Jinzhao Sun

Jinzhao Sun

Research Topics

I have a broad interest in quantum computing, quantum information, and quantum many-body physics. Let us explore a few topics that I have been interested in.

Quantum computing

Quantum problems can be broadly classified into two categories: static problems and dynamics problems. Static problems correspond to finding a quantum system’s lowest energy state or, more generally, its eigenstate. Applications range from drug design to uncovering novel phases of matter, which, to most extent, can be transformed into an eigenstate problem. Dynamics problems include simulating the dynamics of a quantum system, for example, simulating the dynamics governed by a Hamiltonian, also known as Hamiltonian simulation. Applications include identifying dissipative phase transitions and studying information scrambling and transport.

I have been working on improving algorithmic complexity in the two general classes of quantum problems.

Eigenstate problems We have developed several quantum algorithms for finding the ground-state or excited states of a quantum system. One example is a near-optimal eigenstate preparation method, termed quantum algorithmic cooling, in collaboration with Pei and Xiao. The algorithmic cooling operates deterministically without relying on assumptions about parametrised circuits and can guarantee simulation accuracy with near-optimal query complexity in precision, gap, etc. The query complexity (of real-time evolution \(e^{-iHt}\)) for eigenstate property estimation matches the results by QSP and QETU. This shows an advantage over quantum phase estimation and variational methods. The query complexity for eigenenergy estimation achieves the Heisenberg limit, matching the result by QSP and the spectral filter algorithm in paper 1 by Lin and Tong. Find more information in our paper, “Universal quantum algorithmic cooling on a quantum computer” link. Some other related works include ground-state energy estimation in paper 2 by Wang et al, and ground-state property estimation in paper 3 by Zhang et al.

In more recent work in collaboration with Pei, Tom and Myungshik, we provided a full-stack design of a quantum algorithm which considers the gate complexity, as opposed to previous algorithms based on querying either block encoding of the Hamiltonian and time evolution \(e^{-iHt}\). We show that it maintains near-optimal system size and precision scaling. We compared the resource requirements (CNOT gates, T gates and qubit numbers) by state-of-the-art methods, including phase estimation, QSP, and QETU, in tasks of lattice models and molecular problems. For example, we can estimate the resources for typical complex compounds, like FeMoco and a cytochrome enzyme P450, commonly used for resource benchmarking (e.g., paper 1 and paper 2 by Google and paper 3 by Microsoft). The P450 Hamiltonians were provided by Georg and the project benefits from the discussion with Xiao, to whom I’d like to express gratitude.

The intermediate results in this work could find usefulness in other contexts. For example, the composite LCU framework can be useful for improving/analysing other early FTQC algorithms. We provided a toolbox for analysing resource requirements for these advanced methods when compiled at the gate level, which could be useful for resource estimations in the noisy intermediate-scale quantum (NISQ) and fault-tolerant quantum computing (FTQC) era. Find more information in our paper, “High-precision and low-depth eigenstate property estimation: theory and resource estimation” link.

Dynamics problems, i.e., simulating the dynamics of quantum systems, is a fundamental task in quantum physics and is believed to be a major application of quantum computers. Below, I introduce a few related works.

Perturbative approach to quantum dynamics simulation. Perturbation theory brings about great success in quantitative predictions of quantum mechanics. But, challenges remain in solving the major component and computing the power series. We addressed this challenge by developing a conceptually novel approach, perturbative quantum simulation (PQS), which exploits the complementary strength of quantum computing and perturbation theory. We demonstrated that PQS is applicable to simulate classically challenging systems, such as large systems with weak inter-subsystem interactions or intermediate systems with general interactions. Remarkably, PQS shows advantages over conventional quantum simulation algorithms concerning the quantum resource requirements and noise robustness. I have explored applications in interacting bosons, fermions, and quantum spins in different topological structures and studied different quantum phenomena on systems of up to 48 qubits, such as information propagation, charge-spin separation, and magnetism. Find more information in our paper, “Perturbative quantum simulation” link in collaboration with Suguru, Vlatlo, Patrick, Huiping and Xiao.

Adaptive product formulae. We introduced an adaptive product formula which can produce a compact quantum circuit for Hamiltonian simulation. We introduced a measurable quantifier to describe the dynamics simulation error. The simulation error is rigorously analysed. The adaptive product formula is proven to guarantee simulation accuracy, showing an advantage over conventional product formula methods or variational quantum algorithms. The dynamics simulation method can be used as a subroutine in other quantum algorithms, such as eigenstate problems. Our method largely reduces quantum resources for Hamiltonian simulation and thus enables practical implementation with near-term or early fault-tolerant quantum devices. Find more information in our paper, “Low-depth Hamiltonian simulation by an adaptive product formula” link.

