A Domain-agnostic, Noise-resistant Evolutionary Variational Quantum Eigensolver for Hardware-efficient Optimization in the Hilbert Space

Variational quantum algorithms have shown promise in numerous fields due to their versatility in solving problems of scientific and commercial interest. However, leading algorithms for Hamiltonian simulation, such as the Variational Quantum Eigensolver (VQE), use fixed preconstructed ansatzes, limiting their general applicability and accuracy. Thus, variational forms—the quantum circuits that implement ansatzes —are either crafted heuristically or by encoding domainspecific knowledge. In this paper, we present an Evolutionary Variational Quantum Eigensolver (EVQE), a novel variational algorithm that uses evolutionary programming techniques to minimize the expectation value of a given Hamiltonian by dynamically generating and optimizing an ansatz. The algorithm is equally applicable to optimization problems in all domains, obtaining accurate energy evaluations with hardwareefficient ansatzes that are up to 18.6× shallower and use up to 12× fewer CX gates than results obtained with a unitary coupled cluster ansatz. EVQE demonstrates significant noiseresistant properties, obtaining results in noisy simulation with at least 3.6× less error than VQE using any tested ansatz configuration. We successfully evaluated EVQE on a real 5qubit IBMQ quantum computer. The experimental results, which we obtained both via simulation and on real quantum hardware, demonstrate the effectiveness of EVQE for generalpurpose optimization on the quantum computers of the present and near future.

[1]  Risto Miikkulainen,et al.  Evolving Neural Networks through Augmenting Topologies , 2002, Evolutionary Computation.

[2]  Kristan Temme,et al.  Error mitigation extends the computational reach of a noisy quantum processor , 2019, Nature.

[3]  M. Schuld,et al.  Circuit-centric quantum classifiers , 2018, Physical Review A.

[4]  Qing Yang,et al.  Evolving quantum circuits at the gate level with a hybrid quantum-inspired evolutionary algorithm , 2008, Soft Comput..

[5]  Andrew Lucas,et al.  Ising formulations of many NP problems , 2013, Front. Physics.

[6]  J. Gambetta,et al.  Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets , 2017, Nature.

[7]  Masoud Mohseni,et al.  Commercialize quantum technologies in five years , 2017, Nature.

[8]  M. Benedetti,et al.  Quantum circuit structure learning , 2019, 1905.09692.

[9]  Keisuke Fujii,et al.  Quantum circuit learning , 2018, Physical Review A.

[10]  Alexander G. Gray,et al.  Automated Design of Quantum Circuits , 1998, QCQC.

[11]  W. Spears.  Speciation Using Tag Bits , 2007 .

[12]  Alán Aspuru-Guzik,et al.  A variational eigenvalue solver on a photonic quantum processor , 2013, Nature Communications.

[13]  Peter J. Angeline,et al.  An evolutionary algorithm that constructs recurrent neural networks , 1994, IEEE Trans. Neural Networks.

[14]  Andrew W. Cross,et al.  Validating quantum computers using randomized model circuits , 2018, Physical Review A.

[15]  Xiaoxiao Wang,et al.  Synthesis of reversible logic circuit using a species conservation method , 2014, 2014 10th International Conference on Natural Computation (ICNC).

[16]  Samir W. Mahfoud.  Niching methods for genetic algorithms , 1996 .

[17]  Ivano Tavernelli,et al.  Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions , 2018, Physical Review A.

[18]  E. Farhi,et al.  A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.

[19]  Kyusik Chung,et al.  Evolutionary Approach to Quantum and Reversible Circuits Synthesis , 2003, Artificial Intelligence Review.

[20]  David E. Goldberg,et al.  Genetic Algorithms and Walsh Functions: Part II, Deception and Its Analysis , 1989, Complex Syst..

[21]  Dmitri Maslov,et al.  Efficient Circuits for Quantum Search over 2D Square Lattice Architecture , 2019, 2019 56th ACM/IEEE Design Automation Conference (DAC).

[22]  Kristan Temme,et al.  Supervised learning with quantum-enhanced feature spaces , 2018, Nature.

[23]  Kristan Temme,et al.  Error Mitigation for Short-Depth Quantum Circuits. , 2016, Physical review letters.

[24]  J. Gambetta,et al.  Tapering off qubits to simulate fermionic Hamiltonians , 2017, 1701.08213.

[25]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[26]  Harper R. Grimsley,et al.  An adaptive variational algorithm for exact molecular simulations on a quantum computer , 2018, Nature Communications.

[27]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[28]  Sandeep Kaushik,et al.  Big data in healthcare: management, analysis and future prospects , 2019, Journal of Big Data.

[29]  Dmitri Maslov,et al.  Low-cost quantum circuits for classically intractable instances of the Hamiltonian dynamics simulation problem , 2018, npj Quantum Information.

[30]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.