# Research Topics

**Benchmarking quantum hardware**

Conventional methods for quantum fidelity estimation, such as quantum state tomography and randomized benchmarking, are not scalable to large system sizes as too many measurements are needed due to the exponential scaling of Hilbert space dimension. Hence, to benchmark a large-scale quantum device, a new protocol needs to be considered. We have developed a new approach for quantum device benchmarking that can be widely applicable to a variety of quantum many-body platforms including superconducting qubits, trapped ions, itinerant quantum particles in optical lattices, and Rydberg atom arrays. Specifically, our method relies on the universal emergence of random quantum state ensembles during chaotic quantum dynamics, satisfying the condition for being quantum state k-designs in quantum information processing. Inspired by this device-agnostic universality in quantum many-body systems, we have designed an experimentally efficient benchmarking method to verify large-scale quantum devices with only a few measurements. Our group will continue to implement, test, and further improve the benchmarking protocol that could potentially serve as a standardized tool for characterizing quantum hardware on a system level.

## References

**Benchmarking quantum simulators using quantum chaos**

D. K. Mark, J. Choi, A. L. Shaw, M. Endres, and S. Choi**arXiv**:2205.12211* *(2022)

**Preparing random states and benchmarking with many-body quantum chaos**

J. Choi*, A. L. Shaw*, I. S. Madjarov, X. Xie, J. Covey, J. Cotler, D. K. Mark, H. Y. Huang, A. Kale, H. Pichler, F. G.S.L. Brandão, S. Choi, and M. Endres (*equal contribution)**Nature ,** 613, 468 (2023)

** Robust preparation of useful quantum states**

Coherent control fields applied to quantum devices are versatile tools for a myriad of applications ranging from quantum simulation and computing to quantum metrology. Recently, we have developed a unified framework of dynamic Hamiltonian engineering schemes based on periodic (Floquet) pulse sequences, which can be tailored for a broad range of quantum hardware. In view of quantum simulation and information processing, such dynamical Hamiltonian engineering protocols allow for the exploration of a rich interplay between interactions, disorder, and dimensionality in nonequilibrium quantum dynamics, as well as the search for new phases of matter in driven quantum systems. Crucially, however, experimental quantum devices are not perfectly isolated and can undesirably interact with uncontrolled environments. To protect large quantum systems from decoherence and prepare a desired target quantum state with high fidelity, it is essential to understand the effects of noise and dissipation by considering the microscopic details of an experimental platform. To this end, our group aims to develop theoretical models and engineering protocols for open quantum system dynamics, which will provide insight and guidance on how to prepare useful entangled quantum states in noisy quantum devices for practical quantum applications.

## References

**Robust dynamic Hamiltonian engineering of many-body spin systems**

J. Choi*, H. Zhou*, H. S. Knowles, R. Landig, S. Choi, and M. D. Lukin (*equal contribution)**Physics Review X**,** **10, 031002 (2020)

** Quantum chaos and information scrambling**

Quantum chaos in many-body systems provides a bridge between statistical mechanics and quantum physics and plays a central role in understanding the universal properties of complex quantum many-body systems, such as energy spectra and quantum thermalization. While conventional methods of studying quantum chaos often rely on random ensembles of quantum states and Hamiltonians, we have recently discovered that random quantum state ensembles are naturally encoded in a single global wavefunction resulting from chaotic quantum many-body dynamics. Crucially, the emergence of random quantum state ensembles is the universal property of strongly interacting many-body systems, which can be uncovered when the correlations between complementary subsystems are properly captured. In view of quantum information processing, our group is interested in understanding how local information encoded in qubits spreads over time as a result of chaotic many-body dynamics, which is associated with the thermalization of a local subregion in closed quantum systems.

## References

**Preparing random states and benchmarking with many-body quantum chaos**

J. Choi*, A. L. Shaw*, I. S. Madjarov, X. Xie, J. Covey, J. Cotler, D. K. Mark, H. Y. Huang, A. Kale, H. Pichler, F. G.S.L. Brandão, S. Choi, and M. Endres (*equal contribution)**Nature ,** 613, 468 (2023)

**Emergent quantum state designs from individual many-body wavefunctions**

J. S. Cotler, D. K. Mark, H.-Y. Huang, F. Hernandez, J. Choi, A. L. Shaw, M. Endres, and S. Choi**Physics Review X Quantum**, 4, 010311 (2022)

**Critical thermalization of a disordered dipolar spin system in diamond**

G. Kucsko*, S. Choi*, J. Choi*, P. C. Maurer, H. Sumiya, S. Onoda, J. Isoya, F. Jelezko, E. Demler, N. Y. Yao, and M. D. Lukin (*equal contribution)**Physics Review Letters,** 121, 2 (2018)

**Depolarization dynamics in a strongly interacting solid-state spin ensemble**

J. Choi*, S. Choi*, G. Kucsko*, P. C. Maurer, B. J. Shields, H. Sumiya, S. Onoda, J. Isoya, E. Demler, F. Jelezko, N. Y. Yao, and M. D. Lukin (*equal contribution)**Physics Review Letters,** 118, 093601 (2017)

## Quantum matter out of equilibrium

Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. Out-of-equilibrium systems can display a rich variety of phenomena, including self-organized synchronization and dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter; for example, the interplay between periodic driving, disorder, and strong interactions has been shown to result in exotic ‘time-crystalline’ phases, in which a system exhibits temporal correlations at integer multiples of the fundamental driving period, breaking the discrete time-translational symmetry of the underlying drive. Besides the time-crystalline phase, a number of remarkable phenomena in quantum dynamics have recently been observed in driven many-body systems consisting of ten to a few hundred particles. All these observations raise important questions about the role of disorder, long-range interactions, and coupling to the environment in driven systems, and open up several new avenues for fundamental studies and potential applications. To this end, our group focuses on developing novel methods to realize exotic dynamical phases in more complex driven Hamiltonians and to explore whether such phases can be used to create and stabilize coherent quantum superposition states for applications such as quantum metrology.

## References

**Observation of discrete time-crystalline order in a disordered dipolar many-body system**

S. Choi*, J. Choi*, R. Landig*, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, C. von Keyserlingk, N. Y. Yao, E. Demler, and M. D. Lukin (*equal contribution)**Nature,** 543, 221 (2017)*News & Views: Marching to a different quantum beat*

**Probing quantum thermalization of a disordered dipolar spin ensemble with discrete time-crystalline order**

J. Choi*, H. Zhou*, S. Choi, R. Landig, W. W. Ho, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, D. A. Abanin, and M. D. Lukin (*equal contribution)**Physics Review Letters, **122, 043603** **(2019)

**Ultrasensitive quantum many-body sensors**

Quantum sensing is one of the most promising near-term applications of quantum devices. While in principle, entanglement between quantum sensors can boost sensitivities from the standard quantum limit to the so-called Heisenberg limit, in practice, this sensitivity improvement can be challenged by undesired decoherence from the environment. Thus, it is of great importance to investigate a subtle competition between entanglement and decoherence to leverage a metrological gain in ensemble-based quantum sensing. We have designed a robust control pulse sequence for ensemble-based magnetic-field sensing, and have achieved the record-breaking AC-field sensitivity using NV centers in a black diamond. Besides the NV ensemble, we have also developed a novel control pulse sequence for a rare-earth ion qubit that enables efficient polarization and manipulation of lattice nuclear spins in nuclear spin-rich host crystals, demonstrating their potential as a high-precision quantum ensemble sensor. To further enhance sensitivity, our group is interested in engineering strong interactions between sensing particles to create an entanglement structure optimized for quantum sensing. For example, one possibility is to make use of time-crystalline states to demonstrate such entanglement-assisted metrology.

## References

**Quantum metrology with strongly interacting spin systems**

H. Zhou*, J. Choi*, S. Choi, R. Landig, A. M. Douglas, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, P. Cappellaro, H. S. Knowles, H. Park, and M. D. Lukin (*equal contribution)**Physics Review X**,** **10, 031003 (2020)

## Nanoscale quantum thermometry

We are also keen to employ high-precision quantum sensors in various fields such as biology and chemistry. For example, it is well known that temperature is a key control parameter of biological processes, but measuring and controlling temperatures on a cellular-length scale in living organisms remains an outstanding challenge. Applying nanoscale-thermometry techniques to early embryos, we demonstrated that cell divisions can be studied in a highly controlled manner using local laser heating and real-time in vivo temperature readout. Specifically, nitrogen-vacancy centers in nanodiamonds, incorporated into the cells, allow us to map out the temperature distribution of a locally heated embryo with submicrometer spatial resolution and high sensitivity. The simultaneous cell-division imaging under controlled laser heating is used to achieve cell-cycle timing control and inversion, providing insights into timing-regulation mechanisms during early embryogenesis. Inspired by these successful demonstrations, we aim at developing novel techniques and protocols for various interdisciplinary applications, with a focus on improving the sensitivity of nanoscale quantum sensors.

## References

**Probing and manipulating embryogenesis via nanoscale thermometry and temperature control**

J. Choi*, H. Zhou*, R. Landig, H.-Y. Wu, X. Yu, S. V. Stetina, G. Kucsko, S. Mango, D. Needleman, A. D. T. Samuel, P. Maurer, H. Park, and M. D. Lukin (*equal contribution)**PNAS (Proc. Natl. Acad. Sci.)**,** **117, 14636 (2020)

**Stepwise ligand-induced self-assembly for facile fabrication of nanodiamond–gold nanoparticle dimers via noncovalent biotin–streptavidin interactions**

M. S. Chan, R. Landig, J. Choi, H. Zhou, X. Liao, M. D. Lukin, H. Park, and P. K. Lo**Nano Letters,** 19, 3 (2019)