Almost optimal measurement scheduling of molecular Hamiltonian via finite projective plane

Abstract

We propose an efficient and almost optimal scheme for measuring molecular Hamiltonians in quantum chemistry on quantum computers, which requires $2N^2$ distinct measurements in the leading order with $N$ being the number of molecular orbitals. It achieves the state-of-the-art by improving a previous proposal by Bonet-Monroig et al. [Phys. Rev. X 10, 031064 (2020)] which exhibits $\frac{10}{3}{N}^2$ scaling in the leading order. We develop a novel method based on a finite projective plane to construct sets of simultaneously-measurable operators contained in molecular Hamiltonians. Each measurement only requires a depth-$O(N)$ circuit consisting of $O(N^2)$ one- and two-qubit gates under the Jordan-Wigner and parity mapping, assuming the linear connectivity of qubits on quantum hardwares. Because evaluating expectation values of molecular Hamiltonians is one of the major bottlenecks in the applications of quantum devices to quantum chemistry, our finding is expected to accelerate such applications.

arXiv comment20 pages, 6 figures

References in corpus (34)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Improved Simulation of Stabilizer Circuits
• Quantum Chemistry in the Age of Quantum Computing
• Quantum Algorithms Revisited
• Recent developments in the PySCF program package
• The Variational Quantum Eigensolver: a review of methods and best practices
• Fermionic quantum computation
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Efficient quantum measurement of Pauli operators in the presence of finite sampling error
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
• Orbital optimized unitary coupled cluster theory for quantum computer
• Measurement reduction in variational quantum algorithms
• Lowering qubit requirements for quantum simulations of fermionic systems
• Operator Locality in Quantum Simulation of Fermionic Models
• Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States
• Efficient evaluation of quantum observables using entangled measurements
• Cartan sub-algebra approach to efficient measurements of quantum observables
• Calculating transition amplitudes by variational quantum deflation
• Efficient quantum computation of molecular forces and other energy gradients
• Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation Values
• Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver
• Improving quantum measurements by introducing "ghost" Pauli products
• Quantum expectation-value estimation by computational basis sampling
• Perturbation theory with quantum signal processing

Cited by in corpus (2)

• Accelerated variational quantum eigensolver with joint Bell measurement
• A quantum eigenvalue solver based on tensor networks