Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer

Delgado, Alain; Casares, Pablo Antonio Moreno; Reis, Roberto dos; Zini, Modjtaba Shokrian; Campos, Roberto; Hernández, Norge Cruz; Voigt, Arne-Christian; Lowe, Angus; Jahangiri, Soran; Martín-Delgado, M. A.; Mueller, Jonathan E.; Arrazola, Juan Miguel

doi:10.1103/physreva.106.032428

Cited by 25 publications

(6 citation statements)

References 148 publications

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“…Run time estimates for the qubitization-based phase estimation algorithm applied to some industrially relevant molecules (e.g., Li-ion battery compounds) have highlighted the need for further improvements to make it practically applicable in quantum chemistry contexts. − Reducing the computational and resource costs of quantum algorithms can be achieved by narrowing the spectral range while keeping its spectrum unchanged for the eigenstates of interest. The spectral range is defined as Δ E ≡ E max – E min , for E max(min) the maximum(minimum) eigenvalue of Ĥ .…”

Section: Introductionmentioning

confidence: 99%

Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries

Loaiza,

Izmaylov

2023

J. Chem. Theory Comput.

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Computational cost of energy estimation for molecular electronic Hamiltonians via quantum phase estimation (QPE) grows with the difference between the largest and smallest eigenvalues of the Hamiltonian. In this work, we propose a preprocessing procedure that reduces the norm of the Hamiltonian without changing its eigenspectrum for the target states of a particular symmetry. The new procedure, block-invariant symmetry shift (BLISS), builds an operator T̂ such that the cost of implementing is reduced compared to that of Ĥ, yet acts on the subspaces of interest the same way as Ĥ does. BLISS performance is demonstrated for a linear combination of unitaries (LCU)-based QPE approaches on a set of small molecules. Using the number of electrons as the symmetry specifying the target set of states, BLISS provided a factor of 2 reduction of 1-norm for several LCU decompositions compared to their unshifted versions.

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Section: Introductionmentioning

confidence: 99%

Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries

Loaiza,

Izmaylov

2023

J. Chem. Theory Comput.

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“…Several efforts have been made to use symmetries to reduce the number of qubits. – However, these methods are capable of reducing just a few number of qubits. Recent advancements allowed for further reduction of the circuit width by concatenating different VQE approaches to solve an effective Hamiltonian, using tensor-network methods, or by reverting back to first quantization approaches. – In this work, we will let the circuit width be dictated by the Fermion-qubit mapping, which is preferably local, in order to retain a close connection to the underlying orbital scheme.…”

Section: Introductionmentioning

confidence: 99%

Modular Cluster Circuits for the Variational Quantum Eigensolver

Ghasempouri,

Dueck,

De Baerdemacker

2023

J. Phys. Chem. A

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The variational quantum eigensolver algorithm recently became a popular method to compute the quantum chemical properties of molecules on noisy intermediate scale quantum (NISQ) devices. In order to avoid noise accumulation from the NISQ device in the quantum circuit, it is important to keep the so-called quantum depth of the circuit at a minimum, defined as the minimum number of quantum gates that must be operated sequentially. In the present work, we introduce a modular 2-qubit cluster circuit that allows for the design of a shallow-depth quantum circuit compared to previously proposed architectures without loss of chemical accuracy. Moreover, by virtue of the simplicity of the cluster circuit, it is possible to assign a valence bond chemical interpretation to the cluster circuit. The design was tested on the H2, (H2)2, and LiH molecules, as well as the finite-size transverse-field Ising model, as the latter provides additional insights into the construction of the circuit in a resonating valence bond picture.

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“…On the other hand, the resource requirements for quantum simulations are only subject to polynomial growth in many practical circumstances, as in the simulation of local Hamiltonians [3], and more particularly in spin chains [4]. Hence, quantum computers offer a natural paradigm for Hamilto-Oriel Kiss: oriel.kiss@cern.ch nian simulations, with numerous applications in nuclear [5][6][7] and condensed matter physics [8][9][10][11][12], quantum field theory [13][14][15] and quantum chemistry [16][17][18][19][20]. For instance, quantum simulations have been applied to the computation of energy levels via quantum phase estimation [21], chemical reaction rates predictions [22], correlation functions [8,9,23,24], neutrino oscillations [25,26] and scattering experiments [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Importance sampling for stochastic quantum simulations

Kiss

Grossi

Roggero

2023

Quantum

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Simulating many-body quantum systems is a promising task for quantum computers. However, the depth of most algorithms, such as product formulas, scales with the number of terms in the Hamiltonian, and can therefore be challenging to implement on near-term, as well as early fault-tolerant quantum devices. An efficient solution is given by the stochastic compilation protocol known as qDrift, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. In this work, we unify the qDrift protocol with importance sampling, allowing us to sample from arbitrary probability distributions, while controlling both the bias, as well as the statistical fluctuations. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Moreover, we incorporate recent work on composite channel and compute rigorous bounds on the bias and variance, showing how to choose the number of samples, experiments, and time steps for a given target accuracy. These results lead to a more efficient implementation of the qDrift protocol, both with and without the use of composite channels. Theoretical results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.

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Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer

Cited by 25 publications

References 148 publications

Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries

Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries

Modular Cluster Circuits for the Variational Quantum Eigensolver

Importance sampling for stochastic quantum simulations

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