IBM Japan
“High-precision energy calculation method for large-scale molecules and solids using quantum computers” was published in a specialized journal published by Nature Research.
Developing a new quantum calculation method that combines tensor networks and quantum Monte Carlo
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Mitsubishi Chemical Group*1 (hereinafter referred to as “Mitsubishi Chemical”), Keio University (location: Minato-ku, Tokyo, President: Kohei Ito, hereinafter referred to as “Keio University”), and IBM Japan, Inc. (head office: Minato-ku, Tokyo) Tokyo, President and CEO: Akio (hereinafter referred to as “IBM Japan”) will conduct research at the IBM Quantum Network Hub*2 (in the Keio Mass Quantum Computing Center) for the purpose of calculating the energy of large-scale molecules and solids with high precision. We are pleased to announce that we have developed a new calculation method using a quantum computer, and that the paper has been published in the world-authorized journal “NPJ Quantum Information” published by Nature Research.
Mitsubishi Chemical, Keio University, and IBM Japan are using hybrid tensor networks (HTN), a problem decomposition method, and quantum Monte Carlo (QMC), a high-precision calculation method, to accurately determine the energy of large-scale molecules and solids. We have developed a combination of “HTN+QMC” and a “pseudo-Hadamard test” that efficiently calculates the overlap between quantum states on a quantum circuit. Using these methods, we calculated the energy of a photochromic model molecule on IBM’s gated commercial quantum computer “IBM Quantum System One” and determined the ground state with a high accuracy of 0.042 ± 2.0 milli-Hartree, which is comparable to a noise-free simulator. I succeeded in asking.
The results of this research are expected to pave the way for highly accurate analysis of the physical properties of large-scale molecules and solids that exceed the size that can be handled by a single quantum computer.
Mitsubishi Chemical, Keio University, and IBM Japan will continue to establish quantum computer technology for use in a wide range of material development.
*1: Mitsubishi Chemical Group is the collective name for Mitsubishi Chemical Group Corporation and its group companies.
*2: A cutting-edge quantum computer research center established by Keio University and IBM Japan in May 2018 at Keio University’s Faculty of Science and Engineering. IBM Quantum Hub is Asia’s first IBM Quantum Hub, which enables the cloud use of cutting-edge quantum computers developed by IBM, and Mitsubishi Chemical is participating as a founding member as a joint industry-academia research base. *3: URL of published paper = https://www.nature.com/articles/s41534-024-00851-8 that’s all
For your reference
[Points of this research]
・Developed HTN+QMC*4, a large-scale, high-precision energy calculation method, by combining a hybrid tensor network, which is a partitioning method, and quantum Monte Carlo, a high-precision calculation method. ・Developed a pseudo-Hadamard test that efficiently calculates the overlap between quantum states
・Expectations for high-resolution understanding of physical properties of large-scale molecules and solids
【background】
The physical properties of molecules and solids can be determined by calculating the state of the electrons contained in the substance. However, the cost of calculating electronic states increases exponentially with the number of electrons, so current calculations are performed using approximations. DFT*6, which approximates electronic correlation, is widely used to calculate the ground state of electrons*5, but this method has the problem of not being accurate enough for materials with complex electronic structures where Coulomb repulsion is strong. .
Quantum computers are attracting attention as a solution to this problem because they are capable of calculations that conventional (classical) computers cannot perform due to quantum entanglement*7 and quantum superposition*8. However, current quantum computers are limited in the number of qubits and gates, so there has been a need for large-scale, high-precision calculation methods that exceed the performance of quantum computers alone.
[Image 1: https://prtimes.jp/i/46783/506/resize/d46783-506-fbc97d31143897605b56-0.png&s3=46783-506-365fca87c75cd512fc807cc751759352-196×169.png ]
Figure 1. Calculated structure of monoallyldiimidazole. Gray represents carbon, white represents hydrogen, and blue represents nitrogen.
[This result]
In this research, in addition to [A] HTN+QMC, which combines the partitioning method and high-precision calculation method, [B] we developed a pseudo-Hadamard test that efficiently calculates the overlap between quantum states required for HTN+QMC. .
[A] Development of large-scale, high-precision energy calculation method “HTN+QMC” using the division method and high-precision calculation method
In this study, we adopted hybrid tensor network (HTN) as the partitioning method and quantum Monte Carlo (QMC) as the
high-precision calculation method.
Hybrid tensor networks [Figure 2(a)] are a method that combines quantum and classical computers, dividing quantum states larger than the size of a quantum computer into smaller tensors (blocks). In this research, each tensor is handled using a quantum computer, and connections between tensors are handled using a classical computer. This method is called a hybrid tensor network because it uses both quantum and classical techniques. This design allows us to obtain large-scale quantum states while making full use of quantum computers. For example, a 100-bit quantum computer can generate 10,000-bit quantum states.
Quantum Monte Carlo [Figure 2(b)] is a highly accurate energy calculation method, and it is said that calculation accuracy can be improved by using a quantum computer as part of the calculation flow in quantum Monte Carlo. For example, by using the quantum state generated within a quantum circuit*9 during energy evaluation, it is expected that evaluation accuracy will improve.
