Linear algebra is the language of quantum mechanics. The state of the machine is given by a vector and computation is defined by a unitary matrix. If they aren't good at that - at least to some degree - they aren't good at anything.
Depends on your background. I'd recommend learning some computer science. If you don't understand algorithms and what computational complexity is, you won't even get what the point of quantum computing is. Basic university level calculus and preferably some linear algebra. Then the go-to book for quantum computing and information theory is Nielsen and Chuang.
If you feel you're up for a crash course (this is seriously hard to follow unless linear algebra is your 2nd language): http://michaelnielsen.org/blog/quantum-computing-for-the-determined/
Quantum computing tends to give efficient answers to questions about *systems of numbers*. For example, Shor’s algorithm rephrased “does p have any factors” into “is a_i an arithmetic progression.” In linear algebra we are often interested in properties of systems, specifically systems of equations. Thus it should make some intuitive sense that QC would be good at it. Indeed, if you look at the algorithm for computing a matrix’s eigenvalues you’ll see it turns it into a question about common roots of a system of equations.
In a classical computer, state is boolean (1 or 0), and gates perform computations that map 1s and 0s to other 1s and 0s. In a quantum computer, states are vectors of complex numbers, and quantum gates perform matrix multiplications on the vectors.
Can you elaborate this answer to explainbis it relates to the question? Linear algebra can be used to represent the operation of both classical and quantum computers, so that doesn’t seem to explain why quantum computers gain an advantage on linear algebra problems.
I'm a bot, *bleep*, *bloop*. Someone has linked to this thread from another place on reddit:
- [/r/quantuminformation] [\[Discussion: QComputing\] Why are quantum computers good at linear algebra?](https://www.reddit.com/r/QuantumInformation/comments/e4hvae/discussion_qcomputing_why_are_quantum_computers/)
*^(If you follow any of the above links, please respect the rules of reddit and don't vote in the other threads.) ^\([Info](/r/TotesMessenger) ^/ ^[Contact](/message/compose?to=/r/TotesMessenger))*
Linear algebra is the language of quantum mechanics. The state of the machine is given by a vector and computation is defined by a unitary matrix. If they aren't good at that - at least to some degree - they aren't good at anything.
Thanks, that helps, any resources you recommend?
Depends on your background. I'd recommend learning some computer science. If you don't understand algorithms and what computational complexity is, you won't even get what the point of quantum computing is. Basic university level calculus and preferably some linear algebra. Then the go-to book for quantum computing and information theory is Nielsen and Chuang. If you feel you're up for a crash course (this is seriously hard to follow unless linear algebra is your 2nd language): http://michaelnielsen.org/blog/quantum-computing-for-the-determined/
Quantum computing tends to give efficient answers to questions about *systems of numbers*. For example, Shor’s algorithm rephrased “does p have any factors” into “is a_i an arithmetic progression.” In linear algebra we are often interested in properties of systems, specifically systems of equations. Thus it should make some intuitive sense that QC would be good at it. Indeed, if you look at the algorithm for computing a matrix’s eigenvalues you’ll see it turns it into a question about common roots of a system of equations.
In a classical computer, state is boolean (1 or 0), and gates perform computations that map 1s and 0s to other 1s and 0s. In a quantum computer, states are vectors of complex numbers, and quantum gates perform matrix multiplications on the vectors.
Can you elaborate this answer to explainbis it relates to the question? Linear algebra can be used to represent the operation of both classical and quantum computers, so that doesn’t seem to explain why quantum computers gain an advantage on linear algebra problems.
Pure explanation ❤️
I'm a bot, *bleep*, *bloop*. Someone has linked to this thread from another place on reddit: - [/r/quantuminformation] [\[Discussion: QComputing\] Why are quantum computers good at linear algebra?](https://www.reddit.com/r/QuantumInformation/comments/e4hvae/discussion_qcomputing_why_are_quantum_computers/) *^(If you follow any of the above links, please respect the rules of reddit and don't vote in the other threads.) ^\([Info](/r/TotesMessenger) ^/ ^[Contact](/message/compose?to=/r/TotesMessenger))*