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1. DQC-QR: Distributing and Routing Quantum Circuits with Minimum Execution Time

   https://doi.org/10.1145/3757069  

   Sundaram, Ranjani; Gupta, Himanshu; Ramakrishnan, CR (July 2025, ACM Transactions on Quantum Computing)

   Present quantum computers are constrained by limited qubit capacity and restricted physical connectivity, leading to challenges in large-scale quantum computations. Distributing quantum computations across a network of quantum computers is a promising way to circumvent these challenges and facilitate large quantum computations. However, distributed quantum computations require entanglements (to execute remote gates) which can incur significant generation latency and, thus, lead to decoherence of qubits. In this work, we consider the problem of distributing quantum circuits across a quantum network to minimize the execution time. The problem entails mapping the circuit qubits to network memories, including within each computer since limited connectivity within computers can affect the circuit execution time. We provide two-step solutions for the above problem: In the first step, we allocate qubits to memories to minimize the estimated execution time; for this step, we design an efficient algorithm based on an approximation algorithm for the max-quadratic-assignment problem. In the second step, we determine an efficient execution scheme, including generating required entanglements with minimum latency under the network resource and decoherence constraints; for this step, we develop two algorithms with appropriate performance guarantees under certain settings or assumptions. We consider multiple protocols for executing remote gates, viz., telegates and cat-entanglements. With extensive simulations over NetSquid, a quantum network simulator, we demonstrate the effectiveness of our developed techniques and show that they outperform a scheme based on prior work by 40 to\(50\% \)on average and up to 95% in some cases. 

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2. Percolation Theories for Quantum Networks

   https://doi.org/10.3390/e25111564  

   Meng, Xiangyi; Hu, Xinqi; Tian, Yu; Dong, Gaogao; Lambiotte, Renaud; Gao, Jianxi; Havlin, Shlomo (November 2023, Entropy)

   Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network’s indirect connectivity. This realization leads to the emergence of an alternative theory called “concurrence percolation”, which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design. 

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3. Exact Fisher zeros and thermofield dynamics across a quantum critical point

   https://doi.org/10.1103/PhysRevResearch.6.043139  

   Liu, Yang; Lv, Songtai; Meng, Yuchen; Tan, Zefan; Zhao, Erhai; Zou, Haiyuan (November 2024, Physical Review Research)

   By setting the inverse temperature $\beta$ loose to occupy the complex plane, Fisher showed that the zeros of the complex partition function $Z$, if approaching the real $\beta$ axis, reveal a thermodynamic phase transition. More recently, Fisher zeros were used to mark the dynamical phase transition in quench dynamics. It remains unclear, however, how Fisher zeros can be employed to better understand quantum phase transitions or the nonunitary dynamics of open quantum systems. Here we answer this question by a comprehensive analysis of the analytically continued one-dimensional transverse field Ising model. We exhaust all the Fisher zeros to show that in the thermodynamic limit they congregate into a remarkably simple pattern in the form of continuous open or closed lines. These Fisher lines evolve smoothly as the coupling constant is tuned, and a qualitative change identifies the quantum critical point. By exploiting the connection between $Z$ and the thermofield double states, we obtain analytical expressions for the short- and long-time dynamics of the survival amplitude, including its scaling behavior at the quantum critical point. We point out $Z$ can be realized and probed in monitored quantum circuits. The exact analytical results are corroborated by the numerical tensor renormalization group. We further show that similar patterns of Fisher zeros also emerge in other spin models. Therefore, the approach outlined may serve as a powerful tool for interacting quantum systems. 

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4. Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers

   https://doi.org/10.22331/q-2023-06-12-1040  

   Shkolnikov, V. O.; Mayhall, Nicholas J.; Economou, Sophia E.; Barnes, Edwin (June 2023, Quantum)

   Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ansätze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number $n$of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size $2n-2$can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such complete pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings. 

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5. Concurrence percolation threshold of large-scale quantum networks

   https://doi.org/10.1038/s42005-022-00958-4  

   Malik, Omar; Meng, Xiangyi; Havlin, Shlomo; Korniss, Gyorgy; Szymanski, Boleslaw Karol; Gao, Jianxi (December 2022, Communications Physics)

   Abstract Quantum networks describe communication networks that are based on quantum entanglement. A concurrence percolation theory has been recently developed to determine the required entanglement to enable communication between two distant stations in an arbitrary quantum network. Unfortunately, concurrence percolation has been calculated only for very small networks or large networks without loops. Here, we develop a set of mathematical tools for approximating the concurrence percolation threshold for unprecedented large-scale quantum networks by estimating the path-length distribution, under the assumption that all paths between a given pair of nodes have no overlap. We show that our approximate method agrees closely with analytical results from concurrence percolation theory. The numerical results we present include 2D square lattices of 200 2 nodes and complex networks of up to 10 4 nodes. The entanglement percolation threshold of a quantum network is a crucial parameter for constructing a real-world communication network based on entanglement, and our method offers a significant speed-up for the intensive computations involved. 

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