Relationship between differential geometry and quantum computation?
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I have just started reading about quantum computation (Quantum Computation and Quantum Information, Nielsen and Chuang).
In parallel, I have to study differential geometry for a final exam. After the standard part of it, where you must cover the basic topics, the professor lets you present a related topic (it's optional). I was wondering if I can present some connection between differential geometry and quantum computation. The most promising thing I found is a couple of articles by Howard Brandt (see for example this one.) about Riemmanian geometry.
Can anyone give me more recommendations? The two non obligatory constraints are the following:
- I'm a beginner at quantum computation.
- If the relationship has anything to do with Frobenius theorem, much better. I also like Lie algebra.
Thank you very much.
differential-geometry soft-question lie-groups lie-algebras quantum-computation
edited Nov 23 at 6:22
onurcanbektas
3,3081936
asked Nov 13 at 20:24
Guillermo Mosse
867316
add a comment |
up vote
1
down vote
favorite
I have just started reading about quantum computation (Quantum Computation and Quantum Information, Nielsen and Chuang).
In parallel, I have to study differential geometry for a final exam. After the standard part of it, where you must cover the basic topics, the professor lets you present a related topic (it's optional). I was wondering if I can present some connection between differential geometry and quantum computation. The most promising thing I found is a couple of articles by Howard Brandt (see for example this one.) about Riemmanian geometry.
Can anyone give me more recommendations? The two non obligatory constraints are the following:
- I'm a beginner at quantum computation.
- If the relationship has anything to do with Frobenius theorem, much better. I also like Lie algebra.
Thank you very much.
differential-geometry soft-question lie-groups lie-algebras quantum-computation
edited Nov 23 at 6:22
onurcanbektas
3,3081936
asked Nov 13 at 20:24
Guillermo Mosse
867316
1
Perhaps if you add 'Lie Algebras' as a tag more people will see your question and someone may answer
– Esteban Sargiotto
Nov 14 at 15:15
Classical mechanics take place on a symplectic manifold, which is a differentiable manifold equipped with a nondegenerate 2-form. There is some big theory of what it means to "quantise" this situation, to get to a corresponding quantum mechanical theory. But perhaps this is too in-depth (or equally well, too vague!). As a completely different idea, have you looked at topological quantum error correction?
– Joppy
Nov 23 at 12:42
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have just started reading about quantum computation (Quantum Computation and Quantum Information, Nielsen and Chuang).
In parallel, I have to study differential geometry for a final exam. After the standard part of it, where you must cover the basic topics, the professor lets you present a related topic (it's optional). I was wondering if I can present some connection between differential geometry and quantum computation. The most promising thing I found is a couple of articles by Howard Brandt (see for example this one.) about Riemmanian geometry.
Can anyone give me more recommendations? The two non obligatory constraints are the following:
- I'm a beginner at quantum computation.
- If the relationship has anything to do with Frobenius theorem, much better. I also like Lie algebra.
Thank you very much.
differential-geometry soft-question lie-groups lie-algebras quantum-computation
edited Nov 23 at 6:22
onurcanbektas
3,3081936
asked Nov 13 at 20:24
Guillermo Mosse
867316
I have just started reading about quantum computation (Quantum Computation and Quantum Information, Nielsen and Chuang).
In parallel, I have to study differential geometry for a final exam. After the standard part of it, where you must cover the basic topics, the professor lets you present a related topic (it's optional). I was wondering if I can present some connection between differential geometry and quantum computation. The most promising thing I found is a couple of articles by Howard Brandt (see for example this one.) about Riemmanian geometry.
Can anyone give me more recommendations? The two non obligatory constraints are the following:
- I'm a beginner at quantum computation.
- If the relationship has anything to do with Frobenius theorem, much better. I also like Lie algebra.
Thank you very much.
differential-geometry soft-question lie-groups lie-algebras quantum-computation
differential-geometry soft-question lie-groups lie-algebras quantum-computation
edited Nov 23 at 6:22
onurcanbektas
3,3081936
asked Nov 13 at 20:24
Guillermo Mosse
867316
edited Nov 23 at 6:22
onurcanbektas
3,3081936
asked Nov 13 at 20:24
Guillermo Mosse
867316
edited Nov 23 at 6:22
onurcanbektas
3,3081936
edited Nov 23 at 6:22
onurcanbektas
3,3081936
edited Nov 23 at 6:22
onurcanbektas
3,3081936
3,3081936
asked Nov 13 at 20:24
Guillermo Mosse
867316
asked Nov 13 at 20:24
Guillermo Mosse
867316
asked Nov 13 at 20:24
Guillermo Mosse
867316
867316
1
Perhaps if you add 'Lie Algebras' as a tag more people will see your question and someone may answer
– Esteban Sargiotto
Nov 14 at 15:15
Classical mechanics take place on a symplectic manifold, which is a differentiable manifold equipped with a nondegenerate 2-form. There is some big theory of what it means to "quantise" this situation, to get to a corresponding quantum mechanical theory. But perhaps this is too in-depth (or equally well, too vague!). As a completely different idea, have you looked at topological quantum error correction?
– Joppy
Nov 23 at 12:42
add a comment |
1
Perhaps if you add 'Lie Algebras' as a tag more people will see your question and someone may answer
– Esteban Sargiotto
Nov 14 at 15:15
Classical mechanics take place on a symplectic manifold, which is a differentiable manifold equipped with a nondegenerate 2-form. There is some big theory of what it means to "quantise" this situation, to get to a corresponding quantum mechanical theory. But perhaps this is too in-depth (or equally well, too vague!). As a completely different idea, have you looked at topological quantum error correction?
– Joppy
Nov 23 at 12:42
1
1
Perhaps if you add 'Lie Algebras' as a tag more people will see your question and someone may answer
– Esteban Sargiotto
Nov 14 at 15:15
Perhaps if you add 'Lie Algebras' as a tag more people will see your question and someone may answer
– Esteban Sargiotto
Nov 14 at 15:15
Classical mechanics take place on a symplectic manifold, which is a differentiable manifold equipped with a nondegenerate 2-form. There is some big theory of what it means to "quantise" this situation, to get to a corresponding quantum mechanical theory. But perhaps this is too in-depth (or equally well, too vague!). As a completely different idea, have you looked at topological quantum error correction?
– Joppy
Nov 23 at 12:42
Classical mechanics take place on a symplectic manifold, which is a differentiable manifold equipped with a nondegenerate 2-form. There is some big theory of what it means to "quantise" this situation, to get to a corresponding quantum mechanical theory. But perhaps this is too in-depth (or equally well, too vague!). As a completely different idea, have you looked at topological quantum error correction?
– Joppy
Nov 23 at 12:42
add a comment |
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1
Perhaps if you add 'Lie Algebras' as a tag more people will see your question and someone may answer
– Esteban Sargiotto
Nov 14 at 15:15
Classical mechanics take place on a symplectic manifold, which is a differentiable manifold equipped with a nondegenerate 2-form. There is some big theory of what it means to "quantise" this situation, to get to a corresponding quantum mechanical theory. But perhaps this is too in-depth (or equally well, too vague!). As a completely different idea, have you looked at topological quantum error correction?
– Joppy
Nov 23 at 12:42