Name
TNS + BP classical simulation for peaked_heavyhex_49_5072 circuit
Circuit
peaked_circuit_heavy_hex_49x5072
Value
100
Method
TNS + BP
Method proof
To extrapolate to the circuit of size 49 x 5072, we study many circuits built with the same protocol of varying sizes and $N=49$ qubits. The actual protocol is similar to the one discussed in:
https://arxiv.org/abs/2510.25838
For each size, we generate 5 circuits, and simulate using a tensor network state (TNS) with heavyhex geometry and gate evolution with the simple update algorithm. We then use belief propagation (BP) to compute $\langle Z_q \rangle$ for each $q$ to propose the bit of qubit $q$ for the true target bitstring. We also use a method of computing $\langle Z_q \rangle$ which conditions on the expected classical bit of other qubits. More details about the simulation strategy can be found in:
https://arxiv.org/abs/2510.25838
We first look at $T_{\rm break}$ defined as the shortest runtime to break a given circuit, which is shown below. Note that the last two data points in blue have no error bars since only one circuit was solved for that size with the compute resources used. We then fit the data for $CZ \gtrsim 2000$ to a power law, and extrapolate to $CZ=5072$ yielding $T_{\rm break} \sim 1.3 \times 10^7$.
The extrapolation on time directly is challenging, and a smoother quantity to look at is the bond-dimension $\chi$. Below is a plot of $\chi_{\rm break}$, defined as the smallest $\chi$ needed to solve the circuit, as a function of $CZ$. We then fit this to a power law and extrapolate to $CZ=5072$ to estimate $\chi_{\rm break} \sim 2\times 10^4$.
Lastly, we look at the runtime $T$ as a function of $\chi$. Note that for sufficiently large $\chi$, we expect the runtime is dominated by the gate application step, and so we look at $T / CZ$. There is a transition in behavior after around $\chi \gtrsim 256$, and fit this region to a power law. Using this relationship, we find another estimate of $T_{\rm break} = CZ \cdot \chi_{\rm break} \sim 5\times 10^7$.
Authors
Nicholas E. Sherman
Institutions
BlueQubit
Quantum runtime (seconds)
No response
Classical runtime (seconds)
1e7
Compute resources (quantum)
No response
Compute resources (classical)
H100 GPU
Notes
No response
