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As quantum computing continues to scale, the ability to execute quantum circuits across distributed quantum networks is becoming increasingly important. While prior work has largely focused on distributing a single circuit to optimize the number of entanglement pairs (EPs) used or the execution time, future applications will require the efficient scheduling and execution of multiple circuits on a shared quantum network. Therefore, we study the problem of efficiently distributing multiple quantum circuits across a shared quantum network under decoherence and network constraints and seek to minimize the execution time required to execute all circuits (makespan). Solving the above problem involves jointly determining when and where each circuit should be executed, and how to schedule concurrent EP generation required to execute remote gates. We propose several algorithmic approaches for this multi-circuit distribution problem and provide theoretical performance guarantees for special cases. To assess the practical effectiveness of our methods, we conduct extensive simulations using the NetSquid quantum network simulator. 

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. 

Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning, or quantum state estimation. The problem is that, without more information, all that can be determined is the density matrix of the sequence and, in general, density matrices can be decomposed into pure states in many different ways. To solve the problem, additional information, either classical or quantum, is required. We show that if an additional copy of each qubit is supplied (that is, one receives pairs of qubits, both in the same state, rather than single qubits) the task can be accomplished. This is possible because the mixed two-qubit state has a unique decomposition into pure product states. For illustration purposes, we numerically simulate the symmetric, informationally complete measurement of a sequence of qubit pairs and show that the unknown states and their respective probabilities of occurrence can be inferred from the data with high accuracy. Finally, we propose an experiment that employs a product measurement and can be realized with existing technology, and we demonstrate how the data tell us the states and their probabilities. We find that it is enough to detect a few thousand qubit pairs. 

Quantum sensor networks have often been studied in order to determine how accurately they can determine a parameter, such as the strength of a magnetic field, at one of the detectors. A more coarse-grained approach is to try to simply determine whether a detector has interacted with a signal or not, and which detector it was. Such discrete-outcome quantum sensor networks, discrete in the sense that we are seeking answers to yes-no questions, are what we study here. One issue is what is a good initial state for the network, and, in particular, should it be entangled or not. Earlier we looked at the case when only one detector interacted, and here we extend that study in two ways. First, we allow more than one detector to interact, and second, we examine the effect of grouping the detectors. When the detectors are grouped we are only interested in which group contained interacting detectors and not in which individual detectors within a group interacted. We find that in the case of grouping detectors, entangled initial states can be helpful.