 Award ID(s):
 1818914
 NSFPAR ID:
 10339353
 Date Published:
 Journal Name:
 ArXivorg
 ISSN:
 23318422
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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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 hardwareefficient 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., HartreeFock), and enable highaccuracy VQA estimations. CAFQA is wellsuited to classical computation because: a) Cliffordonly 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 HartreeFock initialization. CAFQA achieves mean accuracy improvements of 6.4x and 56.8x, over the stateoftheart, 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 highaccuracy 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 nonClifford (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 Cliffordonly CAFQA accuracy is relatively limited, while remaining classically simulable.more » « less

Quantum errorcorrecting codes can be used to protect qubits involved in quantum computation. This requires that logical operators acting on protected qubits be translated to physical operators (circuits) acting on physical quantum states. We propose a mathematical framework for synthesizing physical circuits that implement logical Clifford operators for stabilizer codes. Circuit synthesis is enabled by representing the desired physical Clifford operator in CN ×N as a 2m × 2m binary sym plectic matrix, where N = 2m. We show that for an [m, m − k] stabilizer code every logical Clifford operator has 2k(k+1)/2 symplectic solutions, and we enumerate them efficiently using symplectic transvections. The desired circuits are then obtained by writing each of the solutions as a product of elementary symplectic matrices. For a given operator, our assembly of all of its physical realizations enables optimization over them with respect to a suitable metric. Our method of circuit synthesis can be applied to any stabilizer code, and this paper provides a proof of concept synthesis of universal Clifford gates for the well known [6, 4, 2] code. Programs implementing our algorithms can be found at https://github.com/nrenga/symplecticarxiv18a.more » « less

We advance the characterization of complexity in quantum manybody systems by examining
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