**The Potential of Quantum Computing to Revolutionize Condensed Matter Systems and Cryptography**

Quantum computing has made significant progress in recent years, and one of its most promising applications is in simulating condensed matter systems. According to Dr. Apsara Guzik, Assistant Professor of Chemistry and Chemical Biology at Harvard's Faculty of Arts and Sciences, there is a fundamental problem with simulating quantum systems using conventional computers. As the size of the system grows, the computational resources required to simulate it grow exponentially, making it a daunting task even for the most powerful classical computers.

"This means that if we can simulate a chemical reaction, we can predict the outcome digitally, which would allow us to design new cures for diseases faster and help us understand the human body in a much deeper level," Dr. Guzik explained. "The potential of quantum computing is huge here." Goldman Sachs has already invested in 2D Wave, a quantum computing company that aims to find new ways to model financial data and better understand key global risk factors. Financial modeling teams use every trick they can to simulate the global market, but quantum computing could help mitigate this risk.

**Accessing Quantum Computing from Anywhere**

One of the exciting aspects of quantum computing is its accessibility. With cloud-based options available from laptops, anyone can try out quantum algorithms in Python using Jupyter Notebooks or IBM's Q Network API. This democratization of access to quantum computing technology has opened up new avenues for research and experimentation.

Dr. Guzik noted that "anyone can use quantum computing in their web or mobile applications." With cloud-based platforms like D-Wave's Leap and IBM's Q Network, users can access quantum computers from anywhere with an internet connection. This makes it possible to explore the capabilities of quantum computing without the need for expensive hardware.

**Post-Quantum Cryptography: A New Era of Security**

Another area where quantum computing has significant implications is in cryptography. As quantum computers become increasingly powerful, classical cryptographic algorithms will no longer be secure against them. This has led to a new field of research focused on developing post-quantum cryptographic algorithms that can resist attacks from both classical and quantum computers.

There are four major research directions currently being pursued: hash-based cryptography, multivariate-based cryptography, code-based cryptography, and lattice-based cryptography. The National Institute of Standards and Technology (NIST) is leading the effort to standardize new post-quantum cryptographic algorithms. Initially, 82 candidates were selected for further consideration, but today there are 26 algorithms still in contention.

**Lattice-Based Cryptography: A Promising Approach**

One of the most promising approaches in post-quantum cryptography is lattice-based cryptography. A lattice can be thought of as any regularly spaced grid of points stretching out to infinity. The security of lattice-based cryptography relies on the hardness of solving problems based on that paradigm.

The New Hope algorithm, developed by Google researchers two years ago, is an example of a method called learning with errors. It creates a secret key value S, which is the private key, and another value E for errors. A public key is then generated based on random numbers A and B. The values of A and B become the public key.

To implement this algorithm, researchers use Python and libraries like NumPy. The key concept here is the use of randomness, which often turns out to be a very useful concept in security. The New Hope technique is actually a variant of the Ring Learning with Errors algorithm, but with several modifications that have been added.

**Quantum Supremacy: A Pivotal Moment**

In 2019, Google achieved quantum supremacy, a pivotal moment in history that marks the beginning of a new era in computing. This milestone has significant implications for fields like medicine, finance, and security.

The achievement of quantum supremacy opens up opportunities for solving incredibly hard problems in these fields. Quantum computing is definitely an area worth learning more about, with great resources available in the video description.

