# Quantum optimization using variational algorithms on near-term quantum devices

@article{Moll2017QuantumOU, title={Quantum optimization using variational algorithms on near-term quantum devices}, author={Nikolaj Moll and Panagiotis Kl. Barkoutsos and Lev S. Bishop and Jerry M. Chow and Andrew W. Cross and Daniel J. Egger and Stefan Filipp and Andreas Fuhrer and Jay M. Gambetta and Marc Ganzhorn and Abhinav Kandala and Antonio Mezzacapo and Peter Barkholt Muller and Walter Riess and G. Salis and John A. Smolin and Ivano Tavernelli and Kristan Temme}, journal={Quantum Science and Technology}, year={2017}, volume={3} }

Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available, near-term quantum devices will provide several hundred qubits and limited error correction. Still, there is a realistic prospect to run useful algorithms within the limited circuit depth of such devices. Particularly promising are optimization algorithms that…

## 399 Citations

### Limitations of optimization algorithms on noisy quantum devices

- Computer Science, PhysicsNature Physics
- 2021

This work presents a transparent way of comparing classical algorithms to quantum ones running on near-term quantum devices for a large family of problems that include optimization problems and approximations to the ground state energy of Hamiltonians.

### Quantum-Classical Variational Approaches with Single-Qubit Operation on Near-Term Quantum Processors

- Physics2022 IEEE 22nd International Conference on Nanotechnology (NANO)
- 2022

Currently developed quantum devices have the potential to show a computational advantage if quantum applications exploit the devices efficiently. Variational quantum algorithms (VQAs) combine a…

### Variational Ansatz preparation to avoid CNOT-gates on noisy quantum devices for combinatorial optimizations

- PhysicsAIP Advances
- 2022

The variational quantum eigensolver (VQE), which is a quantum–classical hybrid approach, has latent powers to leverage near-term quantum devices by effectively managing a limited number of qubits…

### Gate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer

- PhysicsPhysical Review Applied
- 2019

A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with short circuit depth that finish within the available coherence…

### Engineering the Cost Function of a Variational Quantum Algorithm for Implementation on Near-Term Devices

- Physics
- 2020

Variational hybrid quantum-classical algorithms are some of the most promising workloads for near-term quantum computers without error correction. The aim of these variational algorithms is to guide…

### Pulse-Level Optimization of Parameterized Quantum Circuits for Variational Quantum Algorithms

- Computer Science, Physics
- 2022

Pulse-level access to quantum machines and understanding of their two-qubit interactions are utilized to optimize the design of two- qubit entanglers in a manner suitable for VQAs, and results show that pulse-optimized ansatze reduce state preparation times by more than half, maintain expressibility relative to standard PQCs, and are more trainable through local cost function analysis.

### Space-efficient binary optimization for variational quantum computing

- Computer Sciencenpj Quantum Information
- 2022

This paper shows that it is possible to greatly reduce the number of qubits needed for the Travelling Salesman problem, a paradigmatic optimization task, at the cost of having deeper variational circuits, and claims that the approach can be generalized for other problems where the standard bit-encoding is highly inefficient.

### QVECTOR: an algorithm for device-tailored quantum error correction

- Computer Science, Physics
- 2017

This method aims to optimize the average fidelity of encoding and recovery circuits with respect to the actual noise in the device, as opposed to that of an artificial or approximate noise model.

### Numerical hardware-efficient variational quantum simulation of a soliton solution

- Physics, Computer SciencePhysical Review A
- 2021

It is argued that, while being capable of correctly reproducing a uniform magnetic configuration, the hardware-efficient ansatz meets difficulties in providing a detailed description to a noncollinear magnetic structure, which naturally limits the application range of variational quantum computing to solve quantum simulation tasks.

### Variational Quantum Information Processing

- Computer Science, Physics
- 2019

This dissertation presents the application of the variational quantum computing approach to problems in quantum simulation, quantum state preparation, quantum error-correction, and generative modeling, and establishes practical guidelines to implement these methods on near-term quantum computers.

## References

SHOWING 1-10 OF 159 REFERENCES

### Quantum Algorithms for Fixed Qubit Architectures

- Physics
- 2017

Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or…

### Gate count estimates for performing quantum chemistry on small quantum computers

- Physics, Computer Science
- 2014

This paper focuses on the quantum resources required to find the ground state of a molecule twice as large as what current classical computers can solve exactly and suggests that for quantum computation to become useful for quantum chemistry problems, drastic algorithmic improvements will be needed.

### Faster quantum chemistry simulation on fault-tolerant quantum computers

- Computer Science
- 2012

This work proposes methods which substantially improve the performance of a particular form of simulation, ab initio quantum chemistry, on fault-tolerant quantum computers; these methods generalize readily to other quantum simulation problems.

### Characterizing quantum supremacy in near-term devices

- Physics
- 2016

A critical question for quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of…

### Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer

- Physics
- 2015

Quantum chemistry simulations on a quantum computer suffer from the overhead needed for encoding the Fermionic problem in a system of qubits. By exploiting the block diagonality of a Fermionic…

### The theory of variational hybrid quantum-classical algorithms

- Computer Science
- 2015

This work develops a variational adiabatic ansatz and explores unitary coupled cluster where it is shown how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.

### Superconducting quantum circuits at the surface code threshold for fault tolerance

- Physics, Computer ScienceNature
- 2014

The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

### Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing

- Physics, Computer Science
- 2014

The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

### Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets

- PhysicsNature
- 2017

The experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms is demonstrated, determining the ground-state energy for molecules of increasing size, up to BeH2.

### Demonstration of a small programmable quantum computer with atomic qubits

- Computer Science, PhysicsNature
- 2016

A five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates, which provides the flexibility to implement a variety of algorithms without altering the hardware.