Local hidden variable and classical models for quantum systems
Lead Research Organisation:
Brunel University London
Department Name: Mathematics
Abstract
A computer is a physical device that is used to solve mathematical problems. When using a normal electronic computer to solve a problem, you effectively set up the initial state of an electronic circuit, allow it to run according to the laws of physics that govern the circuit's behaviour, and then finally observe the final state of the circuit to obtain the solution to your problem. Modern computers are so well engineered and user friendly that it is not necessary to know the details of this process, but ultimately that is what is happening. Thinking of computation as a physical process in this way leads to the following question - why are the laws that govern the dynamical behaviour of electronic circuits best for doing computation?
Perhaps there are other physical systems obeying different laws that could enable us to build better computers? An important series of discoveries over the last few decades has shown that this is in fact true - if we could build a computer that uses the rules of quantum physics, then there are some mathematical problems that we could solve much more efficiently than the best known method on conventional electronic computers. This has well-known implications for the field of cryptography. A number of commonly used cryptographic schemes rely on assumptions that an eavesdropper cannot solve certain mathematical problems. Some of these problems can be solved easily on quantum computers, and so understanding the computational power of quantum algorithms is important for cryptography.
It is not fully understood how and why these "quantum algorithms" work, however it is something to do with the way that quantum systems grow in complexity as their size increases. The laws of quantum theory are used to describe the smallest constituents of matter, and in many cases are needed to describe larger scale objects too. However in most situations the intricate quantum phenomena that is needed to exploit to build a quantum computer cannot be observed directly. This makes building a quantum computer extremely challenging. Although remarkable progress towards that goal has been made, we are probably still some way off from building a substantial quantum computing device.
However, behind the field of quantum computation, there is one fundamental question that remains unanswered. What is it about quantum physics that makes it able to compute somuch better than conventional (or 'classical') computers? If we could understand this question better, could it lead to further quantum algorithms for other problems? On the other hand, it is possible that quantum computers, or the imperfect error-prone ones we are likely to access in real laboratories, are not that much better than classical computers,and the quantum 'supremacy' over classical algorithms is purely because we have not dreamed up the right algorithms for classical computers.
The goal of this PhD project is to attempt to improve our understanding of questions such as these by developing new methods for simulating interesting classes of quantum systems on classical ones by considering the way in which quantum systems grow in complexity as they are increased in size. The methods rely on ideas from the study of certain types of correlations ('entanglement') in quantum systems and physical theories that are more general than it. While these methods are likely to only apply to certain quantum systems, understanding when they do and do not work will allow us to obtain further insight into the problem of what makes quantum computation special. The results could have implications for the wide variety of mathematical problems to which quantum computers may be applied, such as problems in cryptography or the study of materials.
Perhaps there are other physical systems obeying different laws that could enable us to build better computers? An important series of discoveries over the last few decades has shown that this is in fact true - if we could build a computer that uses the rules of quantum physics, then there are some mathematical problems that we could solve much more efficiently than the best known method on conventional electronic computers. This has well-known implications for the field of cryptography. A number of commonly used cryptographic schemes rely on assumptions that an eavesdropper cannot solve certain mathematical problems. Some of these problems can be solved easily on quantum computers, and so understanding the computational power of quantum algorithms is important for cryptography.
It is not fully understood how and why these "quantum algorithms" work, however it is something to do with the way that quantum systems grow in complexity as their size increases. The laws of quantum theory are used to describe the smallest constituents of matter, and in many cases are needed to describe larger scale objects too. However in most situations the intricate quantum phenomena that is needed to exploit to build a quantum computer cannot be observed directly. This makes building a quantum computer extremely challenging. Although remarkable progress towards that goal has been made, we are probably still some way off from building a substantial quantum computing device.
However, behind the field of quantum computation, there is one fundamental question that remains unanswered. What is it about quantum physics that makes it able to compute somuch better than conventional (or 'classical') computers? If we could understand this question better, could it lead to further quantum algorithms for other problems? On the other hand, it is possible that quantum computers, or the imperfect error-prone ones we are likely to access in real laboratories, are not that much better than classical computers,and the quantum 'supremacy' over classical algorithms is purely because we have not dreamed up the right algorithms for classical computers.
The goal of this PhD project is to attempt to improve our understanding of questions such as these by developing new methods for simulating interesting classes of quantum systems on classical ones by considering the way in which quantum systems grow in complexity as they are increased in size. The methods rely on ideas from the study of certain types of correlations ('entanglement') in quantum systems and physical theories that are more general than it. While these methods are likely to only apply to certain quantum systems, understanding when they do and do not work will allow us to obtain further insight into the problem of what makes quantum computation special. The results could have implications for the wide variety of mathematical problems to which quantum computers may be applied, such as problems in cryptography or the study of materials.
