Virmani
i am a theoretical physicist working in the theory of quantum information and computation. my research to date has covered aspects of entanglement theory, architectures for quantum computing, quantum channel capacities, classical simulation of quantum systems, and the construction of local hidden variable models. for more details on my research, please see my research tab. for a statement on my approach to teaching please see teaching activities. my research concerns quantum information theory and all things related to the complexity of quantum systems. preprints to all my publications can be found on the quant-ph arxiv (here) or on brunel's research archives. here are short summaries of my research work, loosely organised into various themes: entanglement theory and entanglement measures i started out my scientific career as a graduate student at imperial college under the supervision of martin plenio (now at ulm) and peter knight, working on entanglement theory. results include statements about the relative ordering of entanglement measures, bounds on the relative entropy of entanglement, and computation of an asymptotic entanglement measure (a paper for which most credit goes to coauthor koenraad audenaert for his quite heroic contribution). since my phd i have often revisited the topic of entanglement measures with the fortunate assistance of many insightful coauthors, e.g. here and here. quantum computation with triplet/singlet measurements in a collaboration with terry rudolph, i established the "stpbqp" conjecture of michael freedman, matt hastings, and modjtaba shokrian-zini. we did this by building upon the insights of this paper which they wrote to propose and provide evidence for the conjecture, and another one of our own works (here) on a related question. the published proof of the conjecture is available at this link. loosely speaking, the work demonstrates that using only measurements of two qubit total angular momentum, one can perform quantum computation given almost any initial state that is not completely symmetric. this brings natural robustness to a certain form of error, and has interesting fundamental connections to the study of quantum reference frames. it is also perhaps surprising that quantum computation is possible with a single combined dynamical/measurement operation of such a simple and physically natural form, in a way that is almost completely agnostic about the initialisation of the qubits. locc discrimination of quantum states i had an early interest in the locc discrimination of quantum states (loosely speaking - how to distinguish quantum states of many quantum subsystems when you can only measure the subsystems in a distributed way). in collaboration with various colleagues i showed that two pure states can be optimally discriminated even in the locc setting, and obtained bounds on when discrimination is possible given more states, and obtained optimal locc protocols in some settings with high symmetry. correlated error quantum information i was introduced to this topic while i was a postdoc with chiara macchiavello at pavia. we investigated the effect of correlations on the information carrying capacity of two correlated quantum channels. motivated by some intriguing non-analyticity in that example, together with martin plenio i developed connections between correlated error quantum channel capacities and many-body physics, see here and here for details. classical simulation of quantum systems motivated by the ever increasing buzz concerning quantum computing, i became interested in how well classical computers can efficiently simulate quantum systems. together with various coauthors i've developed bounds (e.g. here and here) on the noise that quantum computers can tolerate before losing their advantage over classical computers. in more recent work have shown how ideas from the foundations of physics can be used to develop efficient simulations of some complex quantum systems, even without noise. perhaps the most surprising example of this arises in certain pure entangled modifications of cluster state quantum computing, which we have shown can be efficiently simulated classically (see also here for more explicit examples). some of this work was supported by an epsrc "bright ideas" grant and an epsrc dtp. mathematics is important, and its importance is often not communicated well at the point of learning. for example, we all learn about the pythagoras rule for triangles in school, and we might be told that it is used to help us design buildings or work out the diagonal dimension of a television screen. however, it is not usually explained that without our understanding of pythagoras there would be - for very fundamental reasons - no mri scanners, xray machines, or ultrasound in hospitals (why? you can look it up, but if you are not satisfied with what you hear then drop me an email). so it is not an exaggeration to say that mathematics is a matter of life and death. i could give many many examples other than medical imaging, both positive and negative, that justify that claim (e.g. the misuse of probability in medical and legal cases). having said this, similar importance could be attached to any other subject that helps us understand the way the world and universe we live in seems to work. this strong belief in the importance of mathematics underpins the way that i teach. society needs mathematics not to be the preserve of a few people - if so it is only they who could meaningfully use it and decide how it is used by others. one obstacle to spreading the word about mathematics, or stem in general, is the general idea that some people are just good at it and others aren't. it is much much more nuanced than that. i am not a "genius" and in general i am sceptical of the emphasis on "natural talent" that is often prevalent. any academic or research success i have had has been down to hard work, a healthy dose of luck, and a whole load of setbacks. moreover, there is evidence that the educational assessment system doesn't always reflect people's full potential (see e.g. here), even when we ignore additional hidden factors such as socio-economic disadvantage. so when i teach students i do not spend my time judging "innate ability", i just want to help them grow as best as they can from whatever their starting point. in return i expect a constructive attitude to mathematics - i hope that the students i teach realise that mathematics is important and empowering, and are not just studying it for the degree certificate, but for the knowledge and power that they will gain. i understand that going to university is a big commitment both financially and otherwise. however, it is important to note the strong evidence of the benefits maths degrees bring both in terms of future earnings (see e.g. longitudinal education outcomes (leo) data - gov.uk), and in terms of personal empowerment. over the years i have taught many courses, but at the time of writing i am teaching a second year module in machine learning for ai and a final year module in mathematical finance, as well as supervising final year projects and a phd student.
![Dr Shash Virmani]()
Dr Shash Virmani
I am a theoretical physicist working in the theory of quantum information and computation. My research to date has covered aspects of entanglement theory, architectures for quantum computing, quantum channel capacities, classical simulation of quantum systems, and the construction of local hidden variable models. For more details on my research, please see my research tab. For a statement on my approach to teaching please see teaching activities. My research concerns quantum information theory and all things related to the complexity of quantum systems. Preprints to all my publications can be found on the quant-ph arXiv (here) or on Brunel's research archives. Here are short summaries of my research work, loosely organised into various themes: Entanglement theory and entanglement measures I started out my scientific career as a graduate student at Imperial College under the supervision of Martin Plenio (now at Ulm) and Peter Knight, working on entanglement theory. Results include statements about the relative ordering of entanglement measures, bounds on the relative entropy of entanglement, and computation of an asymptotic entanglement measure (a paper for which most credit goes to coauthor Koenraad Audenaert for his quite heroic contribution). Since my PhD I have often revisited the topic of entanglement measures with the fortunate assistance of many insightful coauthors, e.g. here and here. Quantum Computation with Triplet/Singlet measurements In a collaboration with Terry Rudolph, I established the "STPBQP" conjecture of Michael Freedman, Matt Hastings, and Modjtaba Shokrian-Zini. We did this by building upon the insights of this paper which they wrote to propose and provide evidence for the conjecture, and another one of our own works (here) on a related question. The published proof of the conjecture is available at this link. Loosely speaking, the work demonstrates that using only measurements of two qubit total angular momentum, one can perform quantum computation given almost any initial state that is not completely symmetric. This brings natural robustness to a certain form of error, and has interesting fundamental connections to the study of quantum reference frames. It is also perhaps surprising that quantum computation is possible with a single combined dynamical/measurement operation of such a simple and physically natural form, in a way that is almost completely agnostic about the initialisation of the qubits. LOCC discrimination of quantum states I had an early interest in the LOCC discrimination of quantum states (loosely speaking - how to distinguish quantum states of many quantum subsystems when you can only measure the subsystems in a distributed way). In collaboration with various colleagues I showed that two pure states can be optimally discriminated even in the LOCC setting, and obtained bounds on when discrimination is possible given more states, and obtained optimal LOCC protocols in some settings with high symmetry. Correlated error quantum information I was introduced to this topic while I was a postdoc with Chiara Macchiavello at Pavia. We investigated the effect of correlations on the information carrying capacity of two correlated quantum channels. Motivated by some intriguing non-analyticity in that example, together with Martin Plenio I developed connections between correlated error quantum channel capacities and many-body physics, see here and here for details. Classical simulation of quantum systems Motivated by the ever increasing buzz concerning quantum computing, I became interested in how well classical computers can efficiently simulate quantum systems. Together with various coauthors I've developed bounds (e.g. here and here) on the noise that quantum computers can tolerate before losing their advantage over classical computers. In more recent work have shown how ideas from the foundations of physics can be used to develop efficient simulations of some complex quantum systems, even without noise. Perhaps the most surprising example of this arises in certain pure entangled modifications of cluster state quantum computing, which we have shown can be efficiently simulated classically (see also here for more explicit examples). Some of this work was supported by an EPSRC "Bright Ideas" grant and an EPSRC DTP. Mathematics is important, and its importance is often not communicated well at the point of learning. For example, we all learn about the pythagoras rule for triangles in school, and we might be told that it is used to help us design buildings or work out the diagonal dimension of a television screen. However, it is not usually explained that without our understanding of pythagoras there would be - for very fundamental reasons - no MRI scanners, xray machines, or ultrasound in hospitals (why? you can look it up, but if you are not satisfied with what you hear then drop me an email). So it is not an exaggeration to say that mathematics is a matter of life and death. I could give many many examples other than medical imaging, both positive and negative, that justify that claim (e.g. the misuse of probability in medical and legal cases). Having said this, similar importance could be attached to any other subject that helps us understand the way the world and universe we live in seems to work. This strong belief in the importance of mathematics underpins the way that I teach. Society needs mathematics not to be the preserve of a few people - if so it is only they who could meaningfully use it and decide how it is used by others. One obstacle to spreading the word about mathematics, or STEM in general, is the general idea that some people are just good at it and others aren't. It is much much more nuanced than that. I am not a "genius" and in general I am sceptical of the emphasis on "natural talent" that is often prevalent. Any academic or research success I have had has been down to hard work, a healthy dose of luck, and a whole load of setbacks. Moreover, there is evidence that the educational assessment system doesn't always reflect people's full potential (see e.g. here), even when we ignore additional hidden factors such as socio-economic disadvantage. So when I teach students I do not spend my time judging "innate ability", I just want to help them grow as best as they can from whatever their starting point. In return I expect a constructive attitude to mathematics - I hope that the students I teach realise that mathematics is important and empowering, and are not just studying it for the degree certificate, but for the knowledge and power that they will gain. I understand that going to university is a big commitment both financially and otherwise. However, it is important to note the strong evidence of the benefits maths degrees bring both in terms of future earnings (see e.g. Longitudinal Education Outcomes (LEO) data - GOV.UK), and in terms of personal empowerment. Over the years I have taught many courses, but at the time of writing I am teaching a second year module in Machine learning for AI and a final year module in Mathematical finance, as well as supervising final year projects and a PhD student.