Efficient Strategies for Reducing Sampling Error in Quantum Krylov Subspace Diagonalization
arXiv:2409.02504 · doi:10.1039/D4DD00321G
Abstract
Within the realm of early fault-tolerant quantum computing (EFTQC), quantum Krylov subspace diagonalization (QKSD) has emerged as a promising quantum algorithm for the approximate Hamiltonian diagonalization via projection onto the quantum Krylov subspace. However, the algorithm often requires solving an ill-conditioned generalized eigenvalue problem (GEVP) involving erroneous matrix pairs, which can significantly distort the solution. Since EFTQC assumes limited-scale error correction, finite sampling error becomes a dominant source of error in these matrices. This work focuses on quantifying sampling errors during the measurement of matrix element in the projected Hamiltonian examining two measurement approaches based on the Hamiltonian decompositions: the linear combination of unitaries and diagonalizable fragments. To reduce sampling error within a fixed budget of quantum circuit repetitions, we propose two measurement strategies: the shifting technique and coefficient splitting. The shifting technique eliminates redundant Hamiltonian components that annihilate either the bra or ket states, while coefficient splitting optimizes the measurement of common terms across different circuits. Numerical experiments with electronic structures of small molecules demonstrate the effectiveness of these strategies, reducing sampling costs by a factor of 20-500.
17 pages, 3 figures
References in corpus (43)
- Quantum Computing in the NISQ era and beyond
- Variational Quantum Algorithms
- Barren plateaus in quantum neural network training landscapes
- Noisy intermediate-scale quantum (NISQ) algorithms
- Quantum computational chemistry
- Quantum Chemistry in the Age of Quantum Computing
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
- Logical quantum processor based on reconfigurable atom arrays
- The Variational Quantum Eigensolver: a review of methods and best practices
- Quantum information processing with superconducting circuits: a review
- Quantum algorithms for quantum chemistry and quantum materials science
- Demonstration of a small programmable quantum computer with atomic qubits
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Experimental ten-photon entanglement
- The Bravyi-Kitaev transformation for quantum computation of electronic structure
- Large-scale silicon quantum photonics implementing arbitrary two-qubit processing
- Computing with spin qubits at the surface code error threshold
- Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
- Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
- Demonstration of fault-tolerant universal quantum gate operations
- Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
- Effect of barren plateaus on gradient-free optimization
- Tapering off qubits to simulate fermionic Hamiltonians
- Efficient estimation of Pauli observables by derandomization
- Efficient quantum measurement of Pauli operators in the presence of finite sampling error
- Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
- Measurement reduction in variational quantum algorithms
- Neutral Atom Quantum Computing Hardware: Performance and End-User Perspective
- Early Fault-Tolerant Quantum Computing
- Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families
- Cryogenic setup for trapped ion quantum computing
- Exact and efficient Lanczos method on a quantum computer
- Quantum Filter Diagonalization: Quantum Eigendecomposition without Full Quantum Phase Estimation
- A theory of quantum subspace diagonalization
- Computing Ground State Properties with Early Fault-Tolerant Quantum Computers
- Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
- Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers
- Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver
- Improving quantum measurements by introducing "ghost" Pauli products
- Diagonalization of large many-body Hamiltonians on a quantum processor
- Sampling Error Analysis in Quantum Krylov Subspace Diagonalization
- Adaptive measurement strategy for quantum subspace methods