"WEBVTTKind: captionsLanguage: enwell quantum computing destroy blockchain there is no blockchain hello world it's Suraj and the internet is ablaze with talk about quantum supremacy right now that's because a research paper offered by Google claimed to achieve it it was briefly posted on a NASA website before being removed luckily I found a leaked copy which I've linked for you in the video description in this episode we're going to talk about what they actually did what the applications of quantum supremacy are and we'll learn a quantum resistant encryption algorithm called a new hope in the paper they claimed that their quantum computer was able to perform a certain calculation in 3 minutes and 20 seconds that would take today's most advanced classical computer about 10,000 years yes that did make me salivate but here's the key takeaway Google built a quantum computer that can do something faster than a classical computer not something useful this was a sign of much needed progress in this field because over the past 20 years despite billions of dollars having been spent on quantum computing research no quantum computer was used even once to solve any problem faster than a laptop could or at least not in any way that depended on it being a quantum computer rather than a classical computer Google demonstrated that quantum computing is a real phenomenon there is no fundamental reason why we can't build useful quantum computers just temporary technological limitations quantum supremacy is a word used to describe a quantum computer that could solve some well-defined set of problems that would take orders of magnitude longer to solve with any currently known techniques running on existing computers the calculation that Google attempted was pretty simple to understand unlike Google Buzz their experiment consisted of three components a pseudo-random number generator a random sampling algorithm and an algorithm that can verify randomness based on the sample the pseudo-random number generator was a quantum circuit this circuit consisted of a certain random sequence of single and two qubits logical operations with up to 20 of these operations known as gates randomly strung together the sampling algorithm was another quantum circuit the randomness verification was done by computing the probability that a given random number appears in a random number sequence sample then verifying that it did appear that often this is a pretty simple problem for classical computers to solve for a few random numbers but the more random numbers you give it the harder it gets basically it was able to generate a pseudo-random number in such a way that it would take a much longer amount of time on a conventional computer to reproduce that same pseudo-random number from the same initial conditions so don't break out the tinfoil hats just yet it will built a quantum computer that can do something faster than a classical computer not something useful so even though that isn't really useful we now know that quanta computers can do something faster than classical computers can we can expect the race towards faster quantum computers to speed up as a result as this opens up lots of possibilities for theoretically solving hard problems in many industries there are three that I find the most fascinating security medicine and finance in terms of security there's this belief that quantum computers are going to be able to break all encryption which would mean that banks governments and cryptocurrency networks which use encryption algorithms for security would become hackable yes bitcoin including but in order for that to be a reality it's going to require some more technical advances in quantum computing specifically scalability ie more cubits and robust quantum error correction error correction ensures we get useful results classically it's done by copying and storing information multiple times in case there's an error then the output will still give correct answers based on the majority of information all copied bit scary this turns out to be impossible in quantum computing due to the no-cloning theorem where it states quantum information can't be copied so error correction must be done differently lots of techniques have been proposed in this regard but we still have a ways to go and when that happens quantum computers will only be able to break some types of encryption not all of them but it turns out that those types include most of what we currently use to secure the Internet RSA diffie-hellman elliptic curve cryptography meant these types of attacks when it comes to medicine there is huge potential for quantum computing to enable new solutions the Google team generated a pseudo-random number with their quantum computer but one of the next milestones is likely to be able to use it to do some kind of useful simulation probably of a condensed matter system much faster than any known classical method could one step closer to the matrix along Apsara guzik assistant professor of chemistry and chemical biology in Harvard's Faculty of Arts and Sciences said that there is a fundamental problem with simulating quantum systems such as chemical reactions on conventional computers as the size of a system grows the computational resources required to simulate it grow exponentially for example it might take one day to simulate a reaction involving ten atoms two days for 11 atoms four days for 12 atoms eight days for 13 atoms and so on before long this would exhaust the world's computational power if we can simulate a chemical reaction we can predict the outcome digitally that would allow us to design new cures for diseases faster and help us understand the human body brain included at a much deeper level and then there's finance Goldman Sachs has invested in 2d wave a quantum computing company hoping to find new ways to model financial data that would ultimately help understand key global risk factors the global market is very computationally expensive to simulate and financial modeling teams use every trick they can to do so on some level this helps mitigate risk which allows them to invest smarter quantum computing has huge potential here if we want to experiment with quantum computing technology ourselves we've got a few cloud options that we can access from our laptops d-wave has a quantum api called leap with so much well-documented code jupiter notebooks included yes you can code quantum algorithms in Python I think I'm in love with this technology anyone can use quantum computing in their web or mobile applications accessing it from the cloud there's also IBM's Q Network which also offers an API to try it's machines but a