Abstract
Quantum simulation, one of the most promising applications of a quantum computer, is currently being explored intensely using the variational quantum eigensolver. The feasibility and performance of this algorithm depend critically on the form of the wavefunction ansatz. Recently in Nat. Commun. 10, 3007 (2019), an algorithm termed ADAPT-VQE was introduced to build system-adapted ans\"atze with substantially fewer variational parameters compared to other approaches. This algorithm relies heavily on a predefined operator pool with which it builds the ansatz. However, Nat. Commun. 10, 3007 (2019) did not provide a prescription for how to select the pool, how many operators it must contain, or whether the resulting ansatz will succeed in converging to the ground state. In addition, the pool used in that work leads to state preparation circuits that are too deep for a practical application on near-term devices. Here, we address all these key outstanding issues of the algorithm. We present a hardware-efficient variant of ADAPT-VQE that drastically reduces circuit depths using an operator pool that is guaranteed to contain the operators necessary to construct exact ans\"atze. Moreover, we show that the minimal pool size that achieves this scales linearly with the number of qubits. Through numerical simulations on $\text{H}_4$, LiH and $\text{H}_6$, we show that our algorithm ("qubit-ADAPT") reduces the circuit depth by an order of magnitude while maintaining the same accuracy as the original ADAPT-VQE. A central result of our approach is that the additional measurement overhead of qubit-ADAPT compared to fixed-ansatz variational algorithms scales only linearly with the number of qubits. Our work provides a crucial step forward in running algorithms on near-term quantum devices.
Highlights
Finding the ground state of a many-body interacting electronic Hamiltonian is one of the most important problems in modern quantum chemistry and physics
A second drawback is that unitary coupled-cluster singles and doubles (UCCSD) is generally not exact and suffers from ambiguities in operator ordering upon factorization into a product of exponentiated operators (Trotterization), which is a necessary step in converting the ansatz to a statepreparation circuit [37,38]
It is not clear (i) how the operator pool should be chosen in general, (ii) how many operators it should contain, and (iii) what guarantees that the pool is complete, i.e., that it enables convergence to the ground state. We address these issues by introducing qubit-adaptive derivative assembled pseudo-Trotter (ADAPT)-variational quantum eigensolver (VQE), an algorithm that substantially reduces both the number of measurements and the circuit depths needed to achieve convergence
Summary
Finding the ground state of a many-body interacting electronic Hamiltonian is one of the most important problems in modern quantum chemistry and physics. A second drawback is that UCCSD is generally not exact and suffers from ambiguities in operator ordering upon factorization into a product of exponentiated operators (Trotterization), which is a necessary step in converting the ansatz to a statepreparation circuit [37,38] Another approach to building the ansatz is to use the most accessible gates in the quantum device, alternating single-qubit gates and two-qubit gates layer by layer. [29] translate to a fairly large number of quantum gates, and, while the number of parameters is very low, the circuit depth (which is significantly reduced compared to UCCSD) may still be impractically large, limiting the applicability of ADAPT-VQE to NISQ devices Even more importantly, it is not clear (i) how the operator pool should be chosen in general, (ii) how many operators it should contain, and (iii) what guarantees that the pool is complete, i.e., that it enables convergence to the ground state. Details of the estimate for the circuit depth of fermionic-ADAPT and a constructive proof of the linear scaling of minimal complete pools are included in appendices
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