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The Japan Society of Applied Physics

Construction of quantum circuit for a generic linear combination of unitaries: Simulation of optical absorption spectra of molecules

Taichi Kosugi, Yu‐ichiro Matsushita

Published Jul 9, 2020• 0 citations
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Generic constructin of quantum circuits for nonunitary operations: linear-response functions of molecules

Yu‐ichiro Matsushita, Taichi Kosugi

Bulletin of the American Physical Society•Mar 18, 2021•0 citations

Linear-response functions of molecules on a quantum computer: Charge and spin responses and optical absorption

Taichi Kosugi, Yu‐ichiro Matsushita

This work proposes a generic construction scheme for the quantum circuit implementing a nonunitary operator appearing in electronic-structure calculations. The authors demonstrate that the scheme enables one via probabilistic state preparation to calculate the linear-response functions of diatomic molecules, where simulated measurements and full configuration-interaction results are compared.

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Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries

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A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to approximate a Taylor series by truncating after some order. Here we present an adaptation of that method, optimized for Hamiltonians with terms of widely varying magnitude, as is commonly the case in electronic structure calculations. We show that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative procedure. We obtain bounds on the simulation error for this generalized truncated Taylor method, and for a range of molecular simulations, we report these bounds as well as exact numerical results. We find that our adaptive method can typically improve the simulation accuracy by an order of magnitude, for a given circuit depth.

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Trainability of Parametrised Linear Combinations of Unitaries

Nikhil Khatri, Stefan Zohren, Gabriel Matos

A principal concern in the optimisation of parametrised quantum circuits is the presence of barren plateaus, which present fundamental challenges to the scalability of applications, such as variational algorithms and quantum machine learning models. Recent proposals for these methods have increasingly used the linear combination of unitaries (LCU) procedure as a core component. In this work, we prove that an LCU of trainable parametrised circuits is still trainable. We do so by analytically deriving the expression for the variance of the expectation when applying the LCU to a set of parametrised circuits, taking into account the postselection probability. These results extend to incoherent superpositions. We support our conclusions with numerical results on linear combinations of fermionic Gaussian unitaries (matchgate circuits). Our work shows that sums of trainable parametrised circuits are still trainable, and thus provides a method to construct new families of more expressive trainable circuits. We argue that there is a scope for a quantum speed-up when evaluating these trainable circuits on a quantum device.

arXiv:2506.22310•Jun 27, 2025•0 citations
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to approximate a Taylor series by truncating after some order. Here we present an adaptation of that method, optimized for Hamiltonians with terms of widely varying magnitude, as is commonly the case in electronic structure calculations. We show that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative procedure. We obtain bounds on the simulation error for this generalized truncated Taylor method, and for a range of molecular simulations, we report these bounds as well as exact numerical results. We find that our adaptive method can typically improve the simulation accuracy by an order of magnitude, for a given circuit depth.
A principal concern in the optimisation of parametrised quantum circuits is the presence of barren plateaus, which present fundamental challenges to the scalability of applications, such as variational algorithms and quantum machine learning models. Recent proposals for these methods have increasingly used the linear combination of unitaries (LCU) procedure as a core component. In this work, we prove that an LCU of trainable parametrised circuits is still trainable. We do so by analytically deriving the expression for the variance of the expectation when applying the LCU to a set of parametrised circuits, taking into account the postselection probability. These results extend to incoherent superpositions. We support our conclusions with numerical results on linear combinations of fermionic Gaussian unitaries (matchgate circuits). Our work shows that sums of trainable parametrised circuits are still trainable, and thus provides a method to construct new families of more expressive trainable circuits. We argue that there is a scope for a quantum speed-up when evaluating these trainable circuits on a quantum device.