High-precision Hamiltonian simulation. In more recent work, we introduced a new Hamiltonian simulation method that achieves near-optimal asymptotic scaling in nearly all the parameters, such as system size (number of qubits), time, and precision, in collaboration with Pei, Liang and Qi. This method offers several notable advantages (1) easy implementation (at most one ancillary qubit) (2) near-optimal system size scaling (3) high accuracy \(\log(\epsilon^{-1})\). Find more information in our paper, “Simple and high-precision Hamiltonian simulation by compensating Trotter error with a linear combination of unitary (LCU) operations” link.

Hybrid quantum-classical computing I have been extensively working on hybrid quantum-classical computing. Among this paradigm, variational quantum algorithms are one of the promising candidates. The basic idea is to use a small quantum computer to carry out a hard-to-compute subroutine and a classical computer for optimisation. Hybrid quantum-classical computing has gathered massive attention recently since its proposal. With Suguru, Xiao, Ying and Simon, we proposed variational algorithms for simulating open system dynamics and general processes. Find more information in our paper, “Variational quantum simulation of general processes” (link). An application is to simulate \(\lambda\phi^4\) scalar quantum field theories. We discussed the encoding of the field theory problem under different bases and in either real space or momentum space, variational state preparation, simulation of particle scattering, and resource requirements in collaboration with Junyu, Zimu, Han and Xiao. Find more information in our paper, “Towards a variational Jordan-Lee-Preskill quantum algorithm” link. Other applications in quantum many-body problems are discussed below.

Quantum simulation of molecules and materials

To facilitate the practical applications of quantum computing, I have worked with industrial partners to develop quantum embedding schemes tailored to solving physical problems, particularly in the domains of quantum materials and molecules. We emulated quantum hardware classically and tested the viability of quantum simulation for quantum many-body systems. In a collaborative project with Dingshun and colleagues, we have emulated different materials, from hydrogen chains to nickel oxides, with a problem size of up to 10,000 qubits before resource reduction. This was the largest-scale proof-of-principle quantum simulation in terms of the target problem size at that moment. These works have also stimulated new directions in pushing forward the applications of quantum computing by integrating advanced classical methods. Simulations of molecules and materials can be found link and link.

Quantum computing and spectroscopy

Estimating spectral features of quantum many-body systems has attracted great attention in material science and quantum chemistry. To achieve this task, various experimental and theoretical techniques have been developed, including spectroscopy techniques, and quantum simulation either by engineering controlled quantum devices or executing quantum algorithms. However, probing a quantum system’s behaviour is challenging and demands substantial resources for both approaches. For instance, a real probe by neutron spectroscopy requires access to large-scale facilities with high-intensity neutron beams, while quantum computing of eigenenergies, such as phase estimation, typically requires a long coherence time in engineering controlled quantum devices. In a recent project, we established a framework for probing the excitation spectrum of quantum many-body systems with quantum simulators. This is the first theoretical work that links spectroscopy and quantum simulation. There are many potential follow-up projects that can build upon it, such as understanding the spectral properties of many-body systems by integrating quantum computing and comparing them with experiments, aligning closely with the spectroscopy research. Moreover, it enables us to probe the spectroscopic features in the non-linear response; for example, resolving the continuum of the excitation spectrum by analysing the nonlinear susceptibility.

Find more information in our paper, “Probing spectral features of quantum many-body systems with quantum simulators” published in Nature Communications link in collaboration with Lucia, Myungshik, Andrew and Vlatko.

I have been thinking of the crossover between static problems and dynamics problems, well-established spectroscopy techniques and quantum computing, and many seemingly different subjects. Some philosophical discussions on the notion of quantum machine, quantum simulation and spectroscopy can be found in my thesis.

Quantum error mitigation and its transition to quantum error correction

Quantum error mitigation To effectively demonstrate the utility of quantum computing, we must confront challenges associated with the practical use of noisy quantum computers. Errors are an inherent aspect of quantum computing. Ensuring that quantum computing delivers accurate results in the presence of these errors is a critical consideration. Together with Suguru, Xiao, Simon and Vlatko, we initially proposed new QEM schemes to mitigate realistic noise described by Lindbladian appearing in both digital and analogue quantum devices. For noise from imperfections of the engineered Hamiltonian or additional noise operators, we showed it can be effectively suppressed by a new QEM method, termed stochastic QEM. Our method only requires accurate single qubit controls, and is thus applicable to all digital quantum computers and various analogue simulators. Find more information in our paper, “Mitigating realistic noise in practical noisy intermediate-scale quantum devices” link.

