This study presents a benchmark of quantum noise scaling in GHZ circuits using PennyLane-based simulations. The experiments investigate how increasing the number of qubits and applying noise affect GHZ-state fidelity, while also comparing the computational cost of noisy quantum simulation with classical density-matrix simulation. The benchmark evaluates circuit sizes across multiple qubit counts under controlled simulation conditions and records the resulting state fidelity and computational behavior. The results provide an empirical view of the relationship between qubit scaling, noise, and classical simulation cost. In particular, the study highlights the increasing computational burden associated with density-matrix representations as system size grows. The accompanying implementation, experimental data, and visualization scripts are provided as open-source materials to support reproducibility. The results are intended as a practical benchmark for studying the scaling behavior of noisy quantum circuits on classical simulation backends.
This study presents a benchmark of quantum noise scaling in GHZ circuits using PennyLane-based simulations. The experiments investigate how increasing the number of qubits and applying noise affect GHZ-state fidelity, while also comparing the computational cost of noisy quantum simulation with classical density-matrix simulation. The benchmark evaluates circuit sizes across multiple qubit counts under controlled simulation conditions and records the resulting state fidelity and computational behavior. The results provide an empirical view of the relationship between qubit scaling, noise, and classical simulation cost. In particular, the study highlights the increasing computational burden associated with density-matrix representations as system size grows. The accompanying implementation, experimental data, and visualization scripts are provided as open-source materials to support reproducibility. The results are intended as a practical benchmark for studying the scaling behavior of noisy quantum circuits on classical simulation backends.
Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size.Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models.In this work, we simulate random quantum circuits in one dimension with matrix product density operators (MPDOs), for different noise models such as dephasing, depolarizing, and amplitude damping.We show that the method based on matrix product states (MPSs) fails to approximate the noisy output quantum states for any of the noise models considered, while the MPDO method approximates them well.Compared with the method of matrix product operators (MPOs), the MPDO method reflects a clear physical picture of noise (with inner indices taking care of the noise simulation) and quantum entanglement (with bond indices taking care of two-qubit gate simulation).Consequently, in case of weak system noise, the resource cost of the MPDO will be significantly less than that of the MPO due to a relatively small inner dimension needed for the simulation.In case of strong system noise, a relatively small bond dimension may be sufficient to simulate the noisy circuits, indicating a regime that the noise is large enough for an "easy" classical simulation, which is further supported by a comparison with the experimental results on an IBM cloud device.Moreover, we propose a more effective tensor updates scheme with optimal truncations for both the inner and the bond dimensions, performed after each layer of the circuit, which enjoys a canonical form of the MPDO for improving simulation accuracy.With truncated inner dimension to a maximum value κ and bond dimension to a maximum value χ , the cost of our simulation scales as ∼NDκ 3 χ 3 , for an N-qubit circuit with depth D.
Quantum entanglement is a central resource for quantum computation and state transfer, yet the usefulness of multipartite entanglement depends on how rapidly coherence and nonclassical correlations degrade as the register size and communication depth increase. This methodology paper develops a reproducible density-matrix simulation for studying entanglement and information transfer in multi-qubit systems. GHZ and W states containing 3, 4, 5, 6 and 8 qubits are generated and exposed to independent local depolarizing noise. State fidelity and bipartite negativity are used to quantify preservation of the prepared resource, while an entanglement-assisted multi-hop teleportation model measures the fidelity of transferred single-qubit information. The simulation shows a systematic decrease in state fidelity and negativity with increasing register size at a fixed local error probability. At a local depolarizing probability of 0.02, GHZ fidelity decreases from 0.941 for three qubits to 0.852 for eight qubits, whereas W-state fidelity decreases from 0.943 to 0.877. In a separate transfer experiment with an effective error probability of 0.10 per teleportation hop, average transfer fidelity decreases from 0.933 after one hop to 0.745 after five hops, while remaining above the classical benchmark of 2/3. These results illustrate how multipartite entanglement quality; noise accumulation and path depth jointly determine the reliability of information transfer in multi-qubit computing architectures.
