Three-Qubit Quantum Gate Fidelity Falls Sharply on Real Superconducting Hardware

The controlled-controlled-Z gate, or CCZ, is one of the workhorses of quantum algorithm design, a three-qubit operation that flips the phase of a quantum state only when all three of its qubits are in the state one. Because it lies at the heart of Grover search, quantum arithmetic, phase estimation and many error-correcting protocols, its real-world performance is a critical yardstick for how far superconducting quantum computers have actually come. A new experimental study published in Scientific Reports by Muhammad AbuGhanem of Ain Shams University and Zewail City of Science, Technology and Innovation now delivers one of the most detailed portraits yet of how this gate behaves on IBM Quantum’s 127-qubit superconducting machines, and the picture it paints is both encouraging and sobering.

The central finding is that the fidelity of the CCZ gate is not a single number. It depends strongly on which quantum state the gate acts upon and on which physical processor it runs, a phenomenon the study describes as state-backend-dependent performance. Using quantum state tomography, a technique that reconstructs the full quantum state of a system from many repeated measurements, the researcher evaluated the gate’s output-state fidelity for three algorithmically significant input states: the W state, the Greenberger-Horne-Zeilinger or GHZ state, and the uniform superposition state. Each of these states stresses the hardware in a different way, and the differences turned out to be dramatic.

The GHZ state is a maximally entangled configuration in which three qubits share a single collective quantum phase. It is the standard litmus test for coherence across a multi-qubit system, because any decoherence or correlated noise quickly destroys the delicate entanglement that binds the qubits together. When the CCZ gate was applied to the GHZ state on real hardware, the reconstructed output-state fidelity reached 67.6 percent, the best hardware result in the study. That figure suggests that the processors handle maximally entangled inputs relatively well, preserving enough coherence for the tomographic reconstruction to capture a recognizably quantum output.

The uniform superposition state, in which each qubit is placed in an equal blend of zero and one, probes a different aspect of gate behavior: whether the operation performs identically regardless of the basis-state structure of the input. Here the hardware fidelities dropped to 59.0 percent, a decline of nearly nine percentage points relative to the GHZ case. This gap indicates that the physical errors afflicting the gate are not uniform; they interact with the structure of the input state in ways that idealized gate models do not capture, meaning that algorithm designers cannot assume a single, state-independent error rate when estimating the cost of their circuits.

The most striking degradation appeared for the W state, an entangled configuration in which exactly one of the three qubits is excited while the other two remain in the ground state. Because the W state is inherently asymmetric, it is exquisitely sensitive to errors that affect qubits unevenly, such as differences in relaxation times, readout quality or control calibration across the chip. On hardware, the CCZ gate acting on the W state achieved a fidelity of only 50.3 percent, barely better than a coin flip in terms of the reconstructed output state. The authors note that this state reveals the hardware’s sensitivity to asymmetric errors, and the result quantifies just how punishing such asymmetries can be for multi-qubit operations.

To disentangle the contributions of noise from the intrinsic logic of the gate, the experiments were run across three distinct computational environments. In the noise-free qasm simulator, where the CCZ gate is executed with mathematical perfection and no physical decoherence, output-state fidelities remained above 99.2 percent for all three input states, confirming that the tomographic protocol itself and the gate definition are sound. Noisy simulations, which inject realistic error models into the computation, yielded fidelities clustered around 80 to 82 percent, already a substantial drop that reflects the cumulative effect of modeled decoherence, gate errors and measurement imperfections.

The gap between noisy simulation and real hardware is where the study becomes most consequential. While the noisy simulator predicted fidelities in the low eighties, the three physical machines, ibm_osaka, ibm_brisbane and ibm_sherbrooke, delivered results ranging from roughly 50 to 68 percent depending on the input state. This shortfall of ten to thirty percentage points means that current noise models, however sophisticated, still underestimate the complexity of errors on real superconducting processors. Correlated noise, crosstalk between neighboring qubits, drift in calibration over time and state-dependent readout errors all conspire in ways that standard simulation frameworks struggle to reproduce faithfully.

The practical implications for near-term quantum computing are significant. Many variational and fault-tolerance-oriented algorithms assume that gate errors can be characterized by a single average fidelity, often measured through randomized benchmarking. This study demonstrates that such averages can mask large state-dependent variations: a gate that performs at 67.6 percent on one input may fall to 50.3 percent on another within the same device. For algorithm designers, this means that circuit-level performance forecasts should account for the specific states that flow through each gate, and that benchmarking protocols which sample diverse input states will give a far more honest picture of usable computational quality than single-number metrics alone.

The work also provides a concrete benchmark against which future hardware improvements can be measured. By fixing the gate, the input states and the tomographic method, the study establishes a reproducible baseline for the current generation of 127-qubit IBM processors, and any advance in coherence times, two-qubit gate fidelities or calibration techniques should show up directly in these numbers. The roughly thirty-point gap between the ideal simulator and the best hardware result serves as a quantified statement of how much engineering progress remains before multi-qubit gates can support reliable, error-corrected computation. Until then, the study’s message is clear: in the quest for dependable quantum computation, both the choice of quantum state and the choice of physical backend matter, and neither can be ignored.

Subject of Research: Experimental characterization of state- and backend-dependent fidelity of the three-qubit CCZ gate on IBM superconducting quantum computers using quantum state tomography

Article Title: State-backend-dependent fidelity of the CCZ gate on superconducting quantum computers

Article References: AbuGhanem, M. (2026). State-backend-dependent fidelity of the CCZ gate on superconducting quantum computers. Scientific Reports, 16(1), Article 32077. https://doi.org/10.1038/s41598-026-71155-4

Image Credits: AI Generated

DOI: 10.1038/s41598-026-71155-4

Keywords: CCZ gate, quantum state tomography, superconducting qubits, IBM Quantum, GHZ state, W state, gate fidelity, quantum benchmarking, quantum noise, multi-qubit gates, noisy simulation, quantum computing