Abstract A method for quantum-process reconstruction using fuzzy measurement operators has been developed, where readout errors and decoherence of an ion-trap quantum register are incorporated into the effective measurement operators. The proposed approach outperforms standard methods that neglect measurement errors and decoherence in accurately reconstructing the Mølmer–Sørensen gate. Numerical experiments with entangled two-qubit states confirm that the proposed model significantly improves the fidelity of quantum process reconstruction. The obtained results demonstrate the potential of the proposed approach for creating more reliable and precise control methods in quantum computing on an ion platform, which is important for the development of quantum computing technologies.
Abstract A method for quantum-process reconstruction using fuzzy measurement operators has been developed, where readout errors and decoherence of an ion-trap quantum register are incorporated into the effective measurement operators. The proposed approach outperforms standard methods that neglect measurement errors and decoherence in accurately reconstructing the Mølmer–Sørensen gate. Numerical experiments with entangled two-qubit states confirm that the proposed model significantly improves the fidelity of quantum process reconstruction. The obtained results demonstrate the potential of the proposed approach for creating more reliable and precise control methods in quantum computing on an ion platform, which is important for the development of quantum computing technologies.
Abstract We present a framework for quantum process tomography of two-ion interactions that leverages modulations of the trapping potential and composite pulses from a global laser beam to achieve individual-ion addressing. Tomographic analysis of identity and delay processes reveals dominant error contributions from laser decoherence and slow qubit frequency drift during the tomography experiment. We use this framework on two co-trapped 40 Ca + ions to analyze both an optimized and an overpowered Mølmer–Sørensen gate and to compare the results of this analysis to a less informative Bell-state tomography measurement and to predictions based on a simplified noise model. These results show that the technique is effective for the characterization of two-ion quantum processes and for the extraction of meaningful information about the errors present in the system. The experimental convenience of this method will allow for more widespread use of process tomography for characterizing entangling gates in trapped-ion systems.
Abstract We develop a new method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of logical states. It is not always possible to achieve low error rates during the readout of the quantum states of ion qubits due to the finite lifetime of excited levels, photon scattering, detector dark counts, low numerical aperture, etc. However, the model of fuzzy quantum measurements makes it possible to ensure precise tomography of quantum states. To do this, we developed a fuzzy measurement model based on counting the number of fluorescent photons. A statistically adequate algorithm for the reconstruction of quantum states of ion qubit registers based on fuzzy measurement operators is proposed. The algorithm uses the complete information available in the experiment and makes it possible to account for systematic measurement errors associated with the limited distinguishability of the logical states of ion qubits. We show that the developed model, although computationally more complex, contains significantly more information about the state of the qubit and provides a higher accuracy of state reconstruction compared to the model based on the threshold algorithm.
Abstract The Mølmer–Sørensen gate, a cornerstone entangling operation in trapped-ion systems, represents a promising alternative to standard entangling gates in superconducting quantum architectures. However, its performance on superconducting hardware has remained unverified. In this work, we present a hardware-efficient implementation of the Mølmer–Sørensen gate and characterize its performance using quantum process tomography (QPT) on IBM Quantum’s superconducting processors. Our implementation achieves a process fidelity of 92.47% on the real quantum hardware, a performance competitive with the 93.02% fidelity of the device’s native controlled-NOT (CX) gate. Furthermore, for the ∣00⟩ | 00 ⟩ input state, the gate prepares the target Bell state with 94.2% 94.2 % success probability, confirming its correct logical operation. These results demonstrate that non-native entangling gates can be optimized to perform on par with hardware-native operations. This work expands the effective gate set for algorithm design on fixed-architecture processors and provides a critical benchmark for cross-platform gate evaluation, underscoring the role of hardware-aware compilation in advancing noisy intermediate-scale quantum (NISQ) computing.
The present work is devoted to the development of a method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of the states of a logical value 0 and a logical value 1. In the considered ion qubits, the identification of the quantum state is achieved by measuring the fluorescence of the ion by repeated excitation of the cyclic transition, which includes only the lower energy state that sets a logical value 0 and becomes bright, but does not include the upper metastable state that remains dark and sets logical value 1. It is important to note that it is not always possible to achieve low levels of registration errors due to the finite lifetime of excited levels, photon scattering, dark noise, low numerical aperture values, etc. However, even under such conditions, with use of the model of fuzzy quantum measurements, it is possible to provide precise control of quantum states. We show that a model that is characterized by relatively high levels of errors under conditions, where we have a reliable statistical model of their occurrence, is more accurate than the case when the considered errors are small, but we do not have an adequate statistical model for the occurrence of these errors. In the given illustrative examples, we show that the factor of reducing the loss of accuracy with the use of the model of fuzzy measurements can reach values of the order of 1000 or more in comparison with standard measurements. The obtained results are essential for the development of high-precision methods for controlling the technology of quantum computing on the ion platform.
The present work is devoted to the development of a method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of the states of a logical value 0 and a logical value 1. In the considered ion qubits, the identification of the quantum state is achieved by measuring the fluorescence of the ion by repeated excitation of the cyclic transition, which includes only the lower energy state that sets a logical value 0 and becomes bright, but does not include the upper metastable state that remains dark and sets logical value 1. It is important to note that it is not always possible to achieve low levels of registration errors due to the finite lifetime of excited levels, photon scattering, dark noise, low numerical aperture values, etc. However, even under such conditions, with use of the model of fuzzy quantum measurements, it is possible to provide precise control of quantum states. We show that a model that is characterized by relatively high levels of errors under conditions, where we have a reliable statistical model of their occurrence, is more accurate than the case when the considered errors are small, but we do not have an adequate statistical model for the occurrence of these errors. In the given illustrative examples, we show that the factor of reducing the loss of accuracy with the use of the model of fuzzy measurements can reach values of the order of 1000 or more in comparison with standard measurements. The obtained results are essential for the development of high-precision methods for controlling the technology of quantum computing on the ion platform.
We present a simple tomographic protocol, for two-qubit systems, that relies on a single discriminatory transition and no direct spatially selective imaging. This scheme exploits excess micromotion in the trap to realize all operations required to prepare all input states and analyze all output states. We demonstrate a two-qubit entangling gate with a Bell state production fidelity of 0.981(6), and apply the above protocol to perform the first quantum process tomography of a M\o{}lmer-S\o{}rensen entangling gate. We characterize its $\ensuremath{\chi}$-process matrix, the simplest for an entanglement gate on a separable-states basis, and observe that our dominant source of error is accurately modeled by a quantum depolarization channel.