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Register a new userCharacterizing local noise in QAOA circuits
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Recently Xue et al. [arXiv:1909.02196] demonstrated numerically that QAOA performance varies as a power law in the amount of noise under certain physical noise models. In this short note, we provide a deeper analysis of the origin of this behavior. In particular, we provide an approximate closed form equation for the fidelity and cost in terms of the noise rate, system size, and circuit depth. As an application, we show these equations accurately model the trade off between larger circuits which attain better cost values, at the expense of greater degradation due to noise.
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A significant problem for current quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model often appropriately describes average noise for large circuits involving many qubits and gates. We present a method to mitigate the depolarizing noise by first estimating its rate with a noise-estimation circuit and then correcting the output of the target circuit using the estimated rate. The method is experimentally validated on the simulation of the Heisenberg model. We find that our approach in combination with readout-error correction, randomized compiling, and zero-noise extrapolation produces results close to exact results even for circuits containing hundreds of CNOT gates.
We study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of the QAOA dynamics and the group of classical symmetries of the objective function. The connection is general and includes but is not limited to problems defined on graphs. We show a series of results exploring the connection and highlight examples of hard problem classes where a nontrivial symmetry subgroup can be obtained efficiently. In particular we show how classical objective function symmetries lead to invariant measurement outcome probabilities across states connected by such symmetries, independent of the choice of algorithm parameters or number of layers. To illustrate the power of the developed connection, we apply machine learning techniques towards predicting QAOA performance based on symmetry considerations. We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically important setting where QAOA parameter schedules are constrained to be linear and hence easier to optimize.
Noise mitigation and reduction will be crucial for obtaining useful answers from near-term quantum computers. In this work, we present a general framework based on machine learning for reducing the impact of quantum hardware noise on quantum circuits. Our method, called noise-aware circuit learning (NACL), applies to circuits designed to compute a unitary transformation, prepare a set of quantum states, or estimate an observable of a many-qubit state. Given a task and a device model that captures information about the noise and connectivity of qubits in a device, NACL outputs an optimized circuit to accomplish this task in the presence of noise. It does so by minimizing a task-specific cost function over circuit depths and circuit structures. To demonstrate NACL, we construct circuits resilient to a fine-grained noise model derived from gate set tomography on a superconducting-circuit quantum device, for applications including quantum state overlap, quantum Fourier transform, and W-state preparation.
The $p$-stage Quantum Approximate Optimization Algorithm (QAOA$_p$) is a promising approach for combinatorial optimization on noisy intermediate-scale quantum (NISQ) devices, but its theoretical behavior is not well understood beyond $p=1$. We analyze QAOA$_2$ for the maximum cut problem (MAX-CUT), deriving a graph-size-independent expression for the expected cut fraction on any $D$-regular graph of girth $> 5$ (i.e. without triangles, squares, or pentagons). We show that for all degrees $D ge 2$ and every $D$-regular graph $G$ of girth $> 5$, QAOA$_2$ has a larger expected cut fraction than QAOA$_1$ on $G$. However, we also show that there exists a $2$-local randomized classical algorithm $A$ such that $A$ has a larger expected cut fraction than QAOA$_2$ on all $G$. This supports our conjecture that for every constant $p$, there exists a local classical MAX-CUT algorithm that performs as well as QAOA$_p$ on all graphs.
Quantum noise is the key challenge in Noisy Intermediate-Scale Quantum (NISQ) computers. Previous work for mitigating noise has primarily focused on gate-level or pulse-level noise-adaptive compilation. However, limited research efforts have explored a higher level of optimization by making the quantum circuits themselves resilient to noise. We propose QuantumNAS, a comprehensive framework for noise-adaptive co-search of the variational circuit and qubit mapping. Variational quantum circuits are a promising approach for constructing QML and quantum simulation. However, finding the best variational circuit and its optimal parameters is challenging due to the large design space and parameter training cost. We propose to decouple the circuit search and parameter training by introducing a novel SuperCircuit. The SuperCircuit is constructed with multiple layers of pre-defined parameterized gates and trained by iteratively sampling and updating the parameter subsets (SubCircuits) of it. It provides an accurate estimation of SubCircuits performance trained from scratch. Then we perform an evolutionary co-search of SubCircuit and its qubit mapping. The SubCircuit performance is estimated with parameters inherited from SuperCircuit and simulated with real device noise models. Finally, we perform iterative gate pruning and finetuning to remove redundant gates. Extensively evaluated with 12 QML and VQE benchmarks on 10 quantum comput, QuantumNAS significantly outperforms baselines. For QML, QuantumNAS is the first to demonstrate over 95% 2-class, 85% 4-class, and 32% 10-class classification accuracy on real QC. It also achieves the lowest eigenvalue for VQE tasks on H2, H2O, LiH, CH4, BeH2 compared with UCCSD. We also open-source QuantumEngine (https://github.com/mit-han-lab/pytorch-quantum) for fast training of parameterized quantum circuits to facilitate future research.
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