Preparation of tensor network states

1. ZYW*, D. Malz*, J.I. Cirac. Sequential generation of projected entangled-pair states. PRL (2022)

2. ZYW, D. Malz, J.I. Cirac. Efficient Adiabatic Preparation of Tensor Network States. PR Research (2023) (Letter)

3. D. Malz*, G. Styliaris*, ZYW* (alphabetical order), J.I. Cirac. Preparation of matrix product states with log-depth quantum circuits. PRL (2024)

4. ZYW, D. Malz. State preparation with parallel-sequential circuits. arXiv (2025)

Tensor network states (TNS), such as the matrix product states (MPS) and projected entangled pair states (PEPS), are paradigmatic states to describe the ground states of gapped Hamiltonians, and they include important states such as the cluster, W, GHZ, AKLT states. There is thus increasing interest in finding ways of preparing them in quantum computers or quantum simulators, either for quantum information applications like computing, metrology, communication, and networking, or as variational states for the study of many-body quantum systems. It is well-known that the MPS of the system size N can be prepared with circuit depth T=O(N). However, two pressing questions have not been fully resolved: Which subclass of high-dimensional PEPS can be efficiently prepared, and what is the optimal scaling for preparing different kinds of TNS?

Our works [1-4] are significant steps toward the efficient preparation of TNS. In [1,2], we develop schemes to efficiently prepare high-dimensional PEPS. In [1], we introduce Plaquette-PEPS, which is a subclass of PEPS that encodes important states such as the graph states and topologically ordered states. We provide an efficient scheme to prepare them with the circuit depth that scales with the linear dimension of the system, which is optimal for preparing states with topological order. In [2], we discover an adiabatic path that allows preparing short-range correlated TNS with evolution time T~ polylog N, which serves as the first deterministic method to create the high-dimensional AKLT states. In [3], we prove that one needs at least a logarithmically growing circuit depth to prepare short-range correlated MPS faithfully and develop an algorithm to prepare these MPS with such optimal scaling. By further utilizing measurements, we can prepare almost arbitrary MPS with circuit depth T=O(log log N), which is exponentially faster than known methods to prepare them. In [4], we introduce parallel-sequential (PS) circuits, a family of quantum circuit layouts that unify and generalize the brickwall and sequential circuits, which allows the efficient preparation of many-body ground states. 

Fig. (a) Sequential preparation of (long-range correlated) PEPS. (b) Adiabatic preparation of short-range correlated PEPS (such as AKLT states). (c) Preparation of MPS with log-depth circuits. (d) Parallel-sequential (PS) circuits. 

Kondo impurity in an attractive Fermi-Hubbard bath: Equilibrium and dynamics

5. ZYW*, T. Shi*, J. I. Cirac, E. Demler. Kondo impurity in an attractive Fermi-Hubbard bath: Equilibrium and dynamics. arXiv (2025)

Fig. (a) Kondo impurity in an attractive Hubbard bath. (b) First-order phase transition between the singlet and the doublet ground states. (c) Charge transport dynamics under bias voltage V. (d) Transport dynamical `phase diagram' with rich behaviors.

Physical platforms to create large-scale photonic entanglement

6. ZYW, D. Malz, A.G.-Tudela, J.I. Cirac,. Generation of photonic matrix product states with Rydberg atomic arrays. PR Research (2021)

7. ZYW, J.I. Cirac, D. Malz. Generation of photonic tensor network states with circuit QED. PRA (2022)

A key element in photonic quantum information processing is to prepare large-scale photonic entanglement. We design an efficient light-matter interface using sub-wavelength Rydberg atomic arrays to prepare optical photonic MPS in free space [6] and use a circuit QED system to prepare microwave photonic MPS and PEPS [7]. Both of our schemes can prepare a large number of entangled photons, and relevant experiments have demonstrated the effectiveness of these schemes. 

Fig. Generation and distribution of multi-photon entanglement with (a) Rydberg atomic arrays and (b) microwