Simulating chemical systems on quantum computers has been limited to a few electrons in a minimal basis. We demonstrate experimentally that the virtual quantum subspace expansion [Phys. Rev. X 10, 011004 (2020)] can achieve full basis accuracy for hydrogen and lithium dimers, comparable to simulations requiring twenty or more qubits. We developed an approach to minimize the impact of experimental noise on the stability of the generalized eigenvalue problem, a crucial component of the quantum algorithm. In addition, we were able to obtain an accurate potential energy curve for the nitrogen dimer in a quantum simulation on a classical computer.
Optimizing Subspace Expansion in Quantum Chemistry through Operator Selection and Reference State Choice
Institute of Engineering Thermodynamics, German Aerospace Center (DLR)（德国航空航天中心工程热力学研究所）；Helmholtz Institute Ulm（乌尔姆亥姆霍兹研究所）；HQS Quantum Simulations GmbH（HQS量子模拟有限公司）；University of Ulm（乌尔姆大学）
The impossibility of experiencing the molecular world with our senses hampers teaching and understanding chemistry because very abstract concepts (such as atoms, chemical bonds, molecular structure, reactivity) are required for this process. Virtual reality, especially when based on explicit physical modeling (potentially in real time), offers a solution to this dilemma. Chemistry teaching can make use of advanced technologies such as virtual-reality frameworks and haptic devices. We show how an immersive learning setting could be applied to help students understand the core concepts of typica…
Quantum computing, an innovative computing system carrying prominent processing rate, is meant to be the solutions to problems in many fields. Among these realms, the most intuitive application is to help chemical researchers correctly de-scribe strong correlation and complex systems, which are the great challenge in current chemistry simulation. In this paper, we will present a standalone quantum simulation tool for chemistry, ChemiQ, which is designed to assist people carry out chemical research or molecular calculation on real or virtual quantum computers. Under the idea of modular programm…
Symmetry adapted bases in quantum chemistry and bases adapted to quantum information share a common characteristics: both of them are constructed from subspaces of the representation space of the group SO(3) or its double group (i.e., spinor group) SU(2). We exploit this fact for generating spin bases of relevance for quantum systems with cyclic symmetry and equally well for quantum information and quantum computation. Our approach is based on the use of generalized Pauli matrices arising from a polar decomposition of SU(2). This approach leads to a complete solution for the construction of mu…
Quantum computer provides new opportunities for quantum chemistry. In this article, we present a versatile, extensible, and efficient software package, named Q$^2$Chemistry, for developing quantum algorithms and quantum inspired classical algorithms in the field of quantum chemistry. In Q$^2$Chemistry, wave function and Hamiltonian can be conveniently mapped into the qubit space, then quantum circuits can be generated according to a specific quantum algorithm already implemented in the package or newly developed by the users. The generated circuits can be dispatched to either a physical quantu…
Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD algorithms have focused on solving the eigenpair problem for ground, excited-state, and thermal observable estimation, there has been a lot less work in considering QSD algorithms for the problem of quantum dynamical simulation. In this work, we propose several quantum Krylov fast-forwarding (QKFF) algorithms capable of predicting long-time dynamics well beyo…
Universal gate sets for quantum computing have been known for decades, yet no universal gate set has been proposed for particle-conserving unitaries, which are the operations of interest in quantum chemistry. In this work, we show that controlled single-excitation gates in the form of Givens rotations are universal for particle-conserving unitaries. Single-excitation gates describe an arbitrary $U(2)$ rotation on the two-qubit subspace spanned by the states $|01\rangle, |10\rangle$, while leaving other states unchanged -- a transformation that is analogous to a single-qubit rotation on a dual-…
Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm for estimating the ground and excited-state energies of a quantum many-body system. While QKSD algorithms typically rely on using the Hadamard test for estimating Krylov subspace matrix elements of the form, $\langle ϕ_i|e^{-i\hat{H}τ}|ϕ_j \rangle$, the associated quantum circuits require an ancilla qubit with controlled multi-qubit gates that can be quite costly for near-term quantum hardware. In this work, we show that a wide class of Hamiltonians re…
In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schrödinger equation for molecules in the Born--Oppenheimer approximation. In this article, we analyze the tailored coupled-cluster method (TCC), one particular and promising method for treating molecular electronic-structure problems with static correlation. The TCC method combines the single-reference coupled-cluster (CC) approach with an approximate reference calculation in a subspace [complete active space (CAS)] of the considered Hilbert space that covers the static cor…
We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum chemistry and condensed matter physics. In both of these contexts, a strongly correlated quantum region of the extended system is isolated and self-consistently coupled to its environment via the sampling of reduced density matrices. We analyze the viability of current generation quantum devices to provide the required fidelity of these objects for a robust and e…
Subspace-Search Variational Quantum Eigen solver (SSVQE) is a searching method of multiple states and relies on the unitarity of transformations to ensure the orthogonality of output states for multiple states. Therefore, this method is thought to be a promising method for quantum chemistry because ordinary Variational Quantum Eigen solver (VQE) can only calculate the excited states step by step from the ground state based on Variational Quantum deflation (VQD). We compare the advantage of VQE, SSVQE with/without the constraint term and/or Tabu search term, which is added by the Lagrange multi…
Quantum chemistry with provable convergence via randomized sample-based Krylov quantum diagonalization
IBM Quantum, IBM Research Europe - Zurich（IBM量子，IBM欧洲苏黎世研究实验室）；Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；The Hartree Centre, STFC（哈特里中心，STFC）；Yusuf Hamied Department of Chemistry, University of Cambridge（剑桥大学尤素福·哈米德化学系）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；IBM T.J. Watson Research Center（IBM托马斯·J·沃森研究中心）
A cavity QED implementation of the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with nitrogen-vacancy centers coupled commonly to the whispering-gallery mode of a microsphere cavity, where a universal set of quantum gates can be realized on the qubits. In our implementation, with the assistant of the appropriate driving fields, the quantum evolution is insensitive to the cavity field state, which is only virtually excited. The implemented non-adiabatic holonomies, utilizing optical transitions in the Λ type of three-level configuration of the nitrogen-v…
Energy Landscape Plummeting in Variational Quantum Eigensolver: Subspace Optimization, Non-iterative Corrections and Generator-informed Initialization for Improved Quantum Efficiency
Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilise even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Varia…
Crossing the 12,000-atom barrier with heterogeneous quantum-classical supercomputing: quantum chemistry of protein-ligand complexes
Cleveland Clinic Foundation（克利夫兰诊所基金会）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；IBM Quantum, IBM Research – Tokyo（IBM量子，IBM研究-东京）；IBM Quantum, T.J. Watson Research Center（IBM量子，T.J.沃森研究中心）
Molecular Ground State Simulation by Subspace Restriction and Hund's Rule
National Cheng Kung University（国立成功大学）；Math Division, National Center for Theoretical Sciences, National Taiwan University（台湾大学国家理论科学中心数学组）；Hon Hai Research Institute（鸿海研究院）；Department of Mechanical Engineering, City University of Hong Kong（香港城市大学机械工程系）；Graduate School of Advanced Technology, National Taiwan University（台湾大学先进科技研究生院）；Physics Division, National Center for Theoretical Sciences, National Taiwan University（台湾大学国家理论科学中心物理组）；Department of Material Science and Engineering, City University of Hong Kong（香港城市大学材料科学与工程系）
Quantum Algorithm for Low-Energy Effective Hamiltonians and Subspace Eigenvalue Problem
University of Southern California（南加州大学）；Hon Hai (Foxconn) Quantum Computing Research Center（鸿海（富士康）量子计算研究中心）；Institute of Physics, Academia Sinica（中央研究院物理研究所）；National Taiwan University（台湾大学）
Quantum computers have the potential to simulate chemical systems beyond the capability of classical computers. Recent developments in hybrid quantum-classical approaches enable the determinations of the ground or low energy states of molecular systems. Here, we extend near-term quantum simulations of chemistry to time-dependent processes by simulating energy transfer in organic semiconducting molecules. We developed a multi-scale modeling workflow that combines conventional molecular dynamics and quantum chemistry simulations with hybrid variational quantum algorithm to compute the exciton dy…
The method of increments and frozen natural orbital (MI-FNO) framework is introduced to help expedite the application of noisy, intermediate-scale quantum~(NISQ) devices for quantum chemistry simulations. The MI-FNO framework provides a systematic reduction of the occupied and virtual orbital spaces for quantum chemistry simulations. The correlation energies of the resulting increments from the MI-FNO reduction can then be solved by various algorithms, including quantum algorithms such as the phase estimation algorithm and the variational quantum eigensolver (VQE). The unitary coupled-cluster …
The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that r…
The complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where non-perturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrödinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering …
