itself is only one part of a bigger puzzle. Unlike the portable laptops that people use in everyday life, the computing infrastructure that supports the work a quantum chip does is layered like a Russian doll, with convoluted interconnections within a Rube-Goldberg-like contraption.

However, even with its complicated construction and mind-boggling design, a quantum computer is still a machine that performs operations by employing both hardware and software. Some of those actions are similar to those performed by classical computers. Curious to understand how they function? Popular Science got a look around the quantum center in IBM’s Yorktown Heights, New York campus. Take a closer look at what’s happening inside—starting with something called the qubit (more on what that is in a moment) and zooming out, bit by bit. 

That’s cold 

To exhibit quantum qualities, objects have to either be very small or very cold. For IBM, this layered chandelier-like structure, which looks like an upside-down gold steampunk wedding cake, is called a dilution refrigerator. It keeps their qubits cool and stable, and is the infrastructure that the company created for this 50-qubit chip. It contains multiple plates that get successively colder the closer they are to the ground. Each plate is a different temperature, with the very top layer sitting at room temperature. 

The quantum processor is mounted to the lowest, and coldest, plate of the dilution refrigerator that gets to a temperature around 10 to 15 milli-Kelvin, which is roughly –460 degrees F. The first stage of cooling involves large copper pieces seen draping down in the top layer that are connected to cold heads as part of a closed-cycle helium cryocooler. More tubes feeding into the lower levels introduce another closed cycle of cryogenic material, made up of a mix of helium isotopes.

In the back of the housing structure are the hidden support infrastructure for the chandelier. This includes the gas handling system that supports the cryogenic infrastructure, as well as pumps and temperature monitors. And then there are the custom-built classical control electronics. When users run a program through IBM’s quantum cloud service, they are effectively orchestrating a set of gates and their circuits. Those get turned into microwave pulses that are appropriately sequenced, aligned, and distributed out into the system to control the qubits. And the readout pulses retrieve the states of the qubits, which are translated back into binary values and returned to the users.

Qubits and an ‘artificial atom’

Classical computers represent information using binary one-or-zero bits. In the case of quantum, information is represented through qubits, which can come in a combination of zero and one. This is a phenomenon referred to as superposition. “You have superposition all the time in the real world. Music is a superposition of frequencies, for example,” says Zaira Nazario, the technical lead of theory, algorithms, and applications at IBM Quantum. Because it’s a waveform, it provides an amplitude of zero and one. That means it comes with a phase, and like all waves, they can interfere with one another.

The superconducting qubits sit on the chip and have been packaged into something like a printed circuit board. Wires and coaxial cables for input and output signals protrude off the circuit board. In newer models of higher-qubit chips, IBM has been working towards more compact solutions involving wiring and integrated components to be more efficient with space. Having less clutter means that the components would be easier to cool. Currently, it takes about 48 hours to completely cool down a quantum computer to the desired temperatures. 

For the quantum computer to function correctly, each of the plates must be thermally shielded and isolated to prevent black body radiation from affecting it. Engineers vacuum-seal the whole device to keep out unwanted photons as well as other electromagnetic radiation and magnetic fields.

Qubits are controlled with microwave signals that range from 4 to 7 gigahertz. Classical electronics generate microwave pulses that travel down the cables to bring the input signals to the chip and carry the output signals back. As the signal travels down the chandelier, it goes through components like filters, attenuators, and amplifiers.

IBM works largely with superconducting qubits. They’re little pieces of metal that sit on the wafer, which is used to make the chip. The metal is made up of superconducting materials like niobium, aluminum, and tantalum. A Josephson junction , made by layering a very thin insulator between two superconducting materials, provides the essential nonlinear element needed to turn a superconducting circuit into a qubit. 

“What we’re building is quantum examples of oscillators,” says Jerry Chow, director of quantum infrastructure at IBM. Oscillators convert a direct current from a power source (in this case, microwave photons) into an alternating current, or a wave. 

Unlike typical harmonic oscillators, a nonlinear oscillator gives you an unequal spacing of energy levels, Chow says. “When you have that, you can isolate the lowest two to act as your quantum zero and your quantum one.”

Think of a hydrogen atom. From a physics standpoint, it has a set of energy levels. The right wavelengths of light hitting this atom could promote it to different states. When microwaves hit the qubit, it is doing something similar. “You effectively have this artificial atom,” Chow explains. “We have a quantum of energy, which we move around by putting the right amount of microwave photon at a certain pulse for a certain duration to either excite or de-excite a quantum of energy within this nonlinear microwave oscillator.” 

In a classical computer, there’s an on-state (one), and an off-state (zero). For a quantum computer, the off-state is the ground state of the artificial atom. Adding a pulse of a particular microwave photon of energy would excite it, promoting it to one. If the qubit is hit again with that pulse, it would be brought back down to ground state. Let’s say it takes 5 gigahertz for 20 nanoseconds to promote a qubit fully to the excited state—if you were to halve the amount of energy or halve the amount of time, you would actually drive a superposition state, Chow says. That means if you were to measure the state of the qubit with a resonator, you would have a 50 percent chance of it being in zero, and 50 percent chance of it being in one. 

Users can play around with the circuit elements, pulse frequencies, duration, and energy between different qubits to couple them, swap them, or perform conditional operations like building entangled states and combining single qubit operations to perform universal computation across the entire device. When waves intersect, it can either amplify or deconstruct the message.

What are qubits good for? 

The practical uses for quantum computers have evolved over the last couple of years. “If I look at what people were doing with the system in that 2016, 2017, 2018 timeframe, it was using quantum to research quantum… condensed matter physics, particle physics, things like that,” says Katie Pizzolato, director of strategy and applications research at IBM Quantum. “The key part of this is going to be taking classical resources and making them quantum-aware. We have to make the people who are experts in their field understand where to apply quantum, but not be quantum experts.”

The interest IBM has been seeing in terms of quantum problems posed to their machines can be grouped into three buckets: chemistry and materials, machine learning, and optimization (finding the best solution to a problem from a set of possible options). The key is not to use a quantum computer in every part of the problem—but on the parts that are hardest.

The team at IBM has been continuously searching for real-world problems that are hard for classical computers to solve due to their structure or the math they involve. And there are many interesting places to look for them. 

Classical computers solve basic math problems using binary logic and circuit components such as adders. However, quantum computers are really great at doing linear algebra—multiplying matrices, and representing vectors in space. This is due to unique features in their design. It allows them to perform functions like factoring relatively easily—a problem that is extremely difficult for a classical computer because of the exponentially increasing number of variables and parameters and the interactions between them. “There’s structures within that factoring problem that allow you to take advantage of the entanglements, all the things that you get with these devices. That’s why it’s different,” Pizzolato says.

And with chemistry and materials problems, qubits are just better at simulating properties like bonds and connected electrons. 

“We’re thinking about what types of things you can map to quantum circuits that are not simulable classically, and then what do you do with them,” says Pizzolato. “A lot of the algorithm discussion is how do I exploit the underlying mechanics of this device. How do you map on higher dimensional spaces and how do you use this coordination and multiplications of these matrices to rise up the answer that you want.” 

Remember, qubits can have a value of zero, one, or a combination of the two. Since qubits are waveforms, engineers can rotate the zero or one to give it a negative amplitude. Qubits can also get entangled—a unique quantum mechanics property that doesn’t have a classical analog. Entangled qubits can contain information not just in the zeros and ones themselves, but also in the interactions between all of them. Also, there are gates in quantum circuits that can rotate the qubit to change its phase, and oscillators can entangle those qubits. 

“The art of doing a quantum algorithm is how you manipulate all of those entangled states and then interfere in a way that the incorrect amplitudes cancel out, and the amplitudes of the correct one come forward, and you get your answer,” Nazario says. “You have a lot more room to maneuver in a quantum algorithm because of all these entangled states and this interference compared to an algorithm that only allows you to flip between zeroes and ones.” 

Qiskit , IBM’s open-source development kit for quantum computers, contains information on various types of quantum algorithms and programs at different levels of detail. 

Real-world examples

Still find it tricky to visualize what the qubit is doing? Let’s zoom out to some examples of how IBM’s partners are using quantum computers. For example, biopharmaceutical company Amgen is looking to use quantum computers and machine learning to predict the patients who would be best suited for a drug trial based on health records and other factors. 

And Boeing is applying quantum computing to analyze corrosion coefficients on airplanes. Airplane wings require a certain density of materials. Engineers make them with different layers of various materials, but need help figuring out how they should arrange the layers in a way that makes the wings stronger, cheaper, and lighter. This boils down to a combinatorial optimization problem. 

Goldman Sachs has been using it for options pricing. “These are very complex operations that are very computationally expensive. And they have complex distributions,” Nazario says. It has to do with calculating the derivatives of the variations in those options (a linear algebra operation), which will tell them about risks. 

Finally, in the natural sciences, research groups have been interested in using quantum computers to study photosynthesis . 

Building in parallel

Although IBM has been steadily increasing the processor size for its quantum computers, and building a community of partners from industry, national government hubs, and academic institutions, the company is still figuring out the best ways to move forward both with the hardware and software. 

[Related: We have quantum computers—now Amazon and Harvard want a quantum internet ]

The company has previously said that it would have a machine capable of quantum advantage (in which it can reliably and accurately solve a problem better than a classical computer) ready by 2025 . That means that in addition to developing new components, it needs to iron out some problem areas, and make what already works well, more efficient. 

“This is a big part of the focus of the software. We’ve recognized that a lot of the tools, the error mitigation tools , the intelligent orchestration, the idea of circuit-knitting, how do we break down the problems to extend what we can do on the quantum computer, these are becoming much more prolific in how we can push the technology,” says Pizzolato. 

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Starting your journey to become quantum-safe

• By Michal Braverman-Blumenstyk, Corporate Vice President, Microsoft Security Division CTO, Israel R&D Center Managing Director
• Information protection and governance
• Threat trends

There’s no doubt we are living through a time of rapid technological change. Advances in ubiquitous computing and ambient intelligence transform nearly every aspect of work and life. As the world moves forward with new advancements and distributed technologies, so too does the need to understand the potential security risks. At Microsoft, our mission has always been focused on keeping our customers’ and partners’ information and data safe and secure, and this is why we’re committed to advancing encryption solutions, in order to enable responsible use of new technologies such as AI and quantum computing . As one important example, while scaled quantum computing will help solve some of our toughest problems, like helping us discover new ways of addressing climate change and food scarcity, its development may also create a new set of security challenges and in turn require new encryption standards. As this future quickly approaches, how can we ensure that we reap the benefits of quantum computing while remaining safe in a post-quantum world?

Start your journey with Microsoft towards quantum-safety.

We believe the first step every organization should take toward quantum safety is to be aware of the need to organize, plan, and begin an impact assessment. We recommend prioritizing symmetric encryption where applicable and subsequently adopting post-quantum cryptography (PQC) for asymmetric encryption once standardized and approved by relevant setting bodies and governments, as recommended by cybersecurity agencies globally. Furthermore, we are exploring and experimenting with additional classical and quantum security solution layers through internal experiments, POCs, and collaborations with partners. 

Given that preparing for such an objective will be a multi-year and iterative process that requires strategic foresight, it’s crucial for organizations to start investing time in their planning and execution efforts today. Thanks to our extensive experience in quantum engineering and expertise as a service and security provider, we can serve as a trusted partner to navigate this process across industry and government. 

Tomorrow’s quantum computers threaten today’s data 

In our previous blog post , we discussed the limitations of current quantum computers in terms of breaking today’s encryption technology. In parallel, the emergence of scaled quantum computers with specific algorithms—such as Shor’s algorithm—could put public key encryption at risk and compromise sensitive information. 

While it may take at least 1 million qubits for a quantum computer to break certain encryption algorithms using Shor’s algorithm, today’s long-term and sensitive data could already be at risk: bad actors could carry out a “Harvest Now, Decrypt Later” scenario by recording data today and decrypting it later when cryptographically relevant quantum computers become available. Therefore, knowing which data to secure now is a first step on the path to a quantum-safe future.   

Microsoft’s commitment to keeping our customers and partners secure 

Putting our recommendations into practice, we have taken a comprehensive approach to quantum safety. Because quantum will have a material impact on today’s classical encryption of both hardware and software, we’ve invested time and efforts to set cross-company goals and establish accountability at the most senior levels of our organization. This led to the establishment of the Microsoft Quantum Safe Program , which aims to accelerate and advance all quantum-safe efforts across Microsoft from both technical and business perspectives. The program focuses on Microsoft’s transition to quantum safety and the adoption of PQC algorithms across our products, services, and datacenters. Additionally, it aims to assist and empower our customers and partners on their own journey to quantum safety across their processes, priorities, and requirements.  

As the first step and highest priority, we are ensuring the compliance of our existing symmetric key encryption and hash function algorithms. Symmetric algorithms, such as Advanced Encryption Standard (AES), and hash functions, such as Secure Hash Algorithm (SHA), are resilient to quantum attacks , and can therefore still be used in deployed systems. At Microsoft, we are already using protocols based on symmetric encryption, such as Media Access Control Security (MACsec) point-to-point protocol . 

On top of symmetric encryption, we will prioritize PQC algorithms—still in the process of being standardized by global bodies such as the National Institute of Standards and Technology (NIST) , International Standards Organization (ISO) , and Internet Engineering Task Force (IETF) —to handle future threats where asymmetric encryption is currently used. Today, much of the internet’s data, from e-commerce to Wi-Fi access, is kept secure by public key, or asymmetric key cryptography. Currently used public key algorithms rely on complex mathematical problems considered infeasible for classical computers to break, but that are a perfect task for quantum computers running Shor’s algorithm. This undermines the effectiveness of public key algorithms like RSA and Elliptic Curve Cryptography (ECC), and means that PQC algorithms will need to be deployed quickly once standardized, starting with hybrid encryption schemes in tandem with classical algorithms to accelerate adoption. 

Empowering and collaborating with the global community 

We see the effort to achieve quantum safety as a collaborative effort, and this is why we invest heavily in our ecosystems, global partnerships, and close collaborations with standards-setting bodies, academia, and industry partners alike to foster continuous innovation in the quantum security landscape. The standardization of PQC algorithms, driven by NIST’s efforts, is a key step to achieving PQC compliance.

Because we believe that PQC adoption is the ideal path to follow, we’re collaborating with standard-setting bodies while conducting experiments and assessments to facilitate the adoption of these algorithms across our services and products as needed.  As an example, we are participating in the NIST/NCCoE Migration to PQC to demonstrate vulnerable cryptography detection and drive PQC experiments and integration capabilities. Those efforts, along with our participation in the Open Quantum Safe project, will allow the members to implement and test PQC candidates together, so we can be ready for adoption once the final specs are out.  

Furthermore, as part of our investment to empower and collaborate with the global security community, we co-authored FrodoKEM , a quantum-safe key encapsulation mechanism that has been selected, together with Kyber and Classic McEliece, to be part of the first international ISO standard for PQC (in addition, we are participating as co-editors of the standard). We also recently submitted SQISign, a new quantum-safe signature scheme that we co-authored with several industry and academia partners, to NIST’s call for additional signature schemes. Lastly, we continue to actively participate as founding members of the new post-quantum cryptography coalition by MITRE and will help to drive progress toward a broader understanding of the public adoption of PQC and NIST’s recommendations. 

