Abstract
We develop holographic quantum simulation techniques to prepare correlated electronic ground states in quantum matrix-product-state (QMPS) form, using far fewer qubits than the number of orbitals represented. Our approach starts with a holographic technique to prepare a compressed approximation to electronic mean-field ground states, known as fermionic Gaussian matrix-product states (GMPSs), with a polynomial reduction in qubit and (in select cases gate) resources compared to existing techniques. Correlations are then introduced by augmenting the GMPS circuits in a variational technique, which we denote GMPS+X. We demonstrate this approach on Quantinuum’s System Model H1 trapped-ion quantum processor for one-dimensional (1D) models of correlated metal and Mott-insulating states. Focusing on the 1D Fermi-Hubbard chain as a benchmark, we show that GMPS+X methods faithfully capture the physics of correlated electron states, including Mott insulators and correlated Luttinger liquid metals, using considerably fewer parameters than problem-agnostic variational circuits.
3 More- Received 10 February 2022
- Revised 10 June 2022
- Accepted 5 July 2022
DOI:https://doi.org/10.1103/PRXQuantum.3.030317
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum computers are expected to make a transformative impact on materials science and chemistry by enabling the accurate simulation of complex material properties, molecules, and chemical reactions that lie beyond the reach of even the most powerful conventional supercomputers. However, existing quantum processors have limited memory and are susceptible to noise, creating a large gap between the long-term potential for quantum computation and the capabilities of existing quantum technology.
In this work, we introduce a method to approximately compute the properties of interacting many-electron models, relevant for many materials and chemistry, using an efficient compressed representation called a quantum tensor network. This method both greatly reduces the quantum memory size required to simulate complex materials and molecules, and it also shortens the computation time (reducing the chance for noise to cause errors). Our approach begins by designing quantum circuits to implement an approximate representation of the ground state that can be efficiently calculated using a classical computer. Then we variationally optimize a quantum circuit to build in quantum correlations on top of this classical approximation. A key advantage of this two-step sequence is that it greatly reduces the number of free parameters that must be optimized in the quantum circuit—a key bottleneck for variational quantum algorithms.
We experimentally implement this technique on Quantinuum’s trapped-ion quantum processor, and we benchmark our approach against exact solutions of the Fermi-Hubbard chain—a paradigmatic model of interacting electron physics and quantum magnetism. The efficiency of our approach enables quantitatively accurate calculation of this model using only half as many qubits as electron orbitals being simulated, highlighting the efficiency of the quantum tensor network methods. We also show, through simulations, how these results can be extended to capture two-dimensional and three-dimensional models and to capture thermal properties and phenomena such as superconductivity.