Timeline for Adiabatic Quantum Computing: why not just set the system in its problem Hamiltonian $H_{P}$ immediately?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 30, 2017 at 6:01 | comment | added | tparker | @hii Yes, as I said above, the key ingredients that make $H_0$ much easier to deal with are (a) an unfrustrated ground state and (b) a very large gap to the first excited state. Such Hamiltonians are fairly easy to engineer and fall into their ground states much more quickly than the final "problem" Hamiltonian $H_P$ (which is typically frustrated and complicated to engineer) does. | |
| Jan 29, 2017 at 22:30 | comment | added | Peter Shor | @hii: the initial Hamiltonian is one chosen specifically so that you can force it to be in the ground state. | |
| Jan 29, 2017 at 21:05 | comment | added | Ka Wa Yip | why i can force initial Hamiltonian H0 to be at ground state but not force final hamiltonian to be at ground state? | |
| Jan 5, 2017 at 6:03 | comment | added | tparker | @AlexMichael I don't know the answer to your first question. I'm not sure if I understand your second question, but the adiabatic theorem guarantees that the ground state of the initial Hamiltonian will evolve to the ground state of the final Hamiltonian as long as the Hamiltonian is varied much more slowly then the time scale set by the energy gap to the first excited state, because the system can quantum-tunnel through energy barriers as long as it has enough time to do so. In principle, the details of the initial Hamiltonian are unimportant, just the size of its energy gap. | |
| Jan 4, 2017 at 22:28 | comment | added | Alex Michael | @tparker Thanks, great answer. Is this uniform field (that one applies to the system to hasten it reaching the ground state) what is used in quantum annealing algorithms (such as on the D-Wave machines)? And is this what enables the 'tunneling' between barriers separating local minima in quantum annealing algorithms? | |
| Jan 4, 2017 at 22:22 | vote | accept | Alex Michael | ||
| Jan 4, 2017 at 22:22 | vote | accept | Alex Michael | ||
| Jan 4, 2017 at 22:22 | |||||
| Jan 4, 2017 at 14:22 | comment | added | tparker | @PeterShor True, but I think there are also systems where (a) is hard. D-Wave works ("works") at 15 mK, which isn't too hard to achieve, but aren't there also proposals for AQC in cold atom systems (e.g. arxiv.org/abs/quant-ph/0406144)? That would need to be performed at the nanokelvin scale, which is much, much harder than millikelvin. | |
| Jan 4, 2017 at 14:08 | comment | added | Peter Shor | It's actually fairly easy (at least in theory) to construct systems so that (a) isn't a problem. The big problem is (b). | |
| Jan 4, 2017 at 14:07 | history | answered | tparker | CC BY-SA 3.0 |