Recent advances on quantum computing hardware have pushed quantum computing to the verge of quantum supremacy. Here, we bring together many-body quantum physics and quantum computing by using a method for strongly interacting two-dimensional systems, the projected entangled-pair states, to realize an effective general-purpose simulator of quantum algorithms. The classical computing complexity of this simulator is directly related to the entanglement generation of the underlying quantum circuit rather than the number of qubits or gate operations. We apply our method to study random quantum circuits, which allows us to quantify precisely the memory usage and the time requirements of random quantum circuits. We demonstrate our method by computing one amplitude for a 7×7 lattice of qubits with depth (1+40+1) on the Tianhe-2 supercomputer.
Abstract The development of novel quantum many-body computational algorithms relies on robust benchmarking. However, generating such benchmarks is often hindered by the massive computational resources required for exact diagonalization or quantum Monte Carlo simulations, particularly at finite temperatures. In this work, we propose a new algorithm for obtaining thermal pure quantum states, which allows efficient computation of both mechanical and thermodynamic properties at finite temperatures. We implement this algorithm in our open-source C++ template library, Physica . Combining the improved algorithm with state-of-the-art software engineering, our implementation achieves high performance and numerical stability. As an example, we demonstrate that for the 4 × 4 Hubbard model, our method runs approximately 10 3 times faster than ℋ Φ 3.5.2. Moreover, the accessible temperature range is extended down to β = 32 across arbitrary doping levels. These advances significantly push forward the frontiers of benchmarking for quantum many-body systems.
Establishing quantum advantage requires comparison against the best achievable classical simulation. The Q-CTRL team recently simulated quench dynamics of the one-dimensional Fermi-Hubbard model on an IBM processor, completing a
L=60 evolution to time
t=6 in under three minutes and claiming a
3000× speedup over classical Time-Dependent Variational Principle (TDVP) simulation at bond dimension
χ=4096. Their classical benchmark required over 160 hours on a CPU cluster, failed to converge in the high-entanglement regime
t∈[5.2,6], and left the most challenging window of the experiment unverified. Here, we push the boundaries of classical simulation by exploiting the full
U(1)×SU(2) symmetry of the Fermi-Hubbard Hamiltonian combined with GPU-accelerated tensor contractions. Reaching bond dimensions up to
χ≈62,000 on four NVIDIA H200 GPUs -- among the largest ever achieved in TDVP simulations and fifteen times larger than Q-CTRL's classical baseline -- we achieve fully converged results across the entire simulation window, including rigorous certification of the previously unresolved high-entanglement regime
t∈[5.2,6]. We further advance the classical frontier to
t=7, which lies beyond the quantum hardware experiment and any previously verified classical evolution of the full wavefunction. At the bond dimension comparable to Q-CTRL's best classical run, our GPU implementation completes in
∼100 minutes, directly reducing the claimed
3000× quantum advantage to
∼36×. These results substantially narrow the quantum-classical performance gap and establish a new standard for tensor-network benchmarking of large-scale quantum simulations.