Resource-Optimized Fermionic Local-Hamiltonian Simulation on Quantum Computer for Quantum Chemistry

Abstract

The ability to simulate a fermionic system on a quantum computer is expected to revolutionize chemical engineering, materials design, nuclear physics, to name a few. Thus, optimizing the simulation circuits is of significance in harnessing the power of quantum computers. Here, we address this problem in two aspects. In the fault-tolerant regime, we optimize the $\rzgate$ and $\tgate$ gate counts along with the ancilla qubit counts required, assuming the use of a product-formula algorithm for implementation. We obtain a savings ratio of two in the gate counts and a savings ratio of eleven in the number of ancilla qubits required over the state of the art. In the pre-fault tolerant regime, we optimize the two-qubit gate counts, assuming the use of the variational quantum eigensolver (VQE) approach. Specific to the latter, we present a framework that enables bootstrapping the VQE progression towards the convergence of the ground-state energy of the fermionic system. This framework, based on perturbation theory, is capable of improving the energy estimate at each cycle of the VQE progression, by about a factor of three closer to the known ground-state energy compared to the standard VQE approach in the test-bed, classically-accessible system of the water molecule. The improved energy estimate in turn results in a commensurate level of savings of quantum resources, such as the number of qubits and quantum gates, required to be within a pre-specified tolerance from the known ground-state energy. We also explore a suite of generalized transformations of fermion to qubit operators and show that resource-requirement savings of up to more than $20\%$, in small instances, is possible.

References in corpus (30)

• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Fermionic quantum computation
• Hamiltonian Simulation by Qubitization
• Scalable Quantum Simulation of Molecular Energies
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Elucidating Reaction Mechanisms on Quantum Computers
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Toward the first quantum simulation with quantum speedup
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Cloud Quantum Computing of an Atomic Nucleus
• Gate count estimates for performing quantum chemistry on small quantum computers
• Halving the cost of quantum addition
• Automated optimization of large quantum circuits with continuous parameters
• Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
• On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimization
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Quantum algorithms to simulate many-body physics of correlated fermions
• Efficient synthesis of universal Repeat-Until-Success circuits
• Lowering qubit requirements for quantum simulations of fermionic systems
• Approximate Quantum Fourier Transform with $O(n\log (n))$ T gates
• Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families
• Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
• Use of global interactions in efficient quantum circuit constructions
• Low cost quantum circuits for classically intractable instances of the Hamiltonian dynamics simulation problem
• Toward convergence of effective field theory simulations on digital quantum computers

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