Integrating Julia-ITensors into the Tensor Network Quantum Virtual Machine (TNQVM)

Abstract

The Tensor Network Quantum Virtual Machine (TNQVM) is a high-performance classical circuit simulation backend for the eXtreme-scale ACCelerator (XACC) framework that leverages the Intelligent Tensor (ITensor) library for tensor network--based quantum circuit simulation. However, TNQVM's original C++ ITensor backend is tied to an older integrated release, limiting access to newer tensor network algorithms, diagnostics, and performance improvements available in the actively developed Julia-based ITensors ecosystem. We introduce JuliaITensorTNQVM, an interoperability layer that bridges TNQVM's C++ visitor infrastructure and the Julia-ITensors runtime through a C-compatible application binary interface. This design preserves the existing XACC/TNQVM programming model while enabling access to modern tensor network capabilities, including entanglement entropy diagnostics exposed directly to XACC. We evaluate the implementation through two studies: a Page-curve verification protocol using Haar-random states, and QAOA MaxCut simulations on 3-regular graphs. Within these tested regimes, results are consistent with expected entanglement behavior and established scaling trends, supporting JuliaITensorTNQVM as a practical modernization path for tensor network simulation in TNQVM.

Figures (5)

• Figure 1: Architecture of the XACC/TNQVM execution pipeline. The XACC framework delegates circuit execution to the TNQVM Accelerator, which dispatches gate operations through the visitor interface to backend-specific implementations. The ITensor-based visitor path (right) crosses a C ABI into the JuliaITensorTNQVM compiled library, which manages the Julia runtime and interfaces with the Julia-ITensors numerical backend. Memory management responsibilities are partitioned at this boundary: the C++ side supplies gate metadata as ABI call arguments, while Julia-side allocations are managed by the Julia garbage collector. The ExaTN-based visitor path (left) and its associated sub-visitors are shown for context.
• Figure 2: Convergence analysis for the Page curve verification protocol using a 12-qubit MPS with full bond dimension $\chi = 2^6$. (a) Standard error $\sigma_{M}$ as a function of Monte Carlo iterations $M$ for different bipartition sites $N_A$. Error peaks at the center site ($N_A = N/2 = 6$) where entanglement is maximal. (b) Absolute error $|\Delta S| = |S_{\chi}(N_A) - S_{\rm Page}(N_A)|$ between Monte Carlo estimates and exact Page values as a function of subsystem size $N_A$ for different numbers of Monte Carlo iterations $M$. Error decreases systematically with more Monte Carlo samples. (c) Computed entanglement entropy $S_{\chi}$ (blue points) versus exact Page curve prediction $S_{\rm Page}$ (orange line) as a function of subsystem size $N_A$ for $M = 30$ Monte Carlo samples, demonstrating excellent agreement with analytical predictions across all bipartition sizes.
• Figure 3: Effect of bond dimension truncation on MPS representation quality for Haar-random states. Top: Normalized entanglement entropy $S_{\chi}/(N\ln 2)$ at the center site ($N/2$) versus system size $N$ for various bond dimensions $\chi$. The exact representation ($\chi = 2^{N/2}$, black dashed line) maintains unit fidelity across all system sizes. Bottom: Simulation fidelity $\mathcal{F}_{\rm sim}(\chi) = S_{\chi}(N/2)/S_{\rm Page}(N/2)$ versus system size $N$. Curves are color-coded by bond dimension. Maintaining constant fidelity across system sizes requires exponential scaling $\chi \propto 2^{N/2}$.
• Figure 4: Bond dimension effects on QAOA simulation for 14-qubit MaxCut on 3-regular graphs. Top: Cost function expectation value $\braket{H_P}$ versus QAOA depth $p$. Bottom: Entanglement entropy at the center bipartition (site $N/2=7$) versus QAOA depth. Results are averaged over 25 randomly generated graphs for each bond dimension. Large bond dimensions ($\chi = 64, 128$) show consistent behavior, while smaller values exhibit degraded performance.
• Figure 5: Universal scaling of entanglement entropy and cost function in QAOA MaxCut simulations for system sizes $N = 8, 10, 12, 14, 16$ using single-layer QAOA ($p=1$) on 3-regular graphs. (a) Entanglement entropy at the center bipartition (site $N/2$) versus bond dimension $\chi$. Each system size produces a distinct curve. (b) Collapsed entanglement scaling showing entropy per qubit $S_{\chi}/N$ versus $\ln(\chi)/N$. The collapse is most accurate for $\ln(\chi)/N \lesssim 0.1$. (c) Minimized cost function expectation value $E_{\rm min} \equiv \braket{H_P}$ versus bond dimension $\chi$. (d) Collapsed cost function scaling showing ratio $E_{\rm min}/E_{\rm opt}$ versus $\ln(\chi)/N$, where $E_{\rm opt}$ is the best classical approximation to the minimum energy obtained from the 25-graph ensemble.