Top Tweets for #Randomquantumcircuits

about 1 month ago

More global randomness from less random local gates #Randomquantumcircuits are a central tool in quantum information and many-body physics. But how random should the individual gates actually be? Perhaps surprisingly: less random local gates can generate more global randomness. https://t.co/IBp0QuxtKg In our new work, we show that structured one-dimensional random circuits built from non-Haar-random local gates can converge faster towards global randomness than circuits with #Haar-random gates on exactly the same architecture. The key is that the structure makes the second-moment operator exactly solvable: we derive its full spectrum by establishing a connection to the Kitaev chain. This allows us to show analytically that its spectral gap can be larger than for the corresponding Haar-random circuit. So, in this setting, carefully restricting local randomness actually improves global randomization. Beyond the conceptual surprise, this leads to improved circuit-depth bounds for randomized benchmarking and for generating approximate unitary 2-#designs with shallow circuits. Sometimes, more randomness is not the best route to randomness. Warm thanks to @ryotarosuzuki_, Hoshe Katsura, Yosuke Mitsuhashi, Tomohiro Soejima, and Nobuyuki Yoshioka for the wonderful collaboration.

Jens Eisert

@jenseisert

almost 2 years ago

Random quantum circuits giving rise to unitary designs are key tools in quantum information science and many-body physics. In this work, we investigate a class of #randomquantumcircuits with a specific gate structure. Within this framework, we prove that one-dimensional structured random circuits with non-Haar random local #quantumgates can exhibit substantially more global randomness compared to #Haarrandom circuits with the same underlying circuit architecture. In particular, we derive all the exact eigenvalues and eigenvectors of the second-moment operators for these structured random circuits under a solvable condition, by establishing a link to the #Kitaevchain, and show that their spectral gaps can exceed those of Haar random circuits. Our findings have applications in improving circuit depth bounds for randomized benchmarking and the generation of approximate unitary 2-#designs from #shallowrandomcircuits.

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Jens Eisert

@jenseisert

over 4 years ago

Wohoo. I am extremely happy to see this piece out, on our work reporting results of our attempt of solving the #BrownSusskind conjecture on the linear growth of #complexity of #randomquantumcircuits. https://t.co/gLtsZXaYNR

Jens Eisert

@jenseisert

over 4 years ago

Thanks for the invitation, Gabor Sarosi, to talk about the linear growth of #complexity of #randomquantumcircuits and a #resourcetheory of uncomplexity at @CERN, and possible applications in #holography.

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