# Compilation by stochastic Hamiltonian sparsification

@article{Ouyang2020CompilationBS,
title={Compilation by stochastic Hamiltonian sparsification},
author={Yingkai Ouyang and David R. White and Earl T. Campbell},
journal={Quantum},
year={2020},
volume={4},
pages={235}
}
• Published 14 October 2019
• Computer Science
• Quantum
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the effect of each term during time-evolution is individually computed. For many physical systems, the Hamiltonian has a large number of terms, constraining the scalability of established simulation methods. To address this limitation we introduce a new scheme…

## Figures from this paper

### Simulating time evolution on distributed quantum computers

• Physics
• 2022
We study a variation of the Trotter-Suzuki decomposition, in which a Hamiltonian exponential is approximated by an ordered product of two-qubit operator exponentials such that the Trotter step size

### Variational Hamiltonian simulation for translational invariant systems via classical pre-processing

• Computer Science
• 2021
A variational algorithm which uses solutions of classical optimizations to predict eﬃcient quantum circuits for time evolution of translationally invariant quantum systems, which can improve upon the Trotter-Suzuki accuracy by several orders of magnitude.

### Randomizing multi-product formulas for Hamiltonian simulation

• Computer Science
Quantum
• 2022
This work proposes a framework of randomized sampling that is expected to be useful for programmable quantum simulators and presents two new multi-product formula algorithms tailored to it, and proves rigorous performance bounds as well as the concentration of the randomized sampling procedure.

### Classical Variational Optimization of Gate Sequences for Time Evolution of Translational Invariant Quantum Systems

• Computer Science
• 2021
A variational algorithm which uses solutions of classical optimizations to predict efficient quantum circuits for time evolution of translationally invariant quantum systems, and can improve upon the Trotter-Suzuki accuracy by several orders of magnitude.

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

• Physics
Quantum
• 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.

### Quantum simulation via randomized product formulas: Low gate complexity with accuracy guarantees

• Computer Science
• 2020
This work provides a comprehensive analysis of a single realization of the random product formula produced by qDRIFT, and proves that a typical realizing of the randomized product formula approximates the ideal unitary evolution up to a small diamond-norm error.

### Concentration for Random Product Formulas

• Computer Science
PRX Quantum
• 2021
This work aims to understand the origin of this speed-up by comprehensively analyzing a single realization of the random product formula produced by qDRIFT, and proves that a typical realizing of the randomized product formula approximates the ideal unitary evolution up to a small diamond-norm error.

### 2QAN: a quantum compiler for 2-local qubit hamiltonian simulation algorithms

• Computer Science
ISCA
• 2022
This work develops a compiler, named 2QAN, to optimize quantum circuits for 2-local qubit Hamiltonian simulation problems, a framework which includes the important quantum approximate optimization algorithm (QAOA).

### Nearly tight Trotterization of interacting electrons

• Physics
Quantum
• 2021
It suffices to use O gates to simulate electronic structure in the plane-wave basis with $n$ spin orbitals and $\eta$ electrons up to a negligible factor, improving the best previous result in second quantization while outperforming the first-quantized simulation when $n=\mathcal{O}\left(\eta^2\right)$.

### Simulating quantum chemistry in the seniority-zero space on qubit-based quantum computers

• Computer Science
• 2021
It is shown that using the freed-up quantum resources for increasing the basis set can lead to more accurate results and reductions in the necessary number of quantum computing runs by several orders of magnitude, already for a simple system like lithium hydride.

## References

SHOWING 1-10 OF 49 REFERENCES

### Random Compiler for Fast Hamiltonian Simulation.

A randomized compiler for Hamiltonian simulation where gate probabilities are proportional to the strength of a corresponding term in the Hamiltonian, especially suited to electronic structure Hamiltonians relevant to quantum chemistry.

### Optimal Hamiltonian Simulation by Quantum Signal Processing.

• Physics
Physical review letters
• 2017
It is argued that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation.

### Phase estimation with randomized Hamiltonians

• Physics
• 2019
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an

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

• Physics
Quantum
• 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.

### Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

• Computer Science
• 2007
We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H.

### Exponential improvement in precision for simulating sparse Hamiltonians

• Computer Science
Forum of Mathematics, Sigma
• 2017
The algorithm is based on a significantly improved simulation of the continuous- and fractional- query models using discrete quantum queries, showing that the former models are not much more powerful than the discrete model even for very small error.

### Simulation of electronic structure Hamiltonians using quantum computers

• Physics
• 2011
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However,

### On the Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation

• Computer Science
• 2014
It is argued that chemical properties, such as the maximum nuclear charge in a molecule and the filling fraction of orbitals, can be decisive for determining the cost of a quantum simulation.

### Faster quantum simulation by randomization

• Computer Science
Quantum
• 2019
By simply randomizing how the summands are ordered, one can prove stronger bounds on the quality of approximation for product formulas of any given order, and thereby give more efficient simulations of Hamiltonian dynamics.

### 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.