Quantum error correction (QEC) remains a critical challenge for the realization of fault-tolerant quantum computation. A significant bottleneck in QEC performance stems from the propagation of errors through entangled states. This paper introduces a novel algorithm, Entanglement Routing Algorithm (ERA), designed to optimize the routing of entangled states within a quantum circuit, thereby minimizing error propagation. The core idea revolves around leveraging quantum decoherence theory and implementing a path optimization strategy to identify the most resilient routes. The algorithm constructs a network representation of the quantum circuit and employs a cost function that quantifies the potential for information loss along each path, considering decoherence rates and connectivity. The optimization process then seeks the route that minimizes this cost function. Simulation results demonstrate that ERA can significantly reduce error propagation compared to naive routing strategies, paving the way for more robust and efficient QEC protocols.
Numerous quantum algorithms require the use of quantum error correction to overcome the intrinsic unreliability of physical qubits. However, quantum error correction imposes a unique performance bottleneck, known as T -complexity, that can make an implementation of an algorithm as a quantum program run more slowly than on idealized hardware. In this work, we identify that programming abstractions for control flow, such as the quantum if-statement, can introduce polynomial increases in the T -complexity of a program. If not mitigated, this slowdown can diminish the computational advantage of a quantum algorithm. To enable reasoning about the costs of control flow, we present a cost model that a developer can use to accurately analyze the T -complexity of a program under quantum error correction and pinpoint the sources of slowdown. To enable the mitigation of these costs, we present a set of program-level optimizations that a developer can use to rewrite a program to reduce its T -complexity, predict the T -complexity of the optimized program using the cost model, and then compile it to an efficient circuit via a straightforward strategy. We implement the program-level optimizations in Spire, an extension of the Tower quantum compiler. Using a set of 11 benchmark programs that use control flow, we empirically show that the cost model is accurate, and that Spire's optimizations recover programs that are asymptotically efficient, meaning their runtime T -complexity under error correction is equal to their time complexity on idealized hardware. Our results show that optimizing a program before it is compiled to a circuit can yield better results than compiling the program to an inefficient circuit and then invoking a quantum circuit optimizer found in prior work. For our benchmarks, only 2 of 8 tested quantum circuit optimizers recover circuits with asymptotically efficient T -complexity. Compared to these 2 optimizers, Spire uses 54 × − 2400 × less compile time.
Noise is a major challenge for current quantum computers. It can be broadly categorized into bit-flip and phase-flip errors. These two types do not necessarily affect the executed algorithm, thus also the application, in the same way. We illustrate this general effect for the example of the quantum approximate optimization algorithm (QAOA) applied to a small instance of the flight-gate assignment (FGA) problem. We compare bit-flip and phase-flip Pauli noise under both layer-level and gate-level noise models, using two circuit decompositions of the same ideal QAOA unitary: a CNOT-based decomposition and a native-
RZZ decomposition. In the simulations, bit-flip noise produces the larger degradation in the performance of the quantum optimization. The asymmetry is most visible in the layer-level and native-
RZZ simulations. We explain this by how the errors affect mixing, final measurements, and how they propagate inside the circuit. We then exploit these insights to tackle noise particularly efficiently using asymmetric error-correcting codes. As an illustration, we use the quantum parity code (QPC), a generalization of the 9-qubit Shor code, and show that a smaller asymmetric code can achieve nearly the same improvement as a larger symmetric choice. This demonstrates that error-correction resources should be assigned not only according to physical error rates, but also according to how strongly each error channel affects the application. As a result, asymmetric quantum error correction proves useful even in cases where the noise model is symmetric. Finally, we discuss how information about the noise obtained through calibration can be exploited in our approach.