The electronic complexity of the ground-state of the FeMo cofactor of nitrogenase as relevant to quantum simulations

Li, Zhendong; Li, Junhao; Dattani, Nikesh S.; Umrigar, C. J.; Chan, Garnet Kin‐Lic

doi:10.1063/1.5063376

Cited by 100 publications

(148 citation statements)

References 39 publications

Supporting

Mentioning

145

Contrasting

Order By: Relevance

“…; thus, we take λ = 36,042 a.u. For LLDUC [45], λT = 3,446 a.u., λV = 4,168 a.u. and the maximum value of λW is 20,746 a.u.…”

Section: Rwswt Orbitalsmentioning

confidence: 99%

“…In the case where we limit the number of ancilla qubits used, mostly using the system qubits as "dirty" ancilla, our algorithm can obtain chemical accuracy for FeMoco with about 2 × 10 13 Toffoli gates, using the active spaces of either Reiher, Wiebe, Svore, Wecker, and Troyer (RWSWT) [29] or Li, Li, Dattani, Umrigar, and Chan (LLDUC) [45]. If we allow a large number of ancilla then the number of Toffoli gates achieved with our most efficient approach is about 2 × 10 11 for the RWSWT orbitals, or 8 × 10 10 for the LLDUC orbitals.…”

Section: Introductionmentioning

confidence: 99%

“…Bottom:L (c) Vas a function of c. For RWSWT[29], we can safely truncate at c = 0.0002 a.u., which corresponds to L (c) V = 3,300,568. For LLDUC[45], we can safely truncate at c = 0.0001 a.u., which corresponds to L (c) V = 1,291,648.3. Use another ancilla in an equal superposition over 2 µ values where µ is the number of digits for keep.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization

Berry

Gidney

Motta

et al. 2019

Quantum

156

239

View full text Add to dashboard Cite

Recent work has dramatically reduced the gate complexity required to quantum simulate chemistry by using linear combinations of unitaries based methods to exploit structure in the plane wave basis Coulomb operator. Here, we show that one can achieve similar scaling even for arbitrary basis sets (which can be hundreds of times more compact than plane waves) by using qubitized quantum walks in a fashion that takes advantage of structure in the Coulomb operator, either by directly exploiting sparseness, or via a low rank tensor factorization. We provide circuits for several variants of our algorithm (which all improve over the scaling of prior methods) including one with O(N 3/2 λ) T complexity, where N is number of orbitals and λ is the 1-norm of the chemistry Hamiltonian. We deploy our algorithms to simulate the FeMoco molecule (relevant to Nitrogen fixation) and obtain circuits requiring about seven hundred times less surface code spacetime volume than prior quantum algorithms for this system, despite us using a larger and more accurate active space.algorithms. Today, the best-scaling quantum algorithms for chemistry in second quantization use plane waves; with either O(N 3 ) gate complexity (with small constant factors) [8, 9] or O(N 2 log N ) gate complexity (with large constant factors and more spatial complexity) [10].A major limitation to using plane waves in second quantization is that one needs a very large number of spin-orbitals to represent many molecular systems to chemical accuracy. The work of [11] suggests resolving this problem by simulating the plane wave Hamiltonian in first quantization to achieve O(N 1/3 η 8/3 ) gate complexity, where η is the number of electrons. With such low scaling in N , one might be able to use an extremely large plane wave basis. Unfortunately, the practicality of that algorithm is unclear because it has not been compiled to explicit circuits, and it is unclear how large the basis would need to be [10].The more obvious remedy to the low resolution of plane waves is to use a more compact basis. Indeed, the majority of proposals for the quantum simulation of chemistry focus on using very compact molecular orbitals. However, using molecular orbitals leads to complex Hamiltonians with coefficients defined in terms of integrals and O(N 4 ) distinct terms. As a consequence, the first quantum algorithms in this representation had gate complexity O(N 11 ) [12, 13]. Since then, a large community of researchers has worked to significantly reduce the cost of simulation in this representation through tighter bounds [13][14][15], better mappings between fermions and qubits [16][17][18][19][20], improved state preparation techniques [21][22][23][24], application of new time-evolution strategies [25][26][27], considerations of fault-tolerant overheads [28][29][30] and other representational and algorithmic insights [31][32][33][34][35][36].The lowest rigorous complexity of prior work on second quantized arbitrary basis chemistry simulation is either the O(N 5 ) scaling of [26], or th...

show abstract

“…; thus, we take λ = 36,042 a.u. For LLDUC [45], λT = 3,446 a.u., λV = 4,168 a.u. and the maximum value of λW is 20,746 a.u.…”

Section: Rwswt Orbitalsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization

Berry

Gidney

Motta

et al. 2019

Quantum

156

239

View full text Add to dashboard Cite

show abstract

“…Naturally, there is a wide range of molecular or materials problems that could be chosen, a small number of which are highlighted in Section II. One relevant factor to check when constructing a Hamiltonian benchmark problem is to verify that it is indeed difficult to simulate classically [330]. Ideally, there should be a way to maximally tune the "complexity" for classical simulation, which then defines a natural setting for demonstrating quantum supremacy.…”

Section: Benchmark Systemsmentioning

confidence: 99%

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

et al. 2020

Self Cite

View full text Add to dashboard Cite

As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus, it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman’s idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal-state simulation and analyze their strengths and weaknesses for future developments.

show abstract

“…Open shell multi-nuclear transition metal complexes are oen involved in enzymes as reactive centres. 36,37 Single molecule magnets have been extensively studied as molecular memory devices. 38 To disclose their electronic structures, sophisticated ab initio quantum chemical calculations are powerful and essential tools.…”

Section: Introductionmentioning

confidence: 99%

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

et al. 2021

View full text Add to dashboard Cite

show abstract

The electronic complexity of the ground-state of the FeMo cofactor of nitrogenase as relevant to quantum simulations

Cited by 100 publications

References 39 publications

Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization

Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization

Quantum Algorithms for Quantum Chemistry and Quantum Materials Science

A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

Contact Info

Product

Resources

About