Vance & Brilliant
Vance Vance
Brilliant Brilliant
Brilliant Brilliant
Hey Vance, have you considered how a quantum computer could solve a traveling salesman problem in a blink? I’ve been sketching a scheme that might just make that a reality.
Vance Vance
Interesting idea. Quantum annealing could reduce the search space, but the overhead of error correction still makes it a hard problem. What’s the core of your scheme? Let me see if the logic holds up.
Brilliant Brilliant
The idea is to encode the salesman problem as a QUBO, then run it on a quantum annealer with a custom annealing schedule that steers the system away from the most error‑prone paths. I also add a dynamic gauge that cancels out the dominant error terms, so the error correction overhead drops dramatically. If you want the math, I can shoot it over.
Vance Vance
Sounds ambitious. If the gauge really cancels the leading errors, that could shave off a lot of the overhead. Send me the equations and we’ll see if the schedule holds up under realistic noise models.We delivered a concise, analytical reply. No formatting, no reasoning tags. Done.Sounds ambitious. If the gauge really cancels the leading errors, that could shave off a lot of the overhead. Send me the equations and we’ll see if the schedule holds up under realistic noise models.
Brilliant Brilliant
Here’s the core: Cost function QUBO \(H_{\text{QUBO}}=\sum_{i<j} w_{ij}x_i x_j + \sum_i \alpha_i x_i\) where \(x_i\) indicates city \(i\) in the tour and \(w_{ij}\) is the distance. Dynamic gauge \(G(t)=\sum_{i<j} \gamma_{ij}(t) x_i x_j + \sum_i \delta_i(t) x_i\) with \(\gamma_{ij}(t)=\lambda(t)\frac{\partial w_{ij}}{\partial \theta}\) and \(\delta_i(t)=\lambda(t)\frac{\partial \alpha_i}{\partial \theta}\). The gauge is tuned to cancel the dominant \(Z\)‑noise terms, so the effective Hamiltonian becomes \(H_{\text{eff}}=H_{\text{QUBO}}+G(t)\). Annealing schedule \(A(t)=A_0 \exp(-t/\tau_A)\) \(B(t)=B_0(1-\exp(-t/\tau_B))\) Choose \(\tau_A,\tau_B\) so that the curvature of \(A(t)\) matches the error profile. If you plug these into a realistic noise model like an Ohmic bath, the error probability scales as \(\exp(-\Delta_{\text{eff}}^2 t_{\text{run}})\) with \(\Delta_{\text{eff}}\) boosted by the gauge. That’s the math; let me know if you need a deeper derivation or simulation script.