Peaked Circuits are special quantum circuits in .qasm format where each circuit sets up a single hidden bitstring with high probability.
For example, 1001 is the peak bitstring as it has a much higher probability to be measured.
The .qasm file preparing the state:
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
x q[1];
x q[2];
ry(0.8*pi) q[0];
ry(0.8*pi) q[1];
ry(0.8*pi) q[2];
ry(0.8*pi) q[3];
Peaked circuits are quantum circuits with a non-uniform O(1) distribution of measurement outcomes.
They were introduced by Scott Aaronson [1] to achieve a verifiable quantum advantage that would take supercomputers septillion =10²⁵ years to replicate.
pip install -r requirements.txt
- Scott Aaronson and Yuxuan Zhang. “On Verifiable Quantum Advantage with Peaked Circuit Sampling.” arXiv, May 21, 2024. arXiv:2404.14493
- Krishnageetha Karuppasamy, Varun Puram, Stevens Johnson, and Johnson P. Thomas. “A Comprehensive Review of Quantum Circuit Optimization: Current Trends and Future Directions.” arXiv, Jan. 2, 2025. arXiv:2408.08941
- Xin-Chuan Wu, Marc Grau Davis, Frederic T. Chong, and Costin Iancu. “Reoptimization of Quantum Circuits via Hierarchical Synthesis.” In 2021 International Conference on Rebooting Computing (ICRC), Los Alamitos, CA, USA: IEEE, 2021, pp. 35–46. IEEE Xplore
- J.-H. Bae, Paul M. Alsing, Doyeol Ahn, and Warner A. Miller. “Quantum Circuit Optimization Using Quantum Karnaugh Map.” Scientific Reports, vol. 10, no. 1, Sep. 24, 2020, article 15651. doi:10.1038/s41598-020-72469-7
- John T. M. Campbell. “Bridging Relations between SVD in Tensor Networks and Common Matrix Operations in Quantum Information Theory.” arXiv, Feb. 4, 2024. arXiv:2402.02517