02447nas a2200169 4500008004100000245005000041210004900091260001300140520194800153100002002101700003302121700002102154700002802175700001702203700002002220856003702240 2024 eng d00aComplexity-constrained quantum thermodynamics0 aComplexityconstrained quantum thermodynamics c3/7/20243 a

Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the process's complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state's complexity entropy. The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the complexity relative entropy. The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer's ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy and determine the complexity entropy's behavior under random circuits. Also, we identify information-theoretic applications of the complexity entropy. The complexity entropy quantifies the resources required for data compression if the compression algorithm must use a restricted number of gates. We further introduce a complexity conditional entropy, which arises naturally in a complexity-constrained variant of information-theoretic decoupling. Assuming that this entropy obeys a conjectured chain rule, we show that the entropy bounds the number of qubits that one can decouple from a reference system, as judged by a computationally bounded referee. Overall, our framework extends the resource-theoretic approach to thermodynamics to integrate a notion of time, as quantified by complexity.

1 aMunson, Anthony1 aKothakonda, Naga, Bhavya Tej1 aHaferkamp, Jonas1 aHalpern, Nicole, Yunger1 aEisert, Jens1 aFaist, Philippe uhttps://arxiv.org/abs/2403.0482802447nas a2200169 4500008004100000245005000041210004900091260001300140520194800153100002002101700003302121700002102154700002802175700001702203700002002220856003702240 2024 eng d00aComplexity-constrained quantum thermodynamics0 aComplexityconstrained quantum thermodynamics c3/7/20243 a

Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the process's complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state's complexity entropy. The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the complexity relative entropy. The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer's ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy and determine the complexity entropy's behavior under random circuits. Also, we identify information-theoretic applications of the complexity entropy. The complexity entropy quantifies the resources required for data compression if the compression algorithm must use a restricted number of gates. We further introduce a complexity conditional entropy, which arises naturally in a complexity-constrained variant of information-theoretic decoupling. Assuming that this entropy obeys a conjectured chain rule, we show that the entropy bounds the number of qubits that one can decouple from a reference system, as judged by a computationally bounded referee. Overall, our framework extends the resource-theoretic approach to thermodynamics to integrate a notion of time, as quantified by complexity.

1 aMunson, Anthony1 aKothakonda, Naga, Bhavya Tej1 aHaferkamp, Jonas1 aHalpern, Nicole, Yunger1 aEisert, Jens1 aFaist, Philippe uhttps://arxiv.org/abs/2403.0482801495nas a2200181 4500008004100000245008500041210006900126260001400195490000800209520092100217100001901138700002101157700002701178700002301205700002001228700002801248856003701276 2023 eng d00aCritical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits0 aCritical phase and spin sharpening in SU2symmetric monitored qua c8/17/20230 v1083 a

Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a "spin-sharpening transition." On one side is a phase in which the measurements can efficiently identify the system's total spin quantum number; on the other side is a phase in which measurements cannot.

1 aMajidy, Shayan1 aAgrawal, Utkarsh1 aGopalakrishnan, Sarang1 aPotter, Andrew, C.1 aVasseur, Romain1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/2305.13356