field I find just as interesting as quantum computing is post quantum cryptography the field dedicated to devising cryptographic algorithms that are thought to be secure in the quantum era with security against both classical and quantum computers to build a post quantum crypto system there are four major research directions that are being pursued there's hash based cryptography which focuses on designing digital signature schemes based on the security of cryptographic hash functions there's also multivariate based cryptography its security relies on the hardness of solving multivariate systems of equations there's code based cryptography and its security relies on the hardness of problems from coding theory there's lattice based cryptography a lattice can be thought of as any regularly spaced grid of points stretching out to infinity it's security relies on the hardness of solving problems based on that paradigm one of the most important standard-setting organizations is the National Institute of Standards and Technology NIST it's really influential in determining which standardized cryptographic systems see worldwide adoption all hail NIST at the end of 2016 they announced that they would hold a multi-year open project with the goal of standardizing new post quantum cryptographic algorithms initially they selected 82 candidates for further consideration from all submitted algorithms today there are 26 algorithms still in contention among them there are 12 lattice based schemes 7 code based for multivariate based 1 hash based and two other based it's expected to have the first set of standards by 2025 the research direction that seems to be the most active is lattice based cryptography and a top technique here is titled the new hope algorithm Google researchers invented this two years ago guided by the force probably and it's an example of a method called learning with errors let's discuss how this works at a high level learning with errors is a known quantum robust method of cryptography the idea is that we create a secret key value S which is our private key and another value e for errors then we create a public key based on random numbers a and then generate another set of numbers B B is based on a s and E the values of a and B become our public key a and B are one dimensional matrices when s is a single value if we want s to be a one dimensional matrix instead a will be a two dimensional matrix and B will be a one dimensional matrix it turns out that quantum computers can't find the values which solve this equation where a and B are known we can implement this very simply with PI and numpy the key here is the use of randomness which quite often turns out to be a very useful concept in security the New Hope technique is actually a variant of this algorithm called ring learning with errors but I'll spare you the details since there's a lot of little modifications they added there are three things to remember from this video Google achieved quantum supremacy this is a pivotal moment in history and it means lots of opportunities for solving incredibly hard problems in fields like medicine finance and security a new hope is a quantum resistant algorithm that has the most traction these days and quantum computing is definitely a topic to learn more about I've got great resources for you in the video descriptionwell quantum computing destroy blockchain there is no blockchain hello world it's Suraj and the internet is ablaze with talk about quantum supremacy right now that's because a research paper offered by Google claimed to achieve it it was briefly posted on a NASA website before being removed luckily I found a leaked copy which I've linked for you in the video description in this episode we're going to talk about what they actually did what the applications of quantum supremacy are and we'll learn a quantum resistant encryption algorithm called a new hope in the paper they claimed that their quantum computer was able to perform a certain calculation in 3 minutes and 20 seconds that would take today's most advanced classical computer about 10,000 years yes that did make me salivate but here's the key takeaway Google built a quantum computer that can do something faster than a classical computer not something useful this was a sign of much needed progress in this field because over the past 20 years despite billions of dollars having been spent on quantum computing research no quantum computer was used even once to solve any problem faster than a laptop could or at least not in any way that depended on it being a quantum computer rather than a classical computer Google demonstrated that quantum computing is a real phenomenon there is no fundamental reason why we can't build useful quantum computers just temporary technological limitations quantum supremacy is a word used to describe a quantum computer that could solve some well-defined set of problems that would take orders of magnitude longer to solve with any currently known techniques running on existing computers the calculation that Google attempted was pretty simple to understand unlike Google Buzz their experiment consisted of three components a pseudo-random number generator a random sampling algorithm and an algorithm that can verify randomness based on the sample the pseudo-random number generator was a quantum circuit this circuit consisted of a certain random sequence of single and two qubits logical operations with up to 20 of these operations known as gates randomly strung together the sampling algorithm was another quantum circuit the randomness verification was done by computing the probability that a given random number appears in a random number sequence sample then verifying that it did appear that often this is a pretty simple problem for classical computers to solve for a few random numbers but the more random numbers you give it the harder it gets basically it was able to generate a pseudo-random number in such a way that it would take a much longer amount of time on a conventional computer to reproduce that same pseudo-random number from the same initial conditions so don't break out the tinfoil hats just yet it will built a quantum computer that can do something faster than a classical computer not something useful so even though that isn't really useful we now know that quanta computers can do something faster than classical computers can we can expect the race towards faster quantum computers to speed up as a result as this opens up lots of possibilities for theoretically solving hard problems in many industries there are three that I find the most fascinating security medicine and finance in terms of security