Computing Ground State Properties with Early Fault-Tolerant Quantum Computers

Abstract

Significant effort in applied quantum computing has been devoted to the problem of ground state energy estimation for molecules and materials. Yet, for many applications of practical value, additional properties of the ground state must be estimated. These include Green's functions used to compute electron transport in materials and the one-particle reduced density matrices used to compute electric dipoles of molecules. In this paper, we propose a quantum-classical hybrid algorithm to efficiently estimate such ground state properties with high accuracy using low-depth quantum circuits. We provide an analysis of various costs (circuit repetitions, maximal evolution time, and expected total runtime) as a function of target accuracy, spectral gap, and initial ground state overlap. This algorithm suggests a concrete approach to using early fault tolerant quantum computers for carrying out industry-relevant molecular and materials calculations.

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Cited by in corpus (35)

• Early Fault-Tolerant Quantum Computing
• Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation
• Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision
• On low-depth algorithms for quantum phase estimation
• Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers
• Rapid initial state preparation for the quantum simulation of strongly correlated molecules
• Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method
• Qubit-Efficient Randomized Quantum Algorithms for Linear Algebra
• State Preparation Boosters for Early Fault-Tolerant Quantum Computation
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Certified algorithms for equilibrium states of local quantum Hamiltonians
• Fault-tolerant quantum computation of molecular observables
• Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer
• Quantum Gaussian filter for exploring ground-state properties
• Modeling the Performance of Early Fault-Tolerant Quantum Algorithms
• Simple and high-precision Hamiltonian simulation by compensating Trotter error with linear combination of unitary operations
• Option pricing under stochastic volatility on a quantum computer
• On proving the robustness of algorithms for early fault-tolerant quantum computers
• Sequential optimal selection of a single-qubit gate and its relation to barren plateau in parameterized quantum circuits
• TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry
• Virtual quantum error detection
• Efficient Strategies for Reducing Sampling Error in Quantum Krylov Subspace Diagonalization
• Efficient ground-state energy estimation and certification on early fault-tolerant quantum computers
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories
• Error mitigation and circuit division for early fault-tolerant quantum phase estimation
• Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians
• Double-bracket algorithm for quantum signal processing without post-selection
• Measuring Correlation and Entanglement between Molecular Orbitals on a Trapped-Ion Quantum Computer
• Stabilizer configuration interaction: Finding molecular subspaces with error detection properties
• High-precision and low-depth quantum algorithm design for eigenstate problems
• Towards Practical Quantum Phase Estimation: A Modular, Scalable, and Adaptive Approach
• Arbitrary Ground State Observables from Quantum Computed Moments
• Classical post-processing approach for quantum amplitude estimation
• Calculating potential energy surfaces with quantum computers by measuring only the density along adiabatic transitions
• Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics