Complexity-Constrained Quantum Thermodynamics
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 ta...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-03-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.6.010346 |
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| _version_ | 1850075948903301120 |
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| author | Anthony Munson Naga Bhavya Teja Kothakonda Jonas Haferkamp Nicole Yunger Halpern Jens Eisert Philippe Faist |
| author_facet | Anthony Munson Naga Bhavya Teja Kothakonda Jonas Haferkamp Nicole Yunger Halpern Jens Eisert Philippe Faist |
| author_sort | Anthony Munson |
| collection | DOAJ |
| description | 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 in our model, 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. In a random circuit—a simple model for quantum chaotic dynamics—the complexity entropy transitions from zero to its maximal value around the time corresponding to the observer’s computational-power limit. 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. |
| format | Article |
| id | doaj-art-9f41846f0c6b4bc1a5db079a88eb5ddc |
| institution | DOAJ |
| issn | 2691-3399 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj-art-9f41846f0c6b4bc1a5db079a88eb5ddc2025-08-20T02:46:08ZengAmerican Physical SocietyPRX Quantum2691-33992025-03-016101034610.1103/PRXQuantum.6.010346Complexity-Constrained Quantum ThermodynamicsAnthony MunsonNaga Bhavya Teja KothakondaJonas HaferkampNicole Yunger HalpernJens EisertPhilippe FaistQuantum 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 in our model, 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. In a random circuit—a simple model for quantum chaotic dynamics—the complexity entropy transitions from zero to its maximal value around the time corresponding to the observer’s computational-power limit. 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.http://doi.org/10.1103/PRXQuantum.6.010346 |
| spellingShingle | Anthony Munson Naga Bhavya Teja Kothakonda Jonas Haferkamp Nicole Yunger Halpern Jens Eisert Philippe Faist Complexity-Constrained Quantum Thermodynamics PRX Quantum |
| title | Complexity-Constrained Quantum Thermodynamics |
| title_full | Complexity-Constrained Quantum Thermodynamics |
| title_fullStr | Complexity-Constrained Quantum Thermodynamics |
| title_full_unstemmed | Complexity-Constrained Quantum Thermodynamics |
| title_short | Complexity-Constrained Quantum Thermodynamics |
| title_sort | complexity constrained quantum thermodynamics |
| url | http://doi.org/10.1103/PRXQuantum.6.010346 |
| work_keys_str_mv | AT anthonymunson complexityconstrainedquantumthermodynamics AT nagabhavyatejakothakonda complexityconstrainedquantumthermodynamics AT jonashaferkamp complexityconstrainedquantumthermodynamics AT nicoleyungerhalpern complexityconstrainedquantumthermodynamics AT jenseisert complexityconstrainedquantumthermodynamics AT philippefaist complexityconstrainedquantumthermodynamics |