there's this belief that quantum computers are going to be able to break all encryption which would mean that banks governments and cryptocurrency networks which use encryption algorithms for security would become hackable yes bitcoin including but in order for that to be a reality it's going to require some more technical advances in quantum computing specifically scalability ie more cubits and robust quantum error correction error correction ensures we get useful results classically it's done by copying and storing information multiple times in case there's an error then the output will still give correct answers based on the majority of information all copied bit scary this turns out to be impossible in quantum computing due to the no-cloning theorem where it states quantum information can't be copied so error correction must be done differently lots of techniques have been proposed in this regard but we still have a ways to go and when that happens quantum computers will only be able to break some types of encryption not all of them but it turns out that those types include most of what we currently use to secure the Internet RSA diffie-hellman elliptic curve cryptography meant these types of attacks when it comes to medicine there is huge potential for quantum computing to enable new solutions the Google team generated a pseudo-random number with their quantum computer but one of the next milestones is likely to be able to use it to do some kind of useful simulation probably of a condensed matter system much faster than any known classical method could one step closer to the matrix along Apsara guzik assistant professor of chemistry and chemical biology in Harvard's Faculty of Arts and Sciences said that there is a fundamental problem with simulating quantum systems such as chemical reactions on conventional computers as the size of a system grows the computational resources required to simulate it grow exponentially for example it might take one day to simulate a reaction involving ten atoms two days for 11 atoms four days for 12 atoms eight days for 13 atoms and so on before long this would exhaust the world's computational power if we can simulate a chemical reaction we can predict the outcome digitally that would allow us to design new cures for diseases faster and help us understand the human body brain included at a much deeper level and then there's finance Goldman Sachs has invested in 2d wave a quantum computing company hoping to find new ways to model financial data that would ultimately help understand key global risk factors the global market is very computationally expensive to simulate and financial modeling teams use every trick they can to do so on some level this helps mitigate risk which allows them to invest smarter quantum computing has huge potential here if we want to experiment with quantum computing technology ourselves we've got a few cloud options that we can access from our laptops d-wave has a quantum api called leap with so much well-documented code jupiter notebooks included yes you can code quantum algorithms in Python I think I'm in love with this technology anyone can use quantum computing in their web or mobile applications accessing it from the cloud there's also IBM's Q Network which also offers an API to try it's machines but a field I find just as interesting as quantum computing is post quantum cryptography the field dedicated to devising cryptographic algorithms that are thought to be secure in the quantum era with security against both classical and quantum computers to build a post quantum crypto system there are four major research directions that are being pursued there's hash based cryptography which focuses on designing digital signature schemes based on the security of cryptographic hash functions there's also multivariate based cryptography its security relies on the hardness of solving multivariate systems of equations there's code based cryptography and its security relies on the hardness of problems from coding theory there's lattice based cryptography a lattice can be thought of as any regularly spaced grid of points stretching out to infinity it's security relies on the hardness of solving problems based on that paradigm one of the most important standard-setting organizations is the National Institute of Standards and Technology NIST it's really influential in determining which standardized cryptographic systems see worldwide adoption all hail NIST at the end of 2016 they announced that they would hold a multi-year open project with the goal of standardizing new post quantum cryptographic algorithms initially they selected 82 candidates for further consideration from all submitted algorithms today there are 26 algorithms still in contention among them there are 12 lattice based schemes 7 code based for multivariate based 1 hash based and two other based it's expected to have the first set of standards by 2025 the research direction that seems to be the most active is lattice based cryptography and a top technique here is titled the new hope algorithm Google researchers invented this two years ago guided by the force probably and it's an example of a method called learning with errors let's discuss how this works at a high level learning with errors is a known quantum robust method of cryptography the idea is that we create a secret key value S which is our private key and another value e for errors then we create a public key based on random numbers a and then generate another set of numbers B B is based on a s and E the values of a and B become our public key a and B are one dimensional matrices when s is a single value if we want s to be a one dimensional matrix instead a will be a two dimensional matrix and B will be a one dimensional matrix it turns out that quantum computers can't find the values which solve this equation where a and B are known we can implement this very simply with PI and numpy the key here is the use of randomness which quite often turns out to be a very useful concept in security the New Hope technique is actually a variant of this algorithm called ring learning with errors but I'll spare you the details since there's a lot of little modifications they added there are three things to remember from this video Google achieved quantum supremacy this is a pivotal moment in history and it means lots of opportunities for solving incredibly hard problems in fields like medicine finance and security a new hope is a quantum resistant algorithm that has the most traction these days and quantum computing is definitely a topic to learn more about I've got great resources for you in the video description\n"