Fig. 3: Mirror-symmetric random circuits.

a, A mirror symmetric circuit can be generated for an arbitrary circuit U by concatenating a reversed circuit U^† after the forward evolution U. The tilde in \(\tilde{U}\) highlights the existence of noise. In the noiseless limit, the mirror symmetry circuit UU^† applied on some initial state \(\left\vert \psi \right\rangle\) should keep the state untouched. Due to the noise, \(\tilde{U}{\tilde{U}}^{\dagger }\left\vert \psi \right\rangle =\left\vert \tilde{\psi }\right\rangle \approx \left\vert \psi \right\rangle\). b, An example of \(\tilde{U}\) sampled from Circuit Type I. c, An example of \(\tilde{U}\) sampled from Circuit Type II.