Early fault-tolerant simulations of the Hubbard model

Campbell, Earl T.

doi:10.48550/arxiv.2012.09238

Cited by 3 publications

(7 citation statements)

References 38 publications

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“…2. For comparison, we plot the resource estimates for other algorithms, such as: simulation of the Fermi-Hubbard model [60]; of crystalline materials [61]; of FeMoco [14]; and breaking RSA encryption [26].…”

Section: Fast Injection Of Distilled Magic Statesmentioning

confidence: 99%

“…We assume a linear data block with two multi-level 15-to-1 factories as depicted in Fig.2. For comparison, we plot the resource estimates for other algorithms, such as: simulation of the Fermi-Hubbard model[60]; of crystalline materials[61]; of FeMoco[14]; and breaking RSA encryption[26]. Where necessary, resource estimates for quantum chemistry algorithms have been amended to produce eigenenergies to within chemical accuracy.…”

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confidence: 99%

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Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules

Kim¹,

Lee²,

Liu³

et al. 2021

Preprint

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In this article, we estimate the cost of simulating electrolyte molecules in Li-ion batteries on a fault-tolerant quantum computer, focusing on the molecules that can provide practical solutions to industrially relevant problems. Our resource estimate is based on the fusion-based quantum computing scheme using photons, but can be modified easily to the more conventional gate-based model as well. We find the cost of the magic state factory to constitute no more than ∼ 2% of the total footprint of the quantum computer, which suggests that it is more advantageous to use algorithms that consume many magic states at the same time. We suggest architectural and algorithmic changes that can accommodate such a capability. On the architecture side, we propose a method to consume multiple magic states at the same time, which can potentially lead to an order of magnitude reduction in the overall computation time without incurring additional expense in the footprint. This is based on a fault-tolerant measurement of a Pauli product operator in constant time, which may be useful in other contexts as well. We also introduce a method to implement an arbitrary fermionic basis change in logarithmic depth, which may be of independent interest. * IK's contribution was carried out while he was affiliated with PsiQuantum. IK's current affiliation is the

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Section: Fast Injection Of Distilled Magic Statesmentioning

confidence: 99%

mentioning

confidence: 99%

Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules

Kim¹,

Lee²,

Liu³

et al. 2021

Preprint

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“…( 7), which all have the same rotation angle. Grouping together commuting gates with the same rotation angle allows use of Hamming weight phasing [8,43,44], enabling single-qubit Z rotations to be implemented with one Toffoli gate in the limit of large commuting sets of gates. In practice, one finds that about 20-30 ancillae suffice to (approximately) achieve this this limit.…”

Section: Minimising the Total Complexitymentioning

confidence: 99%

“…The cost of phase estimation-statistical or standardtypically depends on the Hamiltonian sparsity L, the number of terms in the Hamiltonian when decomposed in a suitable basis, such as the Pauli basis. Simple schemes based on implementing U using Trotter formulae have O(L) gate complexity [5][6][7][8][9]. This can be prohibitive for the electronic structure problem in chemistry and materials science, where we typically have L = O(N 4 ) for an Norbital problem [10].…”

Section: Introductionmentioning

confidence: 99%

A randomized quantum algorithm for statistical phase estimation

Wan,

Berta,

Campbell

2021

Preprint

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Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent of the number of terms L in the Hamiltonian. Second, unlike previous L-independent approaches, such as those based on qDRIFT, all sources of error in our algorithm can be suppressed by collecting more data samples, without increasing the circuit depth.

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“…Refs. [11,27] carried out careful resource cost estimation of performing QPE for the Hubbard model using surface code to perform quantum error correction. These are to our best knowledge the only works that addressed ground state energy estimation in the context of early fault-tolerant quantum computers.…”

Section: Introductionmentioning

confidence: 99%

Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers

Lin,

Tong

2021

Preprint

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Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit depth, as well as the ability to perform inverse quantum Fourier transform, making it expensive to implement on an early fault-tolerant quantum computer. We propose an alternative method to estimate the ground state energy of a Hamiltonian with Heisenberg-limited precision scaling, which employs a simple quantum circuit with one ancilla qubit, and a classical post-processing procedure. Besides the ground state energy, our algorithm also produces an approximate cumulative distribution function of the spectral measure, which can be used to compute other spectral properties of the Hamiltonian.

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Early fault-tolerant simulations of the Hubbard model

Cited by 3 publications

References 38 publications

Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules

Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules

A randomized quantum algorithm for statistical phase estimation

Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers

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