Feynman's clock maps arbitrary circuits onto Hamiltonian dynamics whose BBGKY hierarchy enables polynomial-overhead, controllable error mitigation via informed sampling.
The Variational Quantum Eigensolver: A Review of Methods and Best Practices
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
abstract
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are constrained in their accuracy due to the computational limits. The VQE may be used to model complex wavefunctions in polynomial time, making it one of the most promising near-term applications for quantum computing. Finding a path to navigate the relevant literature has rapidly become an overwhelming task, with many methods promising to improve different parts of the algorithm. Despite strong theoretical underpinnings suggesting excellent scaling of individual VQE components, studies have pointed out that their various pre-factors could be too large to reach a quantum computing advantage over conventional methods. This review aims to provide an overview of the progress that has been made on the different parts of the algorithm. All the different components of the algorithm are reviewed in detail including representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process, the post-processing mitigation of errors, and best practices are suggested. We identify four main areas of future research:(1) optimal measurement schemes for reduction of circuit repetitions; (2) large scale parallelization across many quantum computers;(3) ways to overcome the potential appearance of vanishing gradients in the optimization process, and how the number of iterations required for the optimization scales with system size; (4) the extent to which VQE suffers for quantum noise, and whether this noise can be mitigated. The answers to these open research questions will determine the routes for the VQE to achieve quantum advantage as the quantum computing hardware scales up and as the noise levels are reduced.
representative citing papers
Geometric frustration in a square-lattice Ising model with diagonal couplings produces strongly inhomogeneous correlations that standard Hamiltonian-inspired variational ansatze cannot capture efficiently, increasing required circuit depth until bond-resolved parameters are introduced.
The Effective Bethe Ansatz approximates ground and first excited states of the spin-1 bilinear-biquadratic chain in finite windows around both integrable endpoints, with fidelity to exact diagonalization degrading controllably and entanglement entropy reproduced poorly.
The authors convert classical software bug detection into quantum optimization instances and test QAOA, Grover, and QSVT on small examples for potential polynomial speedup.
A synthesis of quantum methods in finance finds that carefully designed hybrid systems offer the strongest practical advantages in optimization, pricing, risk, ML, and cryptography.
citing papers explorer
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Feynman's clock and hierarchy-informed sampling for quantum error mitigation
Feynman's clock maps arbitrary circuits onto Hamiltonian dynamics whose BBGKY hierarchy enables polynomial-overhead, controllable error mitigation via informed sampling.
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Frustration-Induced Expressibility Limitations in Variational Quantum Algorithms
Geometric frustration in a square-lattice Ising model with diagonal couplings produces strongly inhomogeneous correlations that standard Hamiltonian-inspired variational ansatze cannot capture efficiently, increasing required circuit depth until bond-resolved parameters are introduced.
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Effective Bethe Ansatz for Spin-1 Non-integrable Models
The Effective Bethe Ansatz approximates ground and first excited states of the spin-1 bilinear-biquadratic chain in finite windows around both integrable endpoints, with fidelity to exact diagonalization degrading controllably and entanglement entropy reproduced poorly.
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Towards Classical Software Verification using Quantum Computers
The authors convert classical software bug detection into quantum optimization instances and test QAOA, Grover, and QSVT on small examples for potential polynomial speedup.
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Quantum Computing for Financial Transformation: A Review of Optimisation, Pricing, Risk, Machine Learning, and Post-Quantum Security
A synthesis of quantum methods in finance finds that carefully designed hybrid systems offer the strongest practical advantages in optimization, pricing, risk, ML, and cryptography.