# Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction

@article{Lee2021EvenME, title={Even More Efficient Quantum Computations of Chemistry Through Tensor Hypercontraction}, author={Joonho Lee and Dominic W. Berry and Craig Gidney and William J. Huggins and Jarrod R. McClean and Nathan Wiebe and Ryan Babbush}, journal={PRX Quantum}, year={2021} }

We describe quantum circuits with only $\widetilde{\cal O}(N)$ Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of $N$ arbitrary (e.g., molecular) orbitals. With ${\cal O}(\lambda / \epsilon)$ repetitions of these circuits one can use phase estimation to sample in the molecular eigenbasis, where $\lambda$ is the 1-norm of Hamiltonian coefficients and $\epsilon$ is the target precision. This is the lowest complexity that has been shown for quantum…

## 73 Citations

### The impact of hardware specifications on reaching quantum advantage in the fault tolerant regime

- Computer ScienceAVS Quantum Science
- 2022

It is shown that in certain situations, architectures with considerably slower code cycle times will still be able to reach desirable run times, provided enough physical qubits are available.

### Error-resilient Monte Carlo quantum simulation of imaginary time

- Physics, Computer Science
- 2021

This work combines quantum Monte Carlo with quantum computing and proposes an algorithm for simulating the imaginary-time evolution and solving the ground-state problem and shows that Monte Carlo quantum simulation is promising even without a fully fault-tolerant quantum computer.

### Quantum Computation for Periodic Solids in Second Quantization

- Computer Science, Physics
- 2022

It is shown that ground-state energy estimation of Hamiltonians approximated using 200–900 spin orbitals requires ca.

### Halving the cost of quantum multiplexed rotations

- Physics
- 2021

We improve the number of T gates needed for a b-bit approximation of a multiplexed quantum gate with c controls applying n singlequbit arbitrary phase rotations from 4nb + O( √ cnb) to 2nb+O( √ cnb),…

### Reliably assessing the electronic structure of cytochrome P450 on today’s classical computers and tomorrow’s quantum computers

- PhysicsProceedings of the National Academy of Sciences of the United States of America
- 2022

Significance Chemical simulation is one of the most promising applications for future quantum computers. It is thought that quantum computers may enable accurate simulation for complex molecules that…

### TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry

- PhysicsQuantum
- 2022

The basis or the Fermionic encoding seems to be the most obvious: in the case of qDRIFT and Random Hamiltonian because they are the simplest choice, while in the Hybridized method, it inherits the plane wave structure from the Interaction Picture.

### On the complexity of implementing Trotter steps

- Computer ScienceArXiv
- 2022

It is shown that power-law Hamiltonians can be simulated with gate complexity nearly linear in the spacetime volume for all α ≥ 1 and that Trotter steps can be implemented more efficiently when certain blocks of Hamiltonian coefficients exhibit low-rank properties.

### Space-time optimized table lookup

- Computer Science, Physics
- 2022

A space-time optimized circuit for the table lookup subroutine from lattice-surgery surface code primitives respecting 2D grid connectivity is described, allowing the presented circuit to be used for applications ranging from cryptography to quantum chemistry.

### Q3DE: A fault-tolerant quantum computer architecture for multi-bit burst errors by cosmic rays

- Computer Science2022 55th IEEE/ACM International Symposium on Microarchitecture (MICRO)
- 2022

QC architecture Q3DE is proposed, which enhances the tolerance to multi-bit burst errors by cosmic rays with moderate changes and overhead and significantly relaxes the requirement of qubit density and qubit chip size to realize FTQC.

### Purification-based quantum error mitigation of pair-correlated electron simulations

- Physics
- 2022

An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error…

## References

SHOWING 1-10 OF 78 REFERENCES

### Emergence and control of complex behaviors in driven systems of interacting qubits with dissipation

- Physicsnpj Quantum Information
- 2021

Progress in the creation of large-scale, artificial quantum coherent structures demands the investigation of their nonequilibrium dynamics when strong interactions, even between remote parts, are…

### A linear scaling hierarchical block low-rank representation of the electron repulsion integral tensor.

- Computer ScienceThe Journal of chemical physics
- 2020

The H2 hierarchical matrix representation is applied to the ERI tensor with Gaussian basis sets to rapidly calculate the Coulomb matrices in Hartree-Fock and density functional theory calculations and the execution time and storage requirements are compared.

### Near-optimal ground state preparation

- Computer ScienceQuantum
- 2020

A hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to the current state-of-the-art algorithm proposed in [Ge et al. 2019].

### Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction.

- PhysicsJournal of chemical theory and computation
- 2020

The Cholesky-based method provides an alternative and possible more numerically stable method for performing the least-squares fit and is able to generate unique grids tailored to different charge distributions, for example the (ab|, (ai|, and (ij| distributions that arise in the molecular orbital integrals).

### Discontinuous Galerkin discretization for quantum simulation of chemistry

- Computer ScienceNew Journal of Physics
- 2020

A way to interpolate between the two regimes in a systematic and controllable manner, such that the number of functions is minimized while maintaining a block-diagonal structure of the two-body operator and desirable properties of an original, primitive basis is introduced.

### Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers

- Computer Science
- 2019

This work presents a measurement strategy based on a low-rank factorization of the two-electron integral tensor that provides a cubic reduction in term groupings over prior state-of-the-art and enables measurement times three orders of magnitude smaller than those suggested by commonly referenced bounds for the largest systems.

### SciPy 1.0: fundamental algorithms for scientific computing in Python

- Computer ScienceNature Methods
- 2020

An overview of the capabilities and development practices of SciPy 1.0 is provided and some recent technical developments are highlighted.

### Time-dependent Hamiltonian simulation with $L^1$-norm scaling

- PhysicsQuantum
- 2020

Two new techniques are introduced: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schrodinger equation that is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation.

### Magic State Distillation: Not as Costly as You Think

- PhysicsQuantum
- 2019

By writing distillation circuits in a form that separates qubits that are capable of error detection from those that are not, most logical qubits used for distillation can be encoded at a very low code distance, which significantly reduces the space-time cost of distillation, as well as the number of qubits.

### Elements of large-sample theory

- Economics
- 1998

This introductory book on the most useful parts of large-sample theory is designed to be accessible to scientists outside statistics and certainly to master’s-level statistics students who ignore…