Quantum computing carries significant potential for addressing practical problems. However, currently available quantum devices suffer from noisy quantum gates, which degrade the fidelity of executed quantum circuits. Therefore, quantum circuit optimization is crucial for obtaining useful results. In this paper, we present QuCLEAR, a compilation framework designed to optimize quantum circuits. QuCLEAR significantly reduces both the two-qubit gate count and the circuit depth through two novel optimization steps. First, we introduce the concept of Clifford Extraction, which extracts Clifford subcircuits to the end of the circuit while optimizing the gates. Second, since Clifford circuits are classically simulatable, we propose Clifford Absorption, which efficiently processes the extracted Clifford subcircuits classically. We demonstrate our framework on quantum simulation circuits, which have wideranging applications in quantum chemistry simulation, manybody physics, and combinatorial optimization problems. Nearterm algorithms such as VQE and QAOA also fall within this category. Experimental results across various benchmarks show that QuCLEAR achieves up to a 77.7% reduction in CNOT gate count and up to an 84.1% reduction in entangling depth compared with state-of-the-art methods.

Quantum error mitigation plays a crucial role in the current noisy-intermediate-scale-quantum (NISQ) era. As we advance towards achieving a practical quantum advantage in the near term, error mitigation emerges as an indispensable component. One notable prior work, Jigsaw, demonstrates that measurement crosstalk errors can be effectively mitigated by measuring subsets of qubits. Jigsaw operates by running multiple copies of the original circuit, each time measuring only a subset of qubits. The localized distributions yielded from measurement subsetting suffer from less crosstalk and are then used to update the global distribution, thereby achieving improved output fidelity. Inspired by the idea of measurement subsetting, we propose QuTracer, a framework designed to mitigate both gate and measurement errors in subsets of qubits by tracing the states of qubit subsets throughout the computational process. In order to achieve this goal, we introduce a technique, qubit subsetting Pauli checks (QSPC), which utilizes circuit cutting and Pauli Check Sandwiching (PCS) to trace the qubit subsets distribution to mitigate errors. The QuTracer framework can be applied to various algorithms including, but not limited to, VQE, QAOA, quantum arithmetic circuits, QPE, and Hamiltonian simulations. In our experiments, we perform both noisy simulations and real device experiments to demonstrate that QuTracer is scalable and significantly outperforms the state-of-the-art approaches.

Instantaneous nonlocal quantum computation refers to a process in which spacelike separated parties simulate a nonlocal quantum operation on their joint systems through the consumption of pre-shared entanglement. To prevent a violation of causality, this simulation succeeds up to local errors that can only be corrected after the parties communicate classically with one another. However, this communication is non-interactive, and it involves just the broadcasting of local measurement outcomes. We refer to this operational paradigm as local operations and broadcast communication (LOBC) to distinguish it from the standard local operations and (interactive) classical communication (LOCC). In this paper, we show that an arbitrary two-qubit gate can be implemented by LOBC with ϵ-error using O(log(1/ϵ)) entangled bits (ebits). This offers an exponential improvement over the best known two-qubit protocols, whose ebit costs behave as O(1/ϵ). We also consider the family of binary controlled gates on dimensions dA⊗ dB. We find that any hermitian gate of this form can be implemented by LOBC using a single shared ebit. In sharp contrast, a lower bound of log dB ebits is shown in the case of generic (i.e. non-hermitian) gates from this family, even when dA= 2. This demonstrates an unbounded gap between the entanglement costs of LOCC and LOBC gate implementation. Whereas previous lower bounds on the entanglement cost for instantaneous nonlocal computation restrict the minimum dimension of the needed entanglement, we bound its entanglement entropy. To our knowledge this is the first such lower bound of its kind.