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How to really measure operator gradients in ADAPT-VQE
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abstract
ADAPT-VQE is a leading variational quantum algorithm as it circumvents the choice-of-ansatz conundrum by iteratively growing compact and arbitrarily accurate problem-tailored ans\"atze. However, for molecular Hamiltonians and hardware-efficient operator pools, the gradient-measurement step of the algorithm requires the estimation of $\mathcal{O}(N^8)$ observables, which may represent a bottleneck for relevant system sizes on real devices. We present an efficient strategy for measuring the gradients of the three best-performing hardware-efficient operator pools by partitioning the required observables into $\mathcal{O}(N^3)$-sized sets of commuting Paulis that can be simultaneously measured with an at most $N-3$ CNOT overhead. We argue that our approach is robust to shot-noise effects and show that measuring the pool gradients is, in fact, not $\mathcal{O}(N^4)$, but only about $4N$ times as expensive as measuring the energy once. Our proposed measurement strategy significantly ameliorates the measurement overhead of ADAPT-VQE and brings us one step closer to practical implementations on real devices.
Forward citations
Cited by 6 Pith papers
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Hamiltonian-Aware ADAPT Variational Quantum Eigensolver for Molecular Ground-State Simulation
HA-ADAPT-VQE incorporates Hamiltonian data into operator selection and uses adaptive pruning of degraded operators, yielding lower energy errors, smaller ansatze, and reduced measurement costs on strongly correlated m...
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Projector Quantum Variational Ansatz
The Projector Variational Ansatz (PVA) is a new VQE ansatz that can match ISQ-QSP or ADAPT-VQE structures and converges with shallower circuits than standard ADAPT-VQE in experiments.
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Resource-efficient energy-based operator selection in fermionic ADAPT-VQE via exact Hamiltonian transformation
Exact Hamiltonian transformation halves the cost of energy-based operator selection in fermionic ADAPT-VQE while remaining mathematically identical to standard Rotoselect.
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Operator-centric Clifford algebra for variational eigensolvers and finite-shot adaptive selection
For real Hamiltonians, an exact parity rule prunes all even-Y Pauli words from ADAPT-VQE candidate pools, and a confidence-bound racing policy reduces finite-shot measurement cost by 34% in n≤6 simulations.
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Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation
A shot-efficient ADAPT-VQE variant that reuses grouped Pauli measurements from VQE optimization for gradient estimation and adds variance-based shot allocation reaches chemical accuracy with fewer measurements in smal...
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An Optimized Construction of Lie Algebra Generator Pools for Variational Quantum Eigensolvers in Chemistry
The proposed rank test does not determine the Lie algebra generated by a Pauli pool, so the claimed polynomial MCP construction is not established.
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