[Paper Review] Ground-state energy estimation of the water molecule on a trapped ion quantum computer

Yunseong Nam, Jwo-Sy Chen+24 more|arXiv (Cornell University)|Feb 26, 2019

Quantum Computing Algorithms and ArchitectureComputer Science43 references34 citations

TL;DR

The paper demonstrates a co-designed variational quantum eigensolver on a trapped-ion quantum computer to estimate the ground-state energy of H2O, achieving chemical accuracy for the first three beyond-HF corrections without error mitigation.

ABSTRACT

Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly-interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here, we describe a scalable co-design framework for solving chemistry problems on a trapped ion quantum computer, and apply it to compute the ground-state energy of the water molecule. The robust operation of the trapped ion quantum computer yields energy estimates with errors approaching the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics.

Motivation & Objective

• Motivate quantum chemistry as a prime near-term application for quantum computers and define chemical accuracy as ~1.6e-3 Ha.
• Develop a scalable co-design framework optimizing quantum circuits for trapped-ion hardware.
• Demonstrate VQE with UCC ansatz for H2O and evaluate first beyond-HF correction terms.
• Quantify resource requirements (qubits, entangling gates) to reach chemical accuracy.
• Show experimentally that hardware-specific optimizations yield results approaching FCI within chemical accuracy.

Proposed method

• Formulate molecular Hamiltonian via Born-Oppenheimer and second-quantized representation; map to qubits with Jordan-Wigner transformation.
• Use unitary coupled-cluster ansatz with one Trotter step to prepare trial states.
• Partition excitation terms into bosonic and non-bosonic classes and implement with tailored circuits.
• Exploit all-to-all trapped-ion connectivity to minimize SWAP overhead in entangling gates.
• Optimize circuit by representing bosonic excitations with minimal gate sets (XX gates) where possible.
• Characterize SPAM and gate errors; perform bootstrapped uncertainty estimation without error mitigation.

Experimental results

Research questions

• RQ1 Can a trapped-ion quantum computer execute a VQE with a UCC ansatz to approach the full configuration-interaction energy for H2O within chemical accuracy?
• RQ2 How many significant determinants (terms) are needed in the ansatz to reach chemical accuracy, and what are the associated qubit and gate counts?
• RQ3 What hardware-aware circuit optimizations best leverage trapped-ion all-to-all connectivity to minimize entangling gates while preserving accuracy?
• RQ4 How do bosonic versus non-bosonic excitation terms contribute to convergence towards the FCI energy in this system?

Key findings

• Experimentally measured HF+1, HF+2, and HF+3 energies are -74.977(1) Ha, -74.979(2) Ha, and -74.985(5) Ha respectively.
• Chemical accuracy is achieved for the full Hamiltonian with HF+17 terms using 11 qubits and 143 entangling gates (89 CNOTs, 54 small-angle XX gates).
• A reduced Hamiltonian ignoring the innermost MO and a single bosonic determinant reaches within 2.1 mHa of the FCI ground state at HF+16 terms with 10 qubits and 140 entangling gates.
• In-silico VQE simulations show the ground-state energy converging toward the FCI value as more terms are added, reaching chemical accuracy with 17+ terms.
• Experimental results for HF+1 and HF+2 show energies -74.977(1) Ha and -74.979(2) Ha, respectively, with bootstrapped uncertainty.
• Resource-efficient circuit representations (bosonic excitations and optimized eight-term XX-based subcircuits) enable feasible gate counts on near-term trapped-ion hardware.