While we continue to conduct research to further develop state-of-the-art security solutions, we are also exploring the potential of other classical and quantum technologies, such as Quantum Key Distribution (QKD). Holistically, at the core of our mission is a commitment to achieving quantum-safety and ensuring the security of our customers.

Getting started with your PQC transition today  

To support our customers in preparing for and navigating their quantum-safe journey, we offer assistance and guidance: we invite you to start your path with us by filling out this questionnaire . Based on your responses, we can understand your status and priorities, and provide the necessary support, including access to experts.  

As a first step, we recommend starting with a comprehensive planning process and a definition of your organization’s criteria for what constitutes your critical areas and sensitive information, alongside a cryptography inventory and impact assessment of your essential data, code, cryptographic technologies, and the critical services of your organization. This will help you to identify any asymmetric encryption in use that will need to be replaced with the latest PQC standardized algorithms. This process is especially important to identify critical areas and systems that involve or protect sensitive data with a value that extends beyond 10 years and should be prioritized in migrating to PQC. 

By considering which data and code need to be secured now, and which may become less relevant over time, as well as uncovering specific instances where cryptography could be used inappropriately or not ideally, your organization will have a better understanding of where to best mitigate potential risks as a quantum future approaches. This will enable you to confidently make the switch to the latest PQC standardized algorithms and safeguard your sensitive data for years to come. 

Explore CodeQL  

To help, we are contributing to CodeQL : a next-generation program code analysis tool provided by GitHub in collaboration with organizations including NIST and NCCoE. With CodeQL, we are building out a comprehensive set of detections that can empower users to create a complete inventory of all encryption usage within the application layer, helping to produce a cryptographic bill of materials and identify legacy cryptography that requires remediation. This tool can thus help create a cryptography inventory and impact assessment that will drive operational planning and create understanding and clarity around the timeline, resources, and level of risk for which to account.

Try now the Crypto Experience for Resource Estimator  

Furthermore, we recently launched the Crypto Experience for Azure Quantum Resource Estimator . Drawing on published research from Microsoft , this new interactive cryptography experience will show you why a symmetric key could remain safe from quantum attacks, but the current public key is vulnerable. And because it is integrated with Copilot in Azure Quantum, you can use the universal user interface of natural language to ask, learn, and explore more topics within the intersection of quantum computing and cryptography.  

The opportunity to usher in a quantum, and quantum-safe, future is immense. We see how the collective genius of scientists and businesses will revolutionize the building blocks of everyday products to usher in a new era of innovation and growth in many fields. That’s what motivates us at Microsoft to drive new breakthroughs and empower every person and every organization on the planet. Our commitment to our customers, partners, and ecosystem to become quantum-safe and remain secure has never been stronger. We are accountable for having our products and services quantum-resistant and safe and will support and guide our customers through this journey to quantum safety. 

• Start your journey with Microsoft towards quantum-safety by filling out this questionnaire . 
• Learn more about our vision of quantum networking .
• Explore the Open Quantum Safe project for prototyping and evaluating quantum-resistant cryptography.
• Visit the Azure Quantum website and check out the Microsoft Quantum Innovator Series webinars .

To learn more about Microsoft Security solutions, visit our  website.  Bookmark the  Security blog  to keep up with our expert coverage on security matters. Also, follow us on LinkedIn ( Microsoft Security ) and X (formerly known as “Twitter”) ( @MSFTSecurity ) for the latest news and updates on cybersecurity.

A Mathematical Journey to Quantum Mechanics

• © 2021
• Salvatore Capozziello 0 ,
• Wladimir-Georges Boskoff 1

Dipartimento di Fisica, INFN Sezione di Napoli - Università degli Studi “Federico II”, Napoli, Italy

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Department of Mathematics and Informatics, Universitatea Ovidius Constanţa, Constanta, Romania

• Facilitates learning presenting each topic from elementary–intermediate level to advanced
• Shows that parallelism is continuously made between classical mechanics and quantum mechanics formalism
• Gives proofs of theorems with all details necessary to understand

Part of the book series: UNITEXT for Physics (UNITEXTPH)

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A Matter of Principle: The Principles of Quantum Theory, Dirac’s Equation, and Quantum Information

Towards a constructive foundation of quantum mechanics, the development of quantum mechanics.

• Textbook in Quantum Mechanics
• Elementary Particles, Quantum Field Theory
• Quantum Theory
• Theoretical Particle Physics
• Functional Analysis
• Operator Algebra
• Analytic Mechanics
• Lagrangian Mechanics
• Hamiltonian Mechanics

Table of contents (12 chapters)

Front matter, introduction: how to read this book.

• Salvatore Capozziello, Wladimir-Georges Boskoff

Newtonian, Lagrangian and Hamiltonian Mechanics

Can light be described by classical mechanics, why quantum mechanics, the schrödinger equations and their consequences, the mathematics behind the harmonic oscillator, from monochromatic plane waves to wave packets, the heisenberg uncertainty principle and the mathematics behind, the principles of quantum mechanics, consequences of quantum mechanics principles, quantum mechanics at the next level, conclusions, back matter, authors and affiliations.

Salvatore Capozziello

Wladimir-Georges Boskoff

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Book Title : A Mathematical Journey to Quantum Mechanics

Authors : Salvatore Capozziello, Wladimir-Georges Boskoff

Series Title : UNITEXT for Physics

DOI : https://doi.org/10.1007/978-3-030-86098-1

Publisher : Springer Cham

eBook Packages : Physics and Astronomy , Physics and Astronomy (R0)

Copyright Information : The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Hardcover ISBN : 978-3-030-86097-4 Published: 28 September 2021

Softcover ISBN : 978-3-030-86100-1 Published: 29 September 2022

eBook ISBN : 978-3-030-86098-1 Published: 27 September 2021

Series ISSN : 2198-7882

Series E-ISSN : 2198-7890

Edition Number : 1

Number of Pages : XV, 289

Number of Illustrations : 10 illustrations in colour

Topics : Quantum Physics , Atomic/Molecular Structure and Spectra , Theoretical, Mathematical and Computational Physics , Functional Analysis

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Journey from Classical to Quantum in Two Dimensions

• School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia

One of the major challenges in physics today is to describe the behavior of many interacting quantum particles. What makes this problem especially hard is when the motion of the interacting quantum particles is severely restricted by the intrinsic structure of the material. This is true in 2D materials like graphene and in layered structures that exist in exceptionally high-temperature superconductors. Such 2D systems feature strongly enhanced interactions compared to 3D and are notoriously difficult to treat theoretically. Now, two experimental groups have extracted fundamental statistical information about the properties of interacting atoms confined to move in a plane. Chris Vale and colleagues from Swinburne University, Australia [ 1 ], as well as Tilman Enss and collaborators from Heidelberg University, Germany [ 2 ], have measured the equation of state for fermionic atoms in two dimensions (2D), thus determining the relationship between temperature, particle density, and interaction strength. This equation of state reveals the peculiar nature of 2D, where quantum mechanics can fundamentally change the character of interactions, and it provides an important benchmark for theories of two-dimensional interacting systems.

Since the 19th century, physicists have exploited the powerful fact that a single equation can describe the thermodynamics of many substances, even when the constituent particles are very different. A classic example is the ideal gas law, an equation of state that neglects the interparticle interactions and applies to all gases of atoms or molecules at high enough temperatures (corresponding to room temperature in many cases). However, it quickly becomes challenging to construct theories of many-particle systems at lower temperatures, where the quantum nature of the particles and the interactions between them play a significant role.

The situation is even more complex if the particle motion is constrained to lower dimensions such as 2D, giving rise to strikingly different behavior as the gas evolves from classical to quantum. For instance, when the interactions between particles are short ranged, a 2D system of classical particles behaves as if there is no length scale associated with the interactions, unlike in 3D. However, for quantum particles, the uncertainty principle always guarantees a finite length scale: for the case of attractive interactions, it is set by the two-body (dimer) bound state [ 3 ]. This length scale becomes apparent in the equation of state as the temperature is lowered (or, equivalently, the density is increased) such that the de Broglie wavelength of the particles approaches the interparticle separation and the gas enters the quantum regime.

Experiments on optically and magnetically trapped ultracold atoms provide a unique test bed in which to investigate the behavior of such 2D quantum gases since they can be tuned across a range of interactions and temperature regimes [ 4 ]. If the quantum particles are fermions, the physics is particularly rich, since the Pauli exclusion principle provides an additional form of interaction between particles. In this case, the interplay between Fermi statistics and attractive interactions gives rise to a crossover from a weakly attractive Fermi gas to a Bose gas of tightly bound dimers as the attraction is increased [ 3 , 5 ]. Below a critical temperature, the system eventually undergoes a transition to a superfluid phase [ 6 ]. Within this low-temperature regime, the equation of state has already been probed experimentally [ 7 ] and was found to be consistent with the behavior expected from theories at zero temperature [ 5 ]. However, it has remained an open question how the 2D equation of state evolves with temperature.

To address this point, the groups in Swinburne and Heidelberg have had to combine two innovative approaches. First, they have employed a highly anisotropic trapping potential that effectively freezes out motion in one direction and only allows atoms to move freely within a single plane (see Fig. 1). The weak in-plane trapping potential creates a region of high atom density at the trap center, where quantum effects are significant, while leaving the trap edges at low density, where the system behaves like a classical high-temperature gas. By measuring the atom number as a function of position in the plane, they were thus able to probe a wide range of parameter phase space in a single cloud. Second, they constrained errors in the temperature and other experimental observables by using known thermodynamic relations between these quantities, similar to what was done in earlier 3D experiments [ 8 ]. In particular, they could extract the temperature of their 2D gas by fitting the classical outer edge of the atom cloud to an exact high-temperature equation of state that builds on the ideal gas law.

Following such a protocol, the two teams have produced complementary studies of how the particle density depends on temperature and chemical potential: the Swinburne group has focused on the weakly attractive regime while the Heidelberg team’s experiment spans the crossover to a Bose gas of dimers. In both cases, this 2D equation of state clearly displays the impact of the dimer bound state. By comparing the density with that expected for an ideal (noninteracting) Fermi gas, it becomes apparent that the attractive interactions produce the largest density enhancement in the region between the quantum center and the classical edge. This implies that the particle interactions are strongest here in this intermediate location, where the characteristic distance between particles approaches the scale set by the de Broglie wavelength. For higher densities, the effect of interactions diminishes as the interparticle distance becomes small with respect to the dimer state. This behavior is strikingly absent in previous studies of 2D Bose gases [ 9 ] and in recent 3D Fermi gas experiments [ 8 ], where the strongest interactions occur in the quantum regime.

These experiments are just the beginning. Knowledge of the equation of state for a 2D Fermi gas can be used to develop theories of strongly interacting fermions, and it can provide a basis for describing phenomena beyond the equilibrium case, such as spin dynamics [10]. However, there is also a hidden richness here, namely, the fact that the 2D gas is embedded in three dimensions. The layer thickness then corresponds to another tuning knob for the interactions, which could, for example, be used to test whether superfluidity exists at a higher temperature when the gas lies between 2D and 3D [ 11 ].

This research is published in Physical Review Letters .

• K. Fenech, P. Dyke, T. Peppler, M. G. Lingham, S. Hoinka, H. Hu, and C. J. Vale, “Thermodynamics of an Attractive 2D Fermi Gas,” Phys. Rev. Lett. 116 , 045302 (2016) .
• I. Boettcher, L. Bayha, D. Kedar, P. A. Murthy, M. Neidig, M. G. Ries, A. N. Wenz, G. Zürn, S. Jochim, and T. Enss, “Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover,” Phys. Rev. Lett. 116 , 045303 (2016) .
• M. Randeria, J.-M. Duan, and L.-Y. Shieh, “Bound States, Cooper Pairing, and Bose Condensation in Two Dimensions,” Phys. Rev. Lett. 62 , 981 (1989) .
• I. Bloch, J. Dalibard, and W. Zwerger, “Many-body Physics with Ultracold Gases,” Rev. Mod. Phys. 80 , 885 (2008) .
• J. Levinsen and M. M. Parish, “Strongly interacting two-dimensional Fermi gases,” Ann. Rev. Cold Atoms Mol. 3 , 1 (2015) .
• P. A. Murthy, I. Boettcher, L. Bayha, M. Holzmann, D. Kedar, M. Neidig, M. G. Ries, A. N. Wenz, G. Zürn, and S. Jochim, “Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas,” Phys. Rev. Lett. 115 , 010401 (2015) .
• V. Makhalov, K. Martiyanov, and A. Turlapov, “Ground-State Pressure of Quasi-2D Fermi and Bose Gases,” Phys. Rev. Lett. 112 , 045301 (2014) .
• M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, “Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas,” Science 335 , 563 (2012) .
• R. Desbuquois, T. Yefsah, L. Chomaz, C. Weitenberg, L. Corman, S. Nascimbène, and J. Dalibard, “Determination of Scale-Invariant Equations of State without Fitting Parameters: Application to the Two-Dimensional Bose Gas Across the Berezinskii-Kosterlitz-Thouless Transition,” Phys. Rev. Lett. 113 , 020404 (2014) .
• M. Koschorreck, D. Pertot, E. Vogt, and M. Köhl, “Universal Spin Dynamics in Two-Dimensional Fermi Gases,” Nature Phys. 9 , 405 (2013) .
• A. M. Fischer and M. M. Parish, “Quasi-Two-Dimensional Fermi Gases at Finite Temperatures,” Phys. Rev. B 90 , 214503 (2014) .

About the Author

Meera Parish is a Senior Lecturer in theoretical physics at Monash University in Melbourne, Australia. Since obtaining her Ph.D. from the University of Cambridge in 2005, she has been a PCTS postdoctoral fellow at Princeton University; a Director of Studies at Clare College, Cambridge; and a Lecturer and EPSRC research fellow at University College London. Her research focuses on strongly correlated phenomena at the interface between ultracold atomic gases and condensed matter. In 2012, she was awarded the IOP Maxwell medal and prize for her achievements.

Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover Region

I. Boettcher, L. Bayha, D. Kedar, P. A. Murthy, M. Neidig, M. G. Ries, A. N. Wenz, G. Zürn, S. Jochim, and T. Enss

Phys. Rev. Lett. 116 , 045303 (2016)

Published January 27, 2016

Thermodynamics of an Attractive 2D Fermi Gas

K. Fenech, P. Dyke, T. Peppler, M. G. Lingham, S. Hoinka, H. Hu, and C. J. Vale

Phys. Rev. Lett. 116 , 045302 (2016)

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NIST and the long journey to quantum safety

Quantum computing holds the potential to be one of the most era-defining innovations. So much so, that it’s almost impossible to predict the exact effects it will have across the world of technology. But there’s one thing that most in the tech industry agree on – it will eventually signal the end of asymmetric (public-key) cryptography, which underpins the system of machine identities enabling our online world to exist. Now, the world is racing to discover algorithms resistant to cracking by quantum computers and achieve “quantum safety”. And NIST has taken the lead by announcing  the first four contenders .

Forward-thinking CISOs will want to start preparing now, despite change not being imminent. And they should assume that the switch between pre- and post- quantum worlds will be defined by hybrid use of both new and old machine identities.

Cracking the cryptographer’s enigma

Today’s digital systems uses a binary numerical system – zeros and ones – to store and process information. Quantum computers on the other hand use qubits – these are quantum particles that don’t behave according to the traditional rules of physics. This allows them to be a zero and a one simultaneously, which theoretically will reduce the overall time required to solve mathematical problems and process data.

At its core, this presents significant issues for cryptographers. Current public-key encryption systems rely on mathematical challenges, which computers struggle to solve due to sub-standard processing power. On the other hand, quantum computers have the potential to solve these problems in the blink of an eye, meaning they could break current encryption standards with ease.

The internet’s transfusion won’t happen overnight

Why does it matter if our current encryption standards are upended? RSA produced the first crypto system in 1977, establishing public key cryptography as the primary mechanism for determining trust and authentication online. This underpinned the digital certificates and cryptographic keys that give machines an identity and laid the foundations for our entire system of encryption. Now, these machine identities are the primary method for securing all our online communications – from sensitive customer data to financial transactions or even national security secrets.

They ensure that all machines can communicate securely, including everything from servers and applications to Kubernetes clusters and microservices. They run through our digital world like blood travelling around the circulatory system of the body. So, replacing these standards with quantum will be akin to giving the internet a transfusion.

We’ve all seen the discussions around the so-called “crypto-apocalypse” – when quantum computers come online and crack our current systems of cryptography wide open. In truth, the reality isn’t quite as dramatic. There won’t be a single catastrophic doomsday event where the world’s secrets are brought into the light and the global economy ceases to function. No, we’re likely to see a slow and steady journey to quantum which is driven by the needs of leadership teams and markets.

It's now been 40 years since the inception of the original RSA crypto-system, and the journey to achieve our current encryption standards has been long and onerous. The move to quantum resistance is likely to take decades too, if not longer.

Establishing a standard

Leading the charge to develop a post-quantum cryptographic standard for organisations is the US government’s National Institute of Standards and Technology (NIST). There’s been a lot of progress since 2016 when  NIST called on  the world’s leading minds in cryptography to devise new ways to resist attacks from quantum computers. None more so than from July’s update, where the world of cryptography reached a vital milestone when NIST  announced  the first group of four quantum-resistant algorithms. And we are set to see four more announced soon.

By releasing eight algorithms, NIST recognises that cryptography is deployed in a multitude of use cases, and therefore diversity in encryption is a must. It’s also essential to mitigate the risk of potentially vulnerable, early-stage algorithms.

For this, NIST selected the  CRYSTALS-Kyber  algorithm for “general encryption”, due to its relatively small encryption keys and operation speed. And for digital signatures, such as the one’s used within TLS machine identities, it selected the  CRYSTALS-Dilithium ,  FALCON  and  SPHINCS+  algorithms. As the primary algorithm, NIST recommends CRYSTALS-Dilithium, and FALCON is regarded as useful for applications which require smaller signatures. Meanwhile, SPHINCS+ is larger and slower than the others, but is useful as a backup option due to its slightly different mathematical approach.

With things accelerating from a standards perspective, organisations now have a clearer path towards planning their own post-quantum journey.

Beginning the journey

Many will be tempted to turn a blind eye to these early algorithms. They’ll no doubt see that this kind of planning will take considerable effort – after all, we’re talking about a transformation on the same level as changing the way you ride a bike. Yet, while the current machine identity system is working fine now, this won’t always be the case. And sooner or later, CISOs will have to act.

While early-stage standards exist, it makes the most sense to start planning laboratory condition testing. Start by choosing a single application and understanding the performance impact of the new algorithms, how to deal with larger machine identities, and how to operate dual pre- and post-quantum modes. The latter point is especially key, because for the next few decades, the world is likely to transition to quantum safety via a hybrid approach – much like how we’ve seen the switch to electric vehicles via hybrid cars. The old will work alongside the new.

Having a control plane to automate the management of these machine identities will be crucial to this hybrid mode, enabling visibility over what machine identities are being used with different context, and how they perform.

Of course, it will be difficult to truly predict how long this transition period will last. It’s likely that many currently within the industry will not see the end of it. But, like climate change, it’s not something that we can push down the road for a future generation to deal with.

So, pick an application to test and factor it into next year’s budget. Set yourself a five-year plan to have the first quantum-resistant app up and running. While the road may change course, the destination certainly won’t. It’s time to take the first steps.

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Journey to the Quantum Promised Land

Quantinuum and CU Boulder recently  announced  that they created a  logical four-qubit GHZ state  using a  non-local qLDPC code . GHZ states are a simple way of assessing quantum computer hardware, because the qubits should measure all zeroes or all ones – all other measurement outcomes are in error – so it is quick and easy to visualize device quality. qLDPC codes benefit ion trap and neutral atom modalities by leveraging their all-to-all qubit connectivity to reduce circuit depth and lower the counts of gates required to execute an algorithm.

Normally, the big deal here would be that four logical qubits outperformed four physical qubits, surpassing the coveted “breakeven” milestone, but this story has a bigger deal than that.

What’s a “logical” qubit?

We encode information onto physical qubits, but physical qubits are currently too error prone to be useful with the deep quantum circuits we want to run. Fortunately, information can be encoded redundantly across multiple physical qubits such that the error rate of each resultant “logical qubit” is lower than the error rates of its constituent physical qubits.

A few short years ago, estimates were that 1,000 physical qubits would be needed to encode each logical qubit. This ratio had made the notion of large-scale fault-tolerant quantum computing (FTQC) seem implausible. However, this ratio has been improving over recent years with the introduction of novel quantum error correction (QEC) codes and quantum low-density parity check (qLDPC) codes. In fact, Quantinuum surpassed the “breakeven” milestone by encoding 4 logical qubits with only 25 physical qubits.

Why do we need logical qubits?

Breakeven is important, but it’s not enough. Logical qubits don’t just have to be better than physical qubits, they have to be much, much better than physical qubits. And while advancements in both logical and physical qubits are expected to continue in the coming years, advancements in logical qubits are expected to come much faster. Quantinuum anticipates its next breakthrough, for example, might jump from four to eight logical qubits.

Quantum Volume (QV) is a measure of a quantum computer’s computational power, indicating the largest quantum circuit you can expect to run on that particular device. And while QV scores have been rising steadily over the years – Quantinuum doubled its previous record thrice this year – advancements in physical qubits are not expected “to get to the promised land,” as Dr. Dave Hayes puts it. Logical qubits will be needed to get there.

There’s another breakeven milestone.

Quantinuum is already the  recognized leader in QV , so now it’s talking about an analogous  logical QV . In other words, what is the largest quantum circuit that can be run on a quantum computer that encodes quantum information on logical qubits?

If logical QV can follow the history of physical QV, a pivotal moment will occur when logical QV scores begin to pass physical QV scores. At the moment, Quantinuum has only one data point, which is a logical QV of 256. A logical QV of 256 is derived from 2^8, which means that 8 logical qubits can execute a quantum circuit with depth 8. Although there is still a lot of work to do to reach large-scale fault-tolerant quantum computing, the score of 256 is significant in another way.

The highest physical QV scores outside Quantinuum (which currently boasts a physical QV of 2^20=1,048,576) are reported by IBM Quantum, which reported a physical QV of 2^8= 256 on April 6, 2022, and is currently reporting a physical QV of 2^9= 512 . While the jump from 256 to 512 might seem significant, QV scores always increment by doubling. The significance of these numbers is that Quantinuum is already reporting a logical QV of 256, which is only one announcement away from equaling IBM Quantum’s best physical QV, only two announcements away from surpassing it, and already surpassing everyone else’s reported physical QV scores. That certainly seems like a big deal.

Quantinuum still has a way to go to surpass its own physical QV scores, but it is hoping for exponential advancements akin to a “logical Moore’s Law.” At that rate, it could potentially catch up to itself within a few years.

Logical Quantum Volume is a logical – pardon the pun – metric for assessing how close we are to large-scale fault-tolerant quantum computing. If Quantinuum can make the progress it hopes to make, the next few years ought to be exciting.

Speaking of excitement, did you know that you can play with Quantinuum’s hardware for free? Microsoft Azure offers some free time, and you can also apply for some free time through Oak Ridge National Laboratory (ORNL). You can follow along on Quantinuum’s journey, conduct some research of your own, and hopefully reach the “promised land” of quantum computing in less than 40 years.

Categories: quantum computing

Tags: logical qubit , Quantinuum , Quantum , UC Boulder

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Y2Q: A journey to quantum safe cryptograpy

A note on potential largest global migration programs since Y2K

The promise of unprecedented computing power to solve current intractable problems is a very attractive proposition for quantum computers. But these quantum computers also have the potential to pose a significant threat to the security of many cryptographic systems that we currently use. Y2Q is anticipated to be one of the largest global migration programs affecting most of the information and communication systems since Y2K.

Most organizations face challenges in understanding and appreciating the complexity and enormity of this huge migration process. Read more about it in this report that compares Y2Q to Y2K, and discusses similarities and differences, enhancing awareness for this quantum threat and encouraging action.

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• First 10 $672.34
• First 50 $3,586.11
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Editorial Reviews

From the back cover, about the author, product details.

• ASIN ‏ : ‎ B09HB5R583
• Publisher ‏ : ‎ Springer (September 27, 2021)
• Publication date ‏ : ‎ September 27, 2021
• Language ‏ : ‎ English
• File size ‏ : ‎ 72466 KB
• Text-to-Speech ‏ : ‎ Enabled
• Screen Reader ‏ : ‎ Supported
• Enhanced typesetting ‏ : ‎ Enabled
• X-Ray ‏ : ‎ Not Enabled
• Word Wise ‏ : ‎ Enabled
• Print length ‏ : ‎ 310 pages
• #207 in Functional Analysis
• #237 in Molecular Physics (Kindle Store)
• #871 in Mathematical Physics (Kindle Store)

About the author

Wladimir-georges boskoff.

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