Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction

Lee, Joonho; Berry, Dominic W.; Gidney, Craig; Huggins, William J.; McClean, Jarrod R.; Wiebe, Nathan; Babbush, Ryan

doi:10.1103/prxquantum.2.030305

Cited by 164 publications

(230 citation statements)

References 80 publications

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“…While this work has focused on the performance of Trotter methods, so-called post-Trotter methods [20,[62][63][64][65][66] are known to have superior asymptotic performance with respect to target error. These methods have also leveraged Hamiltonian factorizations to reduce costs [16][17][18]. Trotter methods often possess good constant prefactors in the runtime and require few additional ancilla qubits, compared to post-Trotter methods.…”

Section: Discussionmentioning

confidence: 99%

“…In this work, we introduce three factorized decompositions of the electronic structure Hamiltonian in a plane wave dual basis, and use these in conjunction with the fermionic seminorm to obtain tighter Trotter error bounds in practice. Our approach is inspired by prior work using low-rank decompositions to reduce the number of terms in a Hamiltonian and thereby reduce the gate complexity of quantum algorithms [13,[16][17][18]. However, our use of factorized decompositions is purely computational and optimized for tightest error bounds, with no corresponding change in the execution of the quantum algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian

McArdle

Campbell

2022

Phys. Rev. A

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian

McArdle

Campbell

2022

Phys. Rev. A

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“…The most straightforward way to reduce the complexity of the VQE algorithm is to find the smallest possible qubit representation of the studied Hamiltonian. Indeed, much effort today is focused on efficient encodings of fermionic Hamiltonians (see e.g., [57,58] and references therein), as getting rid of extra qubits (and operations on them) decreases noise and can avoid space limitations. To highlight the importance of finding minimal representations, we have chosen two equivalent variants of H 2 molecule Hamiltonian, one using 2 and another one using 4 qubits (see Section 2).…”

Section: Choice Of Hamiltonian and State-preparation Ansatzmentioning

confidence: 99%

The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry

et al. 2022

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New approaches into computational quantum chemistry can be developed through the use of quantum computing. While universal, fault-tolerant quantum computers are still not available, and we want to utilize today’s noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE)—an algorithm for calculating the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, and physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal method of running the hybrid classical-quantum optimization is to: (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but ensure a high final readout precision; (ii) emphasize efficient problem encoding and ansatz parametrization; and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently, it is quite difficult to perform trustworthy calculations of molecular energies.

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“…CNOT gates. Therefore a single Trotter step requires 8 3 n s (16n 2 s − 1) CNOT gates for the free Hamiltonian. However, the number of CNOT operations can be reduced to O(n 2 s ) using fermionic swap networks [94,95,116].…”

Section: Quantum Circuit For the One-body Operatorsmentioning

confidence: 99%

“…A great body of literature exists that shows that quantum computers can provide exponential advantages for certain ab initio electronic structure calculations [3][4][5][6][7][8]. The utility of quantum based devices stems from their ability to directly simulate the dynamics of the Coulomb Hamiltonian without making the approximations that are usually required to make their classical counterparts efficiently tractable.…”

Section: Introductionmentioning

confidence: 99%

Simulating Effective QED on Quantum Computers

Stetina

Ciavarella

et al. 2022

Quantum

Self Cite

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In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated in polynomial time under reasonable assumptions while properly treating all four components of the wavefunction of the fermionic field. In particular, we provide a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. We find that the number of T-gates needed to perform such simulations on a 3D lattice of ns sites scales at worst as O(ns3/ϵ)1+o(1) in the thermodynamic limit for position basis simulations and O(ns4+2/3/ϵ)1+o(1) in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of O~(ns2+2/3/ϵ) for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of O~(ns5+2/3/ϵ). We further provide concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than 1013 non-Clifford operations and also provide a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED which can provide a reasonable initial guess for the ground state. Finally, we estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.

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Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction

Cited by 164 publications

References 80 publications

Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian

Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian

The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry

Simulating Effective QED on Quantum Computers

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