Research Directions

Q. Zhao, Y. Zhou, A. F. Shaw, T. Li, and A. M. Childs, Phys. Rev. Lett., vol. 129, p. 270502 , QIP 2022 contributed talk

The algorithmic error of digital quantum simulations is usually explored in terms of the spectral norm distance between the actual and ideal evolution operators. In practice, this worst-case error analysis may be unnecessarily pessimistic. To address this, we develop a theory of average-case performance of Hamiltonian simulation with random initial states. We relate the average-case error to the Frobenius norm of the multiplicative error and give upper bounds for the product formula (PF) and truncated Taylor series methods. As applications, we estimate average-case error for the digital Hamiltonian simulation of general lattice Hamiltonians and k-local Hamiltonians. In particular, for the nearest-neighbor Heisenberg chain with n spins, the error is quadratically reduced from O(n) in the worst case to O(√n) on average for both the PF method and the Taylor series method. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models. We also apply our results to error analysis in the simulation of quantum scrambling.

W. Yu, J. Xu, and Q. Zhao, Communications Physics, vol. 8, no. 1, p. 340, 2025.

Quantum simulation represents a cornerstone application for quantum computers, offering the potential to solve classically intractable problems in physics, chemistry, and materials science. Despite being one of the most accessible simulation methods, the product formula encounters challenges due to the pessimistic gate count estimation. In this work, we elucidate how observable knowledge can accelerate quantum simulations. By focusing on specific knowledge of observables, we reduce product-formula simulation errors and gate counts in both short-time and arbitrary-time scenarios. For short-time simulations, we deliberately design and tailor product formulas to achieve size-independent errors for local and certain global observables. In arbitrary-time simulations, we reveal that Pauli-summation structured observables generally reduce average errors with a typically quadratic error reduction. Our advanced error analyses, supported by numerical studies, indicate improved gate count estimation. We anticipate that the explored speed-ups can pave the way for efficiently realizing quantum simulations and demonstrating advantages on near-term quantum devices.

P. Zeng, J. Sun, L. Jiang, and Q. Zhao, PRX Quantum, vol. 6, p. 010359, Mar 2025.

Trotter and linear combination of unitary (LCU) operations are two popular Hamiltonian simulation methods. The Trotter method is easy to implement and enjoys good system-size dependence endowed by commutator scaling, while the LCU method admits high-accuracy simulation with a smaller gate cost. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates after the 𝐾⁢th-order Trotter formula, we realize a better time scaling than 2⁢𝐾⁢th-order Trotter. Our first algorithm exponentially improves the accuracy scaling of the 𝐾⁢th-order Trotter formula. For a generic Hamiltonian, the estimated gate counts of the first algorithm can be 2 orders of magnitude smaller than the best analytical bound of fourth-order Trotter formula. In the second algorithm, we consider the detailed structure of Hamiltonians and construct LCU for Trotter errors with commutator scaling. Consequently, for lattice Hamiltonians, the algorithm enjoys almost linear system-size dependence and quadratically improves the accuracy of the 𝐾⁢th-order Trotter. For the lattice system, the second algorithm can achieve 3 to 4 orders of magnitude higher accuracy with the same gate costs as the optimal Trotter algorithm. These algorithms provide an easy-to-implement approach to achieve a low-cost and high-precision Hamiltonian simulation.

X. Yuan, J. Sun, J. Liu, Q. Zhao, and Y. Zhou, Phys. Rev. Lett., vol. 127, p. 040501, Jul 2021.

Here, we introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors, inheriting both their distinct features in efficient representation of many-body wave functions. With the example of hybrid tree tensor networks, we demonstrate efficient quantum simulation using a quantum computer whose size is significantly smaller than the one of the target system.

D. An, J.-P. Liu, D. Wang, and Q. Zhao*, Communications in Mathematical Physics, vol. 406, no. 8, p. 189, 2025.

We consider the one-shot problem of distilling pure coherence from a single instance of a given resource state. Specifically, we determine the distillable coherence with a given fidelity under incoherent operations (IO) through a generalization of the Winter-Yang protocol. We also relate the distillable coherence under strictly incoherent operations (SIO) to a constrained hypothesis testing.

Z.-D. Li, Q. Zhao (Co-first author), R. Zhang, L.-Z. Liu, X.-F. Yin, X. Zhang, Y.-Y. Fei, K. Chen, N.-L. Liu, F. Xu, Y.-A. Chen, L. Li, and J.-W. Pan, Phys. Rev. Lett., vol. 124, p. 160503, Apr 2020.

Here, for the first time, we demonstrate MDIEW for multipartite entangled states. We experimentally detect the genuine entanglement and the entanglement structure of a tripartite entangled state based on an eight-photon interferometry. Furthermore, with the verified multipartite entangled state, we demonstrate quantum randomness generation and open-destination quantum key distribution in an measurement-device-independent manner.

H. Lu, Q. Zhao (Co-first author), Z.-D. Li, X.-F. Yin, X. Yuan, J.-C. Hung, L.-K. Chen, L. Li, N.-L. Liu, C.-Z. Peng, Y.-C. Liang, X. Ma, Y.-A. Chen, and J.-W. Pan, Phys. Rev. X, vol. 8, p. 021072, Jun 2018.

Here, we propose two complementary families of witnesses for the identification of such structures. They are based, respectively, on the detection of entanglement intactness and entanglement depth, each applicable to an arbitrary number of subsystems and whose evaluation requires only the implementation of solely two local measurements. Our method is also robust against noises and other imperfections, as reflected by our experimental implementation of these tools to verify the entanglement structure of five different eight-photon entangled states. In particular, we demonstrate how their entanglement structure can be precisely and systematically inferred from the experimental measurement of these witnesses. In achieving this goal, we also illustrate how the same set of data can be classically postprocessed to learn the most about the measured system.

Y. Liu, Q. Zhao, M.-H. Li, J.-Y. Guan, Y. Zhang, B. Bai,W. Zhang,W.-Z. Liu, C.Wu, X. Yuan, H. Li, W. J. Munro, Z.Wang, L. You, J. Zhang, X. Ma, J. Fan, Q. Zhang, and J.-W. Pan, Nature, vol. 562, no. 7728, p. 548, 2018.

Here we present DIQRNG that is secure against quantum and classical adversaries10–12. We use state-of-the-art quantum optical technology to create, modulate and detect entangled photon pairs, achieving an efficiency of more than 78 per cent from creation to detection at a distance of about 200 metres that greatly exceeds the threshold for closing the ‘detection’ loophole of the Bell test.

H.-L. Huang, Q. Zhao, X. Ma, C. Liu, Z.-E. Su, X.-L.Wang, L. Li, N.-L. Liu, B. C. Sanders, C.-Y. Lu, and J.-W. Pan, Phys. Rev. Lett., vol. 119, p.050503, Aug 2017.

To date, blind quantum computing demonstrations require clients to have weak quantum devices. Here we implement a proof-of-principle experiment for completely classical clients. Via classically interacting with two quantum servers that share entanglement, the client accomplishes the task of having the number 15 factorized by servers who are denied information about the computation itself. This concealment is accompanied by a verification protocol that tests servers' honesty and correctness. Our demonstration shows the feasibility of completely classical clients and thus is a key milestone towards secure cloud quantum computing.