01714nas a2200181 4500008004100000245004400041210004400085260001500129490000800144520120900152100002801361700002801389700002101417700002001438700001701458700002001475856003701495 2022 eng d00aResource theory of quantum uncomplexity0 aResource theory of quantum uncomplexity c12/19/20220 v1063 a

Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state's distance from maximal complexity, or "uncomplexity," the more useful the state is as input to a quantum computation. Separately, resource theories -- simple models for agents subject to constraints -- are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind's conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.

1 aHalpern, Nicole, Yunger1 aKothakonda, Naga, B. T.1 aHaferkamp, Jonas1 aMunson, Anthony1 aEisert, Jens1 aFaist, Philippe uhttps://arxiv.org/abs/2110.1137101694nas a2200169 4500008004100000245004400041210004400085260001500129520120900144100002801353700002801381700002101409700002001430700001701450700002001467856003701487 2021 eng d00aResource theory of quantum uncomplexity0 aResource theory of quantum uncomplexity c10/21/20213 a

Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state's distance from maximal complexity, or ``uncomplexity,'' the more useful the state is as input to a quantum computation. Separately, resource theories -- simple models for agents subject to constraints -- are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind's conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.

1 aHalpern, Nicole, Yunger1 aKothakonda, Naga, B. T.1 aHaferkamp, Jonas1 aMunson, Anthony1 aEisert, Jens1 aFaist, Philippe uhttps://arxiv.org/abs/2110.1137101416nas a2200133 4500008004100000245004200041210004200083260001500125490000600140520105200146100001901198700002801217856003701245 2018 eng d00aResilience of scrambling measurements0 aResilience of scrambling measurements c2018/06/180 vA3 a

Most experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backwards time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum-chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

1 aSwingle, Brian1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/1802.01587