Purification of quantum channels, a systematic way beyond QEM I have been wondering how to overcome the fundamental limits set up by QEM. This motivates us to think about an intermediate form between QEM and QEC. In recent work, we introduced an information-theoretic machinery, a commutation-derived quantum filter, to purify or correct quantum channels. This addresses the exponential sampling problem in QEM. Compared to QEC codes, this quantum filter does not need complicated encoding and decoding, and works in an error reduction sense. This work provides a systematic way to correct errors as the infidelity can be exponentially reduced with the number of ancillary qubits (with the maximum number saturating \(2n\) with \(n\) being the number of qubits) with only Clifford gates (cheap resources in the fault-tolerant regime).

Find more in our paper, “Purification and correction of quantum channels by commutation-derived quantum filters” link, with Sumit, Michael, Balint, and Myungshik.

Quantum computational chemistry

Quantum chemistry simulation with superconducting qubits

The application of quantum computing to computational chemistry faces various experimental and theoretical challenges. In a recent project with USTC and Peking, we addressed the critical challenges associated with solving molecular electronic structures using noisy quantum processors. We demonstrated a quantum simulation that in theory goes beyond the mean-field level.

The protocol presents significant improvements in the circuit depth and running time, key metrics for chemistry simulation. Through systematic hardware enhancements and the integration of error mitigation techniques, we push forward the limit of quantum computational chemistry and successfully scale up the implementation of VQE with an optimised unitary coupled-cluster ansatz. We produced high-precision results of the ground-state energy for molecules with error suppression by around two orders of magnitude; remarkably, we achieved chemical accuracy for small molecules. Find more information in our paper, “Experimental quantum computational chemistry with optimised unitary coupled cluster ansatz” link.

I’d like to thank Weitang, Vlatko, Myungshik, Heng, Changsu, Dingshun and Junjie for very useful related discussions and the great support for this project.

Quantum state measurements and a unified measurement framework

Apart from the circuit generation method developed in this work, fast quantum state measurement is crucial. This leverages the overlapped grouping method that was developed before. Find more information in our paper, “Experimental quantum state measurement with classical shadows” link, and “Overlapped grouping measurement: A unified framework for measuring quantum states” link. Interestingly, the current advanced measurement schemes, like the classical shadow method and its variants (derandomised shadow and adaptive shadow), can be understood in the framework presented in the paper and paper.

Minimal number of measurments for quantum state tomography

Pauli proposed a problem in 1933: can an arbitrary wave function be uniquely determined by measuring its position and momentum? This Pauli problem was further generalised and cast into a quantum information question: whether an unknown pure state can be uniquely determined using two measurement bases. The answer to the Pauli problem is, unfortunately, negative: four bases are needed in general. However, we prove that two measurements are sufficient to determine any pure state generated by quantum gates (with arbitrary, but finite, number of gates, say Clifford + T gates). More generally, we prove that they are informationally complete for determining any algebraic pure states, which covers all pure states that are physically accessible. Our work provides an affirmative answer to this long-standing question. Find more inforamtion in our paper.

Quantum many-body phenomena

I have been interested in interesting many-body phenomena since my undergraduate study. I wonder if we could have a better understanding of emergent quantum phenomena in quantum materials, especially high-temperature superconductors and magnetic materials. In my undergraduate thesis, I explored the microscopic origin of electronic nematic order in iron-selenide-based superconductors advised by Yuan Li. Drop me a line if you’d like to know more about my undergraduate thesis.

A longstanding question in iron-based superconductors is why superconductivity appears, but the magnetic order is absent in FeSe. It is important because it will enhance our understanding of the mechanism of unconventional superconductivity. One scenario is that the stripe magnetic order in FeSe is absent because of the development of other competing instabilities, in particular, the in-plane frustrated magnetic interactions. The results of a series of experiments suggest a ferromagnetic inter-layer coupling in FeSe, which sheds light on the absence of magnetic order. Some interesting findings on the \(L\) modulation in FeSe-based superconductors are shown in the paper.

Some other works on unconventional superconductivity, magnetism, and topological materials can be found here and here.

Other research topics will be updated later.