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Register a new userGeneral-purpose quantum circuit simulator with Projected Entangled-Pair States and the quantum supremacy frontier
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Recent advances on quantum computing hardware have pushed quantum computing to the verge of quantum supremacy. Random quantum circuits are outstanding candidates to demonstrate quantum supremacy, which could be implemented on a quantum device that supports nearest-neighbour gate operations on a two-dimensional configuration. Here we show that using the Projected Entangled-Pair States algorithm, a tool to study two-dimensional strongly interacting many-body quantum systems, we can realize an effective general-purpose simulator of quantum algorithms. This technique allows to quantify precisely the memory usage and the time requirements of random quantum circuits, thus showing the frontier of quantum supremacy. With this approach we can compute the full wave-function of the system, from which single amplitudes can be sampled with unit fidelity. Applying this general quantum circuit simulator we measured amplitudes for a $7times 7$ lattice of qubits with depth $1+40+1$ and double-precision numbers in 31 minutes using less than $93$ TB memory on the Tianhe-2 supercomputer.
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We introduce plaquette projected entangled-pair states, a class of states in a lattice that can be generated by applying sequential unitaries acting on plaquettes of overlapping regions. They satisfy area-law entanglement, possess long-range correlations, and naturally generalize other relevant classes of tensor network states. We identify a subclass that can be more efficiently prepared in a radial fashion and that contains the family of isometric tensor network states. We also show how such subclass can be efficiently prepared using an array of photon sources.
Quantum circuit simulators have a long tradition of exploiting massive hardware parallelism. Most of the times, parallelism has been supported by special purpose libraries tailored specifically for the quantum circuits. Quantum circuit simulators are integral part of quantum software stacks, which are mostly written in Python. Our focus has been on ease of use, implementation and maintainability within the Python ecosystem. We report the performance gains we obtained by using CuPy, a general purpose library (linear algebra) developed specifically for CUDA-based GPUs, to simulate quantum circuits. For supremacy circuits the speedup is around 2x, and for quantum multipliers almost 22x compared to state-of-the-art C++-based simulators.
Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While MPS are comprehensively understood, in PEPS fundamental questions, relevant analytically as well as numerically, remain open, such as how to encode symmetries in full generality, or how to stabilize numerical methods using canonical forms. Here, we show that these key problems, as well as a number of related questions, are algorithmically undecidable, that is, they cannot be fully resolved in a systematic way. Our work thereby exposes fundamental limitations to a full and unbiased understanding of quantum many-body systems using PEPS.
Tensor network states, and in particular projected entangled pair states (PEPS), suggest an innovative approach for the study of lattice gauge theories, both from a pure theoretic point of view, and as a tool for the analysis of the recent proposals for quantum simulations of lattice gauge theories. In this paper we present a framework for describing locally gauge invariant states on lattices using PEPS. The PEPS constructed hereby shall include both bosonic and fermionic states, suitable for all combinations of matter and gauge fields in lattice gauge theories defined by either finite or compact Lie groups.
The projected entangled pair states (PEPS) methods have been proved to be powerful tools to solve the strongly correlated quantum many-body problems in two-dimension. However, due to the high computational scaling with the virtual bond dimension $D$, in a practical application PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, the frustrated systems. The optimization of the ground state using time evolution method with simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. Here, we demonstrate that combining the time evolution method with simple update, Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking the advantages of massive parallel computing, we can study the quantum systems with larger bond dimensions up to $D$=10 without resorting to any symmetry. Benchmark tests of the method on the $J_1$-$J_2$ model give impressive accuracy compared with exact results.
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