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Thermal Area Law in Long-Range Interacting Systems.

The area law of the bipartite information measure characterizes one of the most fundamental aspects of quantum many-body physics. In thermal equilibrium, the area law for the mutual information universally holds at arbitrary temperatures as long as the systems have short-range interactions. In systems with power-law decaying interactions, r^{-α} (r: distance), conditions for the thermal area law are elusive. In this Letter, we aim to clarify the optimal condition α>α_{c} such that the thermal area law universally holds. A standard approach to considering the conditions is to focus on the magnitude of the boundary interaction between two subsystems. However, we find here that the thermal area law is more robust than this conventional argument suggests. We show the optimal threshold for the thermal area law by α_{c}=(D+1)/2 (D: the spatial dimension of the lattice), assuming a power-law decay of the clustering for the bipartite correlations. Remarkably, this condition encompasses even the thermodynamically unstable regimes α<D. We verify this condition numerically, finding that it is qualitatively accurate for both integrable and nonintegrable systems. Unconditional proof of the thermal area law is possible by developing the power-law clustering theorem for α>D above a threshold temperature. Furthermore, the numerical calculation for the logarithmic negativity shows that the same criterion α>(D+1)/2 applies to the thermal area law for quantum entanglement.

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Experimental computations of atomic properties on a superconducting quantum processor

We experimentally compute relativistic and correlation effects in the atomic properties by using a superconducting qubit processor. Specifically, we compute the relativistic ground-state energies and magnetic-dipole hyperfine structure constants for four Li-like atomic systems ranging from very light to moderately heavy to very heavy in terms of nuclear charge. A symmetry-conserving Bravyi-Kitaev transformation is used to reduce the original six-qubit problem to a four-qubit problem, which is experimentally contrived by reducing the hardware requirement by employing a virtual two-qubit gate. It enables the simulation of four-qubit circuits using two physical qubits with additional circuit evaluations. The ground-state wave functions, required for computing atomic properties, are obtained by using quantum state tomography. Our results show that the averaged relative errors for the ground-state energies are ≈0.3±1%. However, for the hyperfine structure constants, the mean values of the relative errors are less than 15%, with their estimated upper bound of relative errors of ≈±10% (with the exception of 7.2±47% for neutral Li7). Notably, our results for the hyperfine structure constants exhibit higher sensitivity to errors as compared to energies; a trend which we also confirm through additional numerical simulations. Published by the American Physical Society 2024

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Diamond-shaped quantum circuit for real-time quantum dynamics in one dimension

In recent years, quantum computing has evolved as an exciting frontier, with the development of numerous algorithms dedicated to constructing quantum circuits that adeptly represent quantum many-body states. However, this domain remains in its early stages and requires further refinement to better understand the effective construction of highly entangled quantum states within quantum circuits. Here, we demonstrate that quantum many-body states can be universally represented using a quantum circuit comprising multiqubit gates. Furthermore, we evaluate the efficiency of a quantum circuit constructed with two-qubit gates in quench dynamics for the transverse-field Ising model. In this specific model, despite the initial state being classical without entanglement, it undergoes long-time evolution, eventually leading to a highly entangled quantum state. Our results reveal that a diamond-shaped quantum circuit, designed to approximate the multiqubit gate-based quantum circuit, remarkably excels in accurately representing the long-time dynamics of the system. Moreover, the diamond-shaped circuit follows the volume law behavior in entanglement entropy, offering a significant advantage over alternative quantum circuit constructions employing two-qubit gates. Published by the American Physical Society 2024

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Fixing detailed balance in ancilla-based dissipative state engineering

Dissipative state engineering is a general term for a protocol which prepares the ground state of a complex many-body Hamiltonian using engineered dissipation or engineered environments. Recently, it was shown that a version of this protocol, where the engineered environment consists of one or more dissipative qubit ancillas tuned to be resonant with the low-energy transitions of a many-body system, resulted in the combined system evolving to reasonable approximation to the ground state. This potentially broadens the applicability of the method beyond nonfrustrated systems, to which it was previously restricted. Here we argue that this approach has an intrinsic limitation because the ancillas, seen as an effective bath by the system in the weak-coupling limit, do not give the detailed balance expected for a true zero-temperature environment. Our argument is based on the study of a similar approach employing linear coupling to bosonic ancillas. We explore overcoming this limitation using a recently developed open quantum systems technique called pseudomodes. With a simple example model of a one-dimensional quantum Ising chain, we show that detailed balance can be fixed, and a more accurate estimation of the ground state obtained, at the cost of two additional unphysical dissipative modes and the extrapolation error of implementing those modes in physical systems. Published by the American Physical Society 2024

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