The development of complex circuits for practical applications in the current quantum computing ecosystem is based on basic primitives such as Bell states, which provide superposition, entanglement, and coherence. The range of domain-specific quantum applications has been greatly expanded by the availability of simulators and platforms such as IBM Quantum, which are supported by Qiskit. However, disparities between ideal simulator outputs and actual quantum processing unit (QPU) executions in the Noisy Intermediate-Scale Quantum (NISQ) era require the application of quantum error mitigation techniques. Limitations arise from hardware constraints in superconducting qubit systems and from the limited resources of classical simulators as quantum circuits grow. Quantum decoherence, which lowers gate fidelity and builds up at the circuit level with increasing depth, is specifically caused by material-induced flaws and interfaces. This creates a clear connection between circuit reliability, device performance, and material attributes. To address this, the current work uses both simulation and actual hardware on the IBM Sherbrooke 127-qubit processor to study three basic circuit classes over 4 to 10 qubits: the quantum Fourier transform, the Greenberger-Horne-Zeilinger state, and the W state. The study examines trade-offs between circuit complexity, noise robustness, and resource utilization by contrasting simulator and QPU results. The results imply that circuit fidelity can serve as an indirect probe of material-limited noise, opening the door to a framework for designing quantum circuits that accounts for both hardware and materials to achieve scalable quantum advantage.
Effective methods for characterizing the noise in quantum computing devices are essential for programming and debugging circuit performance. Existing approaches vary in the information obtained as well as the amount of quantum and classical resources required, with more information generally requiring more resources. Here we benchmark the characterization methods of gate set tomography, Pauli channel noise reconstruction, and empirical direct characterization for developing models that describe noisy quantum circuit performance on a 27-qubit superconducting transmon device. We evaluate these models by comparing the accuracy of noisy circuit simulations with the corresponding experimental observations. We find that the agreement of noise model to experiment does not correlate with the information gained by characterization and that the underlying circuit strongly influences the best choice of characterization approach. Empirical direct characterization scales best of the methods we tested and produced the most accurate characterizations across our benchmarks.
The increasing complexity of quantum algorithms and the limitations of current Noisy Intermediate-Scale Quantum (NISQ) hardware underscore the importance of efficient classical simulators. To support informed decision-making by users of quantum circuit simulators, we benchmark seven statevector-based quantum circuit simulators (Qiskit, Qulacs, Qibo, Qsimov, Cirq, Pennylane and the Intel Quantum Simulator (IQS)) on a multicore node of the Lusitania high-performance computing (HPC) system. We evaluate their performance in terms of execution time, memory usage and core scalability using Grover’s algorithm, the quantum Fourier transform (QFT), and quantum volume (QV) circuits, across qubit counts ranging from 3 to 30. Our results reveal that Qulacs offers the best performance for circuits below 22 qubits, while Qiskit becomes the fastest for larger and more complex circuits. Qiskit and Qulacs achieve the most efficient parallel performance across multiple cores, while others display limited scaling benefits. IQS shows the lowest memory consumption in QFT and QV benchmarks for systems under 24 qubits; however, it suffers from higher execution times, particularly for Grover’s algorithm. The experimental implementation of Qsimov consistently underperforms in both runtime and scalability; for this reason, it is employed as a baseline in our measurements, serving to highlight the importance of performance optimizations in statevector-based quantum circuit simulators. Previous findings provide a comprehensive performance landscape to guide researchers in selecting appropriate simulators for both standard and large-scale quantum workloads on HPC infrastructures.
Since quantum computers can solve important problems faster than classical computers, many resources have gone into the development of this technology in recent decades. Despite the tremendous progress that has already been made toward the development of quantum computers, they are still an emerging technology, which restricts access and reliability. Thus, research on quantum algorithms still heavily relies on quantum circuit simulators that run on classical hardware. However, simulating the execution of a quantum computer on conventional hardware is exponentially difficult, which is also the reason why quantum computing is an interesting technology in the first place. Particularly complex is noise-aware simulation of quantum computers, i.e., the consideration of noise effects that are common in today’s quantum hardware during quantum circuit simulation. In this work, we investigate the use of decision diagrams for this task. To this end, we present two distinct approaches for noise-aware quantum circuit simulation, investigate how they can be realized using decision diagrams, and implement decision diagram-based solutions for each of the presented noise-aware simulation schemes. In an extensive evaluation, we unveil potential for further improvements and also demonstrate substantial speed-ups compared to the current state of the art.