Organisations
People |
ORCID iD |
Shashank Virmani (Primary Supervisor) | |
Michael Garn (Student) |
Publications
Atallah Sahar
(2022)
Efficient classical simulation of cluster state quantum circuits with alternative inputs
in arXiv e-prints
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/N509437/1 | 01/10/2016 | 30/09/2021 | |||
2360717 | Studentship | EP/N509437/1 | 01/04/2020 | 31/03/2023 | Michael Garn |
EP/R512990/1 | 01/10/2018 | 30/09/2023 | |||
2360717 | Studentship | EP/R512990/1 | 01/04/2020 | 31/03/2023 | Michael Garn |
Description | An open question in physics and computer science is how easy or difficult is it to model a complex quantum system on conventional computers. The motivation for this question is the realisation that if it is possible to build and precisely control sufficiently complex quantum systems, then we could efficiently solve certain mathematical problems for which no efficient solution is achievable using the best known methods on conventional computers. However, it is still conceivable that with better algorithms, conventional "classical" computers could be more powerful than currently anticipated. To understand this problem, it is necessary to understand why or why not quantum systems are so hard to simulate classically. In this work, we contribute to this endeavour by developing a new method for efficiently simulating an important class of complex quantum system on conventional "classical" computers. This new method has significant scope for further development and we believe that it could be used to simulate an even wider class of quantum system. The method is also fascinating because it has fundamental connections to hypothetical classes of theory that go beyond quantum theory. |
Exploitation Route | There is significant scope for improvement of these methods and application to a wider range of quantum systems. There is also a possibility that the methods may lead to new techniques for efficiently verifying the behaviour of complex quantum systems, including prototype quantum devices with many constituent particles. |
Sectors | Aerospace, Defence and Marine,Chemicals,Digital/Communication/Information Technologies (including Software),Education,Energy,Financial Services, and Management Consultancy,Healthcare,Pharmaceuticals and Medical Biotechnology,Security and Diplomacy,Transport,Other |
URL | https://arxiv.org/abs/2201.07655 |
Description | This was work has had impact by developing new methods used to study quantum systems, and in the process has solved the problem of simulating an important class of quantum systems. This gives insights into what properties a quantum computer may need to outperform conventional computers, leads to new approaches for verifying complex quantum processes, and shows that classical computers can efficiently simulate a system that was previously considered to be very complex. The development of new computational tools, whether they be quantum or classical, is fundamentally important to a wide range of human endeavours ranging from drug design, cybersecurity, novel material technologies for green energy security, finance, among others. |
First Year Of Impact | 2022 |
Sector | Digital/Communication/Information Technologies (including Software),Other |
Impact Types | Societal |
Description | LMS Early Career Research Travel Grant |
Amount | £500 (GBP) |
Funding ID | ECR-2122-12 |
Organisation | London Mathematical Society |
Sector | Academic/University |
Country | United Kingdom |
Start | 07/2022 |
End | 07/2022 |
Description | Small Grant Scheme |
Amount | £600 (GBP) |
Organisation | Institute of Mathematics and its Applications |
Sector | Academic/University |
Country | United Kingdom |
Start | 07/2022 |
End | 07/2022 |
Description | Invitation to give a talk at Quantinuum |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Industry/Business |
Results and Impact | We were invited to give a talk on our recent results on classical simulation, which involved discussions and questions leading to new ideas. |
Year(s) Of Engagement Activity | 2022 |
URL | https://www.quantinuum.com/ |
Description | Poster presented at The Theory of Quantum Computation, Communication and Cryptography (TQC) 2022 conference |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | I presented a poster of our work at a prestigious international conference, held in the USA. The work was well received and generated interest with the wider community. Presenting our work also led to interesting discussions, as well as feedback and potential future research directions. |
Year(s) Of Engagement Activity | 2022 |
URL | https://tqc2022-conference.iquist.illinois.edu/ |
Description | Poster presented at the Quantum Information Processing 2023 conference (Belgium) |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | I presented our work at the premier quantum computing conference QIP in Ghent, Belgium. The poster was well received and generated a lot of interest from the community. Presenting our work at the conference has led to our work gaining further exposure, interesting discussions and potential new research directions. |
Year(s) Of Engagement Activity | 2023 |
URL | https://indico.cern.ch/event/1175020/ |