Error mitigation is essential for near-term quantum devices, and two promising techniques are universal frame randomization and Randomized Compilation. These methods insert random twirling gates into a circuit to reduce errors while preserving unitarity and depth. We apply universal frame randomization and Randomized Compilation to the quantum approximate optimization algorithm (QAOA) with $p=1$ on a superconducting quantum circuit system, demonstrating its potential to improve energy calculations. Specifically, we investigate the use of QAOA to calculate the lowest energy state of a frustrated Ising ring system and compare the results of randomized circuits generated using both techniques. Our results show that both methods can mitigate errors, with expected extremal energy values of $5.25\pm0.145$ and $4.08\pm0.36$ , for Randomized Compilation and universal frame randomization respectively, compared to $2.63\pm0.068$ without randomization and $5.676\pm0.006$ with a noiseless simulator.Error mitigation is essential for near-term quantum devices, and two promising techniques are universal frame randomization and Randomized Compilation. These methods insert random twirling gates into a circuit to reduce errors while preserving unitarity and depth. We apply universal frame randomization and Randomized Compilation to the quantum approximate optimization algorithm (QAOA) with $p=1$ on a superconducting quantum circuit system, demonstrating its potential to improve energy calculations. Specifically, we investigate the use of QAOA to calculate the lowest energy state of a frustrated Ising ring system and compare the results of randomized circuits generated using both techniques. Our results show that both methods can mitigate errors, with expected extremal energy values of $5.25\pm0.145$ and $4.08\pm0.36$, for Randomized Compilation and universal frame randomization respectively, compared to $2.63\pm0.068$ without randomization and $5.676\pm0.006$ with a noiseless simulator.

arXiv:2508.14142Aug 19, 20250 citations

DETERMINISM IN RANDOMNESS

WORLD SCIENTIFIC eBooksMar 2, 20170 citations

Randomness from vacuum

Gaia Donati

Nature PhotonicsAug 31, 20160 citations

Phase diagrams and universality classes of random antiferromagnetic spin ladders

José A. Hoyos, E. Miranda

The random antiferromagnetic two-leg and zigzag spin- $1∕2$ ladders are investigated using the real space renormalization group scheme and their complete phase diagrams are determined. We demonstrate that the first system belongs to the same universality class of the dimerized random spin- $1∕2$ chain. The zigzag ladder, on the other hand, is in a random singlet phase at weak frustration and disorder. Otherwise, we give additional evidence that it belongs to the universality class of the random antiferromagnetic and ferromagnetic quantum spin chains, although the universal fixed point found in the latter system is never realized. We find, however, a new universal fixed point at intermediate disorder.The random antiferromagnetic two-leg and zigzag spin-$1∕2$ ladders are investigated using the real space renormalization group scheme and their complete phase diagrams are determined. We demonstrate that the first system belongs to the same universality class of the dimerized random spin-$1∕2$ chain. The zigzag ladder, on the other hand, is in a random singlet phase at weak frustration and disorder. Otherwise, we give additional evidence that it belongs to the universality class of the random antiferromagnetic and ferromagnetic quantum spin chains, although the universal fixed point found in the latter system is never realized. We find, however, a new universal fixed point at intermediate disorder.

arXiv:cond-mat/0404444Physical Review BJun 9, 200423 citations

Randomness and Probability

Andy Lawrence

Undergraduate lecture notes in physicsJan 1, 20190 citations

Criticality and entanglement in random quantum systems

G Refael, Joel E. Moore

We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum criticality of these systems and an understanding of their relationship to non-random (‘pure’) quantum criticality. The entanglement near many such critical points in one dimension shows a logarithmic divergence in subsystem size, similar to that in the pure case but with a different universal coefficient. Such universal coefficients are examples of universal critical amplitudes in a random system. Possible measurements are reviewed along with the one-particle entanglement scaling at certain Anderson localization transitions. We also comment briefly on higher dimensions and challenges for the future.We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum criticality of these systems and an understanding of their relationship to non-random (‘pure’) quantum criticality. The entanglement near many such critical points in one dimension shows a logarithmic divergence in subsystem size, similar to that in the pure case but with a different universal coefficient. Such universal coefficients are examples of universal critical amplitudes in a random system. Possible measurements are reviewed along with the one-particle entanglement scaling at certain Anderson localization transitions. We also comment briefly on higher dimensions and challenges for the future.

arXiv:0908.1986Journal of Physics A Mathematical and TheoreticalDec 2, 2009100 citations

p=1

on a superconducting quantum circuit system, demonstrating its potential to improve energy calculations. Specifically, we investigate the use of QAOA to calculate the lowest energy state of a frustrated Ising ring system and compare the results of randomized circuits generated using both techniques. Our results show that both methods can mitigate errors, with expected extremal energy values of

5.25\pm0.145

and

4.08\pm0.36

, for Randomized Compilation and universal frame randomization respectively, compared to

2.63\pm0.068

without randomization and

5.676\pm0.006

with a noiseless simulator.

The random antiferromagnetic two-leg and zigzag spin-

1∕2

ladders are investigated using the real space renormalization group scheme and their complete phase diagrams are determined. We demonstrate that the first system belongs to the same universality class of the dimerized random spin-

1∕2

chain. The zigzag ladder, on the other hand, is in a random singlet phase at weak frustration and disorder. Otherwise, we give additional evidence that it belongs to the universality class of the random antiferromagnetic and ferromagnetic quantum spin chains, although the universal fixed point found in the latter system is never realized. We find, however, a new universal fixed point at intermediate disorder.