## Topic Overview

### Research and development organization

Research and Development Project Leader

Takeshi Sato (Associate Professor at the Graduate School of Engineering, the University of Tokyo)

Participating institutions (Educational)

The University of Tokyo / RIKEN / Okinawa Institute of Science and Technology Graduate University

Participating institutions(Corporate)

Quemix Corporation / JSR Corporation / Toyota Motor Corporation / International Business Machines Corporation / Mizuho Research & Technologies / Mitsubishi Chemical Corporation

### Characteristics of this topic

- Theory
- Common aspects among isolated electrons, periodic system electrons, and nuclear system Optimization and time evolution of both the many-body (quantum circuit) and one-body (orbital function) wave functions

- Implementation
- Modulation + Common interface Classical-quantum hybrid algorithms.

### Purpose of this topic

- Development of a common platform for molecular/solid-state/nuclear simulation.
- Advancement of simulation techniques.
- Classical–quantum hybrid simulation.

## Research Highlights

### Development of the solid-state version of TD-OUCCD

- The Time-Dependent Variational Quantum Solver (TD-VQS) was extended to the solid-state version of Time-Dependent Optimized Unitary Coupled Cluster with Doubles (TD-OUCCD).
- The solid-state version of TD-OUCCD extends the TD-OUCCD method developed for molecules to periodic systems and implements imaginary time evolution on a quantum circuit simulator.
- In this method, both orbital functions and quantum circuit parameters are optimized, allowing for high-precision calculations with fewer qubits compared to similar studies that optimize only the quantum circuit parameters.
- Applying the solid-state version of TD-OUCCD with Gaussian basis functions to a one-dimensional hydrogen chain confirmed its ability to accurately calculate the potential energy curve of the ground state

### Extension of TD-VQS

- The team is working on extending the to nuclear systems.
- The similarities and differences between the TD-VQS for isolated electron systems and nuclear many-body theory were organized. By extending the TD-VQS framework, a prototype computational code capable of handling multi-component quantum many-body systems,including atomic nuclei, was created.
- Variational Quantum Eigensolver (VQE) calculations for the ground state of a 6Li nucleus using a quantum circuit simulator were successfully performed.
- The application of the natural expansion of wave functions revealed that it is possible to construct an equivalent variational quantum circuit with fewer CNOT gates compared to similar previous studies.
- By applying the natural decomposition of wave functions, it was discovered that it is possible to construct a variational quantum circuit equivalent to those in previous similar studies with fewer CNOT gates.

### Quantum gate sequence search

- Using deep reinforcement learning, a search for quantum gate sequences was conducted to reproduce the probability distribution output by quantum computations.
- The discovered reinforcement quantum circuits exhibit output patterns similar to those of quantum inverse Fourier transform circuits but with fewer quantum gates.
- The discovered reinforcement quantum circuits were executed on a superconducting quantum computer, demonstrating that, at the current level of quantum gate errors, the lower-gate-count reinforcement quantum circuits improve the computational accuracy.
- Theoretical analysis revealed that the reinforcement quantum circuits achieve a simpler computational algorithm by extracting only the necessary computational processes.

### Cold atomic gases

- Research is being conducted on the phase transition from superfluid to insulator in two-component cold atomic gases.
- It has been discovered that when a small number of strongly correlated impurities are embedded in a large Bose-Einstein condensate (BEC), the impurities self-organize into a periodic structure within the matter wave lattice.
- The transition from superfluid to Mott insulator in lattice systems was studied,allowing for the simulation of phononic excitations in coupled many-body systems.
- Research on the correlation effects in quantum batteries is also being conducted,with simulations of these devices on quantum hardware.
- Simulation of quench dynamics in the Ising model was performed to determine the maximum amount of energy that can be extracted using optimal unitary operations.
- The optimization precision depends on the system size and correlations, and current benchmarking of algorithms is underway, with plans for future execution on quantum hardware.

## Future Prospects

- Completion of the development of a prototype for the solid-state version of the TD-VQS. To be implemented based on the time-dependent variational principle with zero-noise extrapolation incorporated.
- Completion of a prototype for the nuclear version of the TD-VQS. Development of the TD-VQS nuclear version code for real-time simulation of nuclear processes.
- Verification of a highly parallel quantum circuit simulator. Establishment of a computing environment using the Braket parallel quantum circuit simulator (https://github.com/naoki-yoshioka/braket).
- Embarking on applications to other quantum many-body systems, such as cold atomic gases. Analysis of the properties of phase transitions between new superfluid and insulator states in systems with interacting cold atoms.

Sharing a common simulation platform prototype to facilitate the development cycle.

- Development of a shared simulation infrastructure (Main Task).
- Advancement of the simulation infrastructure/integration with quantum embedding, quantum optimization, and quantum HPC.
- Integration of quantum AI with quantum simulation.
- Industry–academia co-creation/collaboration with participating industries.