# Error Mitigation for Deep Quantum Optimization Circuits by Leveraging Problem Symmetries

@article{Shaydulin2021ErrorMF, title={Error Mitigation for Deep Quantum Optimization Circuits by Leveraging Problem Symmetries}, author={Ruslan Shaydulin and Alexey Galda}, journal={2021 IEEE International Conference on Quantum Computing and Engineering (QCE)}, year={2021}, pages={291-300} }

High error rates and limited fidelity of quantum gates in near-term quantum devices are the central obstacles to successful execution of the Quantum Approximate Optimization Algorithm (QAOA). In this paper we introduce an application-specific approach for mitigating the errors in QAOA evolution by leveraging the symmetries present in the classical objective function to be optimized. Specifically, the QAOA state is projected into the symmetry-restricted subspace, with projection being performed…

## 8 Citations

### Characterizing Error Mitigation by Symmetry Verification in QAOA

- Physics, Computer Science
- 2022

A theoretical framework for analyzing symmetry veriﬁcation under local noise is developed and explicit formulas for ﬁdelity improvements on problems with global Z 2 symmetry are derived.

### Error mitigation for variational quantum algorithms through mid-circuit measurements

- Computer Science
- 2021

This paper presents mid-circuit post-selection schemes for frequently used encodings such as one-hot, binary, gray, and domain-wall encoding, and proposes a method that works by compressing the full Hilbert space to a smaller subspace, allowing projecting to the desired subspace without using any ancilla qubits.

### Quantum Approximate Optimization Algorithm with Sparsified Phase Operator

- Computer ScienceArXiv
- 2022

If the ground state energy is not preserved, the approximation ratio obtained by QAOA with such phase separating operator is likely to decrease, and it is shown that a better alignment of the low energy subspace of the alternative operator leads to better performance.

### Constrained Quantum Optimization for Extractive Summarization on a Trapped-ion Quantum Computer

- Computer Science, PhysicsArXiv
- 2022

This work considers the extractive summarization constrained-optimization problem and shows the necessity of directly encoding the constraints into the quantum circuit by showing the trade-off between the in-constraint probability and the quality of the solution that is implicit if unconstrained quantum optimization methods are used.

### Quantum Error Mitigation by Pauli Check Sandwiching

- Computer ScienceArXiv
- 2022

It is proved that this technique can recover the noiseless state under the assumption of noise not affecting the checks, and it can be easily combined with other error mitigation techniques.

### Mixer-phaser Ansätze for quantum optimization with hard constraints

- PhysicsQuantum Mach. Intell.
- 2022

We introduce multiple parametrized circuit ansätze and present the results of a numerical study comparing their performance with a standard Quantum Alternating Operator Ansatz approach. The ansätze…

### QAOAKit: A Toolkit for Reproducible Study, Application, and Verification of the QAOA

- Computer Science2021 IEEE/ACM Second International Workshop on Quantum Computing Software (QCS)
- 2021

QAOAKit is a unified repository of preoptimized QAOA parameters and circuit generators for common quantum simulation frameworks that can be used to reproduce, compare, and extend known results from various sources in the literature.

### Augmenting QAOA Ansatz with Multiparameter Problem-Independent Layer

- Computer Science
- 2022

An alternative ansatz is proposed, which is called QAOA+, that augments the traditional p = 1QAOA ansatz with an additional multiparameter problem-independent layer, that outperforms alternative multiangle QAoa ansatz in most cases.

## References

SHOWING 1-10 OF 36 REFERENCES

### Exploiting Symmetry Reduces the Cost of Training QAOA

- Computer ScienceIEEE Transactions on Quantum Engineering
- 2021

A novel approach for accelerating the evaluation of QAOA energy by leveraging the symmetry of the problem by showing a connection between classical symmetries of the objective function and the symmetry of the terms of the cost Hamiltonian with respect to the QAoa energy.

### Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

- Physics, Computer ScienceProceedings of the National Academy of Sciences
- 2020

This work applies a variational quantum algorithm (QAOA) to approximate the ground-state energy of a long-range Ising model, both quantum and classical, and investigates the algorithm performance on a trapped-ion quantum simulator, observing that the QAOA performance does not degrade significantly as the authors scale up the system size and that the runtime is approximately independent from the number of qubits.

### Obstacles to Variational Quantum Optimization from Symmetry Protection.

- Computer SciencePhysical review letters
- 2020

This work proposes a nonlocal version of the QAOA and gives numerical evidence that it significantly outperforms the standard QAoa for frustrated Ising models and reveals fundamental limitations of theQAOA resulting from the symmetry and the locality of variational states.

### Towards Optimal Topology Aware Quantum Circuit Synthesis

- Computer Science2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
- 2020

An algorithm for compiling arbitrary unitaries into a sequence of gates native to a quantum processor, which minimizes their count while accounting for connectivity, and discusses the formulation of synthesis as a search problem as well as an algorithm to find solutions.

### Experimental error mitigation via symmetry verification in a variational quantum eigensolver

- PhysicsPhysical Review A
- 2019

Variational quantum eigensolvers offer a small-scale testbed to demonstrate the performance of error mitigation techniques with low experimental overhead. We present successful error mitigation by…

### Low-cost error mitigation by symmetry verification

- PhysicsPhysical Review A
- 2018

We investigate the performance of error mitigation via measurement of conserved symmetries on near-term devices. We present two protocols to measure conserved symmetries during the bulk of an…

### Empirical performance bounds for quantum approximate optimization

- Computer ScienceQuantum Inf. Process.
- 2021

Testing up to three layers of QAOA depth, it is found that distributions of the approximation ratio narrow with increasing depth while the probability of recovering the maximum cut generally broadens and QAoa exceeds the Goemans-Williamson approximation ratio bound for most graphs.

### Quantum algorithms with local particle-number conservation: Noise effects and error correction

- Physics
- 2020

The probability of staying in symmetry-preserved subspaces under noise is analyzed, providing an exact formula for local depolarizing noise and a simple adaption of the bit flip code to correct for symmetry-breaking errors with reduced resources is discussed.

### Practical and Reliable Error Bars in Quantum Tomography.

- Computer SciencePhysical review letters
- 2016

This work proposes a practical yet robust method for obtaining error bars by introducing a novel representation of the output of the tomography procedure, the quantum error bars, and presents an algorithm for computing this representation and provides ready-to-use software.

### From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz

- PhysicsAlgorithms
- 2019

The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter.