Classical variational optimization of a PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians

We propose a method for constructing circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes and plays a crucial role in the state-of-the-art efficient implementations of quantum phase estimation. We employ the automatic quantum circuit encoding algorithm [Shirakawa , ] to construct circuits, which requires classical simulations of quantum circuits of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>O</a:mi><a:mo>(</a:mo><a:mo form="prefix">log</a:mo><a:mi>N</a:mi><a:mo>)</a:mo></a:mrow></a:math> qubits with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>N</c:mi></c:math> being the number of qubits of the Hamiltonian. The generated circuits do not need any ancillary qubit. We demonstrate our method by investigating the number of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>T</d:mi></d:math>-gates of the obtained circuits for quantum chemistry Hamiltonians of various molecules, which shows a constant-factor reduction compared to previous approaches that do not use ancillary qubits. Since the number of available logical qubits and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>T</e:mi></e:math> gates will be limited at the early stage of the fault-tolerant quantum computing, the proposed method is particularly of use for performing the quantum phase estimation with such limited capability. Published by the American Physical Society 2024