CAFQA: A Classical Simulation Bootstrap for Variational Quantum Algorithms

Conference · 21 December 2022 · Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 1

DOI:https://doi.org/10.1145/3567955.3567958· OSTI ID:1986248

Ravi, Gokul Subramanian ^[1]; Gokhale, Pranav ^[2]; Ding, Yi ^[3]; Kirby, William ^[4]; Smith, Kaitlin N. ^[1]; Baker, Jonathan M. ^[1]; Love, Peter J. ^[4]; Hoffmann, Henry ^[1]; Brown, Kenneth R. ^[5]; Chong, Frederic T. ^[1]

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1. University of Chicago, IL (United States)
2. SuperTech, TN (United States)
3. Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
4. Tufts University, Medford, MA (United States)
5. Duke University, Durham, NC (United States)

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. Here, 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.

• Research Organization: University of Chicago, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF); ARO
• DOE Contract Number: SC0020289; SC0014195; DGE-1842474; CCF-2119184; CNS-1956180; CNS-1952050; CCF-1823032; CNS-1764039; W911NF1920321
• OSTI ID: 1986248
• Journal Information: Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 1, Conference: ASPLOS '23: 28. ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Vancouver, BC (Canada), 25-29 Mar 2023
• Country of Publication: United States
• Language: English

Related Subjects

quantum computing
variational quantum algorithms
chemistry
clifford
bayesian optimization
noisy intermediate-scale quantum
variational quantum eigensolver