AVS 71 Session QS1-TuM: Quantum Simulations and Quantum-Inspired Technologies

Understanding spin dynamics has long intrigued physicists, as it plays a vital role in revealing the characteristics of quantum magnets, with potential applications in spintronic devices and spin qubits. Evaluating the dynamical properties of large spin systems is often challenging for classical computers due to the exponential growth in memory requirements. Since Hamiltonian dynamics can be efficiently simulated using quantum circuits, the evaluation of time-dependent properties has generated significant interest within the quantum computing community.

While time-dependent magnetization and the one-time dynamical structure factor have been simulated on quantum computers before, there has been no simulation of the spin-current autocorrelation function (ACF). The one-time spin-current ACF can be used to identify the diffusion behavior of spin systems and is directly related to their coherence properties and device performance. In this research, we first consider the spin-1/2 XXZ Heisenberg model as it serves as the framework for studying magnetic interaction.

Here, we introduce a simple yet efficient direct measurement scheme for evaluating the one-time spin-current ACF. Unlike the standard Hadamard test, our method eliminates the need for control gates with ancilla qubits and reduces the number of required circuits by a factor of N, where N is the number of qubits. We demonstrate the circuit design and measurement protocol and validate it through a quantum experiment on the ibm_marrakesh hardware. In the 20-qubit experiment with the Néel state, we achieve excellent agreement with the numerical results for both the real and imaginary parts, highlighting the effectiveness of our method. Moreover, we present a design for measuring the two-time spin-current ACF and demonstrate good agreement between statevector-simulated results and numerical results, further showcasing the utility of our approach. Furthermore, our method can be potentially extended to measure any ACF, benefiting the study of spin dynamics.

This work is supported by Taiwan UIUC scholarship, and we acknowledge support by the IBM Illinois Discovery Accelerator Institute and the IBM Externship Program. This work made use of the Illinois Campus Cluster, a computing resource that is operated by the Illinois Campus Cluster Program in conjunction with the National Center for Supercomputing Applications and which is supported by funds from UIUC. The research at IBM and Purdue is supported by National Quantum Initiative Science Research Centers, Quantum Science Center, managed by ORNL for the US-DOE.

Quantum error correction (QEC) is essential for fault-tolerant quantum computing, ensuring that logical informationremains protected from physical noise during the execution of quantum algorithms. Traditional QEC strategies achieve this by redundantly encoding logical qubits across many physical qubits, incurring significant hardware overhead. At Nord Quantique, we leverage the large Hilbert space of quantum oscillators to perform QEC within a single physical system, offering a potentially more hardware-efficient path to fault-tolerant quantum computing.

Among such bosonic codes, grid codes are particularly promising, as they encode discrete-variable logical information in translationally invariant lattices in phase space. Recent experimental demonstrations in superconducting circuits have validated this approach with single-mode grid codes, enabling QEC that helps more than it hurts. A key challenge in these demonstrations were the silent logical errors induced by auxiliary control systems (e.g., transmons). One promising avenue to circumvent this for FTQC are multi-mode grid codes, where auxiliary errors may move the state outside of the logical space rather than inducing silent logical errors.

In this talk, we will present our experimental resultsalong two axes toward FTQC: gates for single-mode grid qubits, and QEC for two-mode grid qubits. For the two-mode so-called tesseract code, we will demonstrate its enhanced features by leveraging mid-circuit measurement outcomes to suppress logical decay in a hardware-efficient architecture.These results validate Nord Quantique’s vision of multimode grid codes as a promising pathway toward FTQC.

Quantum processors have become quite large and sophisticated machines over the last several years, with many tech companies racing to develop the first quantum computer of practical utility. While the progress has been impressive, quantum processors still face significant hurdles such as short coherence times and high error rates. They are not yet able to compete with classical information processing technologies in solving problems of practical interest. I will discuss my group’s contributions across the quantum information processing stack, from the control of quantum hardware to quantum algorithm development and back.