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/2403.0482801130nas a2200121 4500008004100000245005500041210005500096260001300151520076600164100002400930700001700954856003700971 2022 eng d00aComputational advantage of quantum random sampling0 aComputational advantage of quantum random sampling c6/8/20223 a

Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the boundary of what can be simulated on existing classical hardware. In this article, we comprehensively review the theoretical underpinning of quantum random sampling in terms of computational complexity and verifiability, as well as the practical aspects of its experimental implementation using superconducting and photonic devices and its classical simulation. We discuss in detail open questions in the field and provide perspectives for the road ahead, including potential applications of quantum random sampling.

1 aHangleiter, Dominik1 aEisert, Jens uhttps://arxiv.org/abs/2206.0407901526nas a2200157 4500008004100000245005100041210005000092260001500142520108300157100002201240700001901262700001701281700001601298700001701314856003701331 2011 eng d00aContinuous-variable quantum compressed sensing0 aContinuousvariable quantum compressed sensing c2011/11/033 a We significantly extend recently developed methods to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. Our new method is general enough to allow for measurements from a continuous family, and is also applicable to continuous-variable states. As a technical result, this work generalizes quantum compressed sensing to the situation where the measured observables are taken from a so-called tight frame (rather than an orthonormal basis) --- hence covering most realistic measurement scenarios. As an application, we discuss the reconstruction of quantum states of light from homodyne detection and other types of measurements, and we present simulations that show the advantage of the proposed compressed sensing technique over present methods. Finally, we introduce a method to construct a certificate which guarantees the success of the reconstruction with no assumption on the state, and we show how slightly more measurements give rise to "universal" state reconstruction that is highly robust to noise. 1 aOhliger, Matthias1 aNesme, Vincent1 aGross, David1 aLiu, Yi-Kai1 aEisert, Jens uhttp://arxiv.org/abs/1111.0853v3