The newly developed “HTN+QMC” [Fig. 2(c)] uses a hybrid tensor network to generate quantum states, and solves chemical calculation problems with spin orbits larger than the size of a quantum computer. This is a method that allows you to perform quantum Monte Carlo using
[Image 2: https://prtimes.jp/i/46783/506/resize/d46783-506-cbab5af2009698419d87-1.png&s3=46783-506-f8f3bf5072f81e921559a112cd07f8c8-1438×919.png ]
Figure 2. Overview of HTN+QMC
(a) Hybrid tensor network (HTN). In this study, we used a two-layer tree-type tensor network consisting of an orange lower tensor and a blue upper tensor. Each tensor is composed of quantum circuits. Divide the model into groups of qubits (=spin orbits) and assign them to each lower tensor. The upper tensor is used to integrate the lower tensor. (b) Quantum Monte Carlo (QMC). In the complete configuration interaction Monte Carlo used in this study, an approximate ground state is generated by changing the amplitude of the quantum state based on stochastic imaginary time evolution. The amplitude color represents the sign of the amplitude.
(c) HTN+QMC. In QMC calculations, by using the quantum state generated by HTN for the energy evaluation formula, projected energy, it is expected that the accuracy of QMC will improve for large-scale systems.
[B] Development of the “pseudo-Hadamard test” to efficiently calculate the overlap between quantum states
To perform HTN+QMC, it is necessary to calculate the overlap between quantum states. The calculation steps are as shown in Figure 3(a): 1. Prepare a quantum gate to generate an approximate ground state by optimization etc., 2. Entangle the obtained gate and auxiliary bits, and obtains the overlap by performing control calculations (red part in the figure). Step 2 is called the Hadamard test, and there is a problem in that the calculation cost increases depending on the number of gates prepared during execution. In particular, superconducting quantum computers are a serious problem because they are not good at performing operations between qubits that are far apart. The newly developed “Pseudo-Amadal test” [Figure 3(a) bottom] has the following advantages: 1. By optimizing for a quantum gate that involves auxiliary bits at the time of quantum gate optimization, 2. The cost of overlap calculation The increase can be avoided [Figure 3(b)]. In general overlap calculation using the Hadamard test, it is necessary to perform a control operation on the gate, but in this method, the overlap is calculated without using this explicit control operation, so it can be used as a pseudo-Hadamard test. I named it.
By combining the methods [A] and [B] developed this time, we can calculate the ground state of monoallyldiimidazole (Figure 1), a photochromic*10 model molecule, using IBM’s gated commercial quantum computer “IBM Quantum System One.” ” was used. As a result, we were able to calculate the ground state with a high accuracy of 0.042±2.0 milli-Hartree, which is comparable to a noise-free simulator (generally, the accuracy required to understand chemical phenomena is 1.6 milli-Hartree). It has been).
[Image 3: https://prtimes.jp/i/46783/506/resize/d46783-506-c28ccf0ba332af436a4f-2.png&s3=46783-506-dde593dd36f6429982abf07e5de84899-1438×1647.png ]
Figure 3. Overview of pseudo-Hadamard test and resource comparison (a) Overview of the pseudo-Hadamard test. Calculate the overlap between the quantum state you want to generate in the quantum circuit and the orthogonal basis of index [see Figure 2(a)]. The upper part of the figure is the conventional method, and the lower part is the newly developed method. is a gate for generating , for example, it consists of a group of gates like the one in the center of the figure (the gate group inside the dotted line is repeated multiple times). Note that is a gate for generating , which can be easily implemented.
(b) Comparison of the number of 2-qubit gates required in Hadamard test and pseudo-Hadamard test *11
[Future outlook]
The newly developed HTN+QMC is a method developed to calculate the ground state of chemical substances, but it can be applied to a wide range of tasks such as machine learning and optimization. In addition, the pseudo-Hadamard test is not limited to HTN+QMC, but can be applied to general overlaps between quantum states and transition amplitudes. Therefore, this research can be said to open a new path not only to chemical calculations but also to high-precision calculations using quantum computers for large-scale tasks.
[Term explanation]
*4：HTN+QMC
Abbreviation for hybrid tensor network + quantum Monte Carlo developed in this research.
*5: Ground state
lowest energy electronic state.
*6: DFT
Abbreviation for density functional theory method.
*7: Quantum entanglement
The property of a qubit being in multiple states at the same time. *8: Quantum superposition
A relationship in which the states of multiple qubits are mutually dependent. *9: Quantum circuit
A combination of quantum gates and measurements that control the quantum state of a qubit.
*10: Photochromic
The property of a material that changes color in response to changes in the intensity of light.
*11: Comparison of number of 2-qubit gates
Assuming gate depth = number of system qubits for nearest connected device. In the Hadamard test, we estimated the case where a round trip using bit swapping occurs from the original position to the vicinity of the auxiliary bit when performing control calculations for each CNOT gate from the auxiliary bit.
-Co-author list-
・Mitsubishi Chemical Group: Shiyu Kanno, Takao Kobayashi, Ling Taka ・IBM Research-Tokyo: Hajime Nakamura
・Keio University: Miho Hatanaka, Jisho Gomachi, Naoki Yamamoto [Reference press release]
・“A new calculation method using quantum computers to determine the energy of photofunctional materials” was published in a specialized journal published by Nature Research (February 9, 2023)
https://www.mcgc.com/news_release/pdf/01485/01723.pdf
・Research results on prediction of organic EL luminescent material performance published in Nature specialized journal (May 26, 2021) https://www.mcgc.com/news_mcc/2021/__icsFiles/afieldfile/2021/05/26/qhubjp.pdf that’s all
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