A variational eigenvalue solver on a photonic quantum processor

By Alberto Peruzzo, Jarrod R. McClean, Peter Shadbolt, Man-Hong Yung, Xiaoqi Zhou, Peter J. Love, Alán Aspuru-Guzik, Jeremy Lloyd O'Brien. Nature Communications, 2013

5,028 citations recorded by the source corpus.

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansätze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry—calculating the ground-state molecular energy for He–H+. The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future. Quantum computers promise to efficiently solve problems that would be practically impossible with a normal computer. Peruzzo et al. develop a variational computation approach that uses any available quantum resources and, with a photonic quantum processing unit, find the ground-state molecular energy of He–H+.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/80cc953f8ad11bb05876e11e84c50f809533db75

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Citations in the corpus

Variational Quantum Linear Solver (2019, background): “The assumption that A is given in this form is analogous to the assumption that the Hamiltonian H in the variational quantum eigensolver [20] is given as a linear combination of Pauli operators H = =1 c l σ l , where naturally one makes the assumption that L is only a polynomial function of the…”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, methodology): “The variational method has shown huge potentials in applications such as quantum machine learning [4], [7], [56], [63], numerical analysis [37], [39], quantum simulation [30], [31], [52], and optimizations [18], [47].”
Grand Unification of Quantum Algorithms (2021, methodology): “[41] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, ManHong Yung, Xiao-Qi Zhou, Peter J.”
Continuous-variable quantum neural networks (2018, background): “[82] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’Brien.”
A generative modeling approach for benchmarking and training shallow quantum circuits (2018, methodology): “Figure 2 on the top left panel shows patterns belonging to BAS(2, 2), while the top central panel shows the remaining patterns.”
Circuit-centric quantum classifiers (2018, background): “[18] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, ManHong Yung, Xiao-Qi Zhou, Peter J Love, Alán AspuruGuzik, and Jeremy L Obrien.”
Quantum Chemistry in the Age of Quantum Computing. (2018, background): “oy a quadratic number of gates302,326,335,336. In the case of Slater determinants, the preparation is often described in terms of a rotation Uapplied to a single determinant, j si= Uc y 1 c y Njvaci; (52) where cy k and ck represent fermionic operators in an easy to prepare basis (e.g. the computati”
Open Quantum Assembly Language (2017, methodology): “This includes pre-processing of problem data (e.g. in Shor’s algorithm [27]), post-processing of measurement outcomes (e.g. in tomography [16]) or further generation of circuits based on those (e.g. the outer loop of variational algorithms [28]).”
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity (2018, background): “More recently, experimental demonstrations [11 – 15] have focused on the development of variational algorithms [16,17], which are often [18,19], but not always [20,21], inspired by time-evolution primitives.”
Efficient Variational Quantum Simulator Incorporating Active Error Minimization (2016, methodology): “An example is the unitary coupled cluster method [10, 44], in which the energy of the trial state can be evaluated using a quantum computer when it is hard for a classical computer to do so.”