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Classical computing plays a critical role in the advancement of quantum frontiers in the NISQ era. In this spirit, this work uses classical simulation to bootstrap Variational Quantum Algorithms (VQAs). VQAs rely upon the iterative optimization of a parameterized unitary circuit (ansatz) with respect to an objective function. Since quantum machines are noisy and expensive resources, it is imperative to classically choose the VQA ansatz initial parameters to be as close to optimal as possible to improve VQA accuracy and accelerate their convergence on today’s devices. This work tackles the problem of finding a good ansatz initialization, by proposing CAFQA, a Clifford Ansatz For Quantum Accuracy. The CAFQA ansatz is a hardware-efficient circuit built with only Clifford gates. In this ansatz, the parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation. The resulting initial states always equal or outperform traditional classical initialization (e.g., Hartree-Fock), and enable high-accuracy VQA estimations. CAFQA is well-suited to classical computation because: a) Clifford-only quantum circuits can be exactly simulated classically in polynomial time, and b) the discrete Clifford space is searched efficiently via Bayesian Optimization. For the Variational Quantum Eigensolver (VQE) task of molecular ground state energy estimation (up to 18 qubits), CAFQA’s Clifford Ansatz achieves a mean accuracy of nearly 99% and recovers as much as 99.99% of the molecular correlation energy that is lost in Hartree-Fock initialization. CAFQA achieves mean accuracy improvements of 6.4x and 56.8x, over the state-of-the-art, on different metrics. The scalability of the approach allows for preliminary ground state energy estimation of the challenging chromium dimer (Cr2) molecule. With CAFQA’s high-accuracy initialization, the convergence of VQAs is shown to accelerate by 2.5x, even for small molecules. Furthermore, preliminary exploration of allowing a limited number of non-Clifford (T) gates in the CAFQA framework, shows that as much as 99.9% of the correlation energy can be recovered at bond lengths for which Clifford-only CAFQA accuracy is relatively limited, while remaining classically simulable.
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Distributionally Robust Variational Quantum Algorithms With Shifted Noise
Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is that quantum noise is highly unstable and thus it is likely to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the quantum approximate optimization algorithm and the variational quantum eigensolver with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step toward improving the reliability of VQAs influenced by shifted noise from the parameter optimization perspective
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- Award ID(s):
- 1846476
- PAR ID:
- 10627652
- Publisher / Repository:
- IEEE Transactions on Quantum Engineering
- Date Published:
- Journal Name:
- IEEE Transactions on Quantum Engineering
- Volume:
- 5
- ISSN:
- 2689-1808
- Page Range / eLocation ID:
- 1 to 12
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Variational Quantum Algorithms (VQAs) rely upon the iterative optimization of a parameterized unitary circuit with respect to an objective function. Since quantum machines are noisy and expensive resources, it is imperative to choose a VQA's ansatz appropriately and its initial parameters to be close to optimal. This work tackles the problem of finding initial ansatz parameters by proposing CAFQA, a Clifford ansatz for quantum accuracy. The CAFQA ansatz is a hardware-efficient circuit built with only Clifford gates. In this ansatz, the initial parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation, thereby producing a suitable stabilizer state. The stabilizer states produced are shown to always equal or outperform traditional classical initialization (e.g., Hartree-Fock), and often produce high accuracy estimations prior to quantum exploration. Furthermore, the technique is classically suited since a) Clifford circuits can be exactly simulated classically in polynomial time and b) the discrete Clifford space, while scaling exponentially in the number of qubits, is searched efficiently via Bayesian Optimization. For the Variational Quantum Eigensolver (VQE) task of molecular ground state energy estimation up to 20 qubits, CAFQA's Clifford Ansatz achieves a mean accuracy of near 99%, recovering as much as 99.99% of the correlation energy over Hartree-Fock. Notably, the scalability of the approach allows for preliminary ground state energy estimation of the challenging Chromium dimer with an accuracy greater than Hartree-Fock. With CAFQA's initialization, VQA convergence is accelerated by a factor of 2.5x. In all, this work shows that stabilizer states are an accurate ansatz initialization for VQAs. Furthermore, it highlights the potential for quantum-inspired classical techniques to support VQAs.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TQE.2024.3409309
