The paper "Optimal Quantum Circuit Cuts with Application to Clustered Hamiltonian Simulation" by Aram W. Harrow and Angus Lowe explores methods to replace entangling operations with random local operations in quantum computations, aiming to reduce the number of required executions. The authors introduce two types of circuit cutting: "space-like cuts" and "time-like cuts." In space-like cuts, an entangling unitary is replaced by a set of local unitaries acting on the original systems and ancilla qubits. The paper introduces a new measure called the *product extent* to bound the cost of this replacement. This measure is shown to be optimal for many 2-qubit gates, SWAP operators, and transversal operations. The authors also provide an efficient algorithm for clustered Hamiltonian simulation, demonstrating that interactions can be removed at a cost exponential in the sum of their strengths times the evolution time. In time-like cuts, a subset of wires in a circuit is replaced by measure-and-prepare operations, increasing the circuit size and the number of executions. The paper gives an improved upper bound on the cost of this replacement and proves a matching information-theoretic lower bound when estimating output probabilities. The authors also discuss related work and provide a detailed analysis of the proposed methods, including theoretical bounds and practical implications for quantum computing applications.The paper "Optimal Quantum Circuit Cuts with Application to Clustered Hamiltonian Simulation" by Aram W. Harrow and Angus Lowe explores methods to replace entangling operations with random local operations in quantum computations, aiming to reduce the number of required executions. The authors introduce two types of circuit cutting: "space-like cuts" and "time-like cuts." In space-like cuts, an entangling unitary is replaced by a set of local unitaries acting on the original systems and ancilla qubits. The paper introduces a new measure called the *product extent* to bound the cost of this replacement. This measure is shown to be optimal for many 2-qubit gates, SWAP operators, and transversal operations. The authors also provide an efficient algorithm for clustered Hamiltonian simulation, demonstrating that interactions can be removed at a cost exponential in the sum of their strengths times the evolution time. In time-like cuts, a subset of wires in a circuit is replaced by measure-and-prepare operations, increasing the circuit size and the number of executions. The paper gives an improved upper bound on the cost of this replacement and proves a matching information-theoretic lower bound when estimating output probabilities. The authors also discuss related work and provide a detailed analysis of the proposed methods, including theoretical bounds and practical implications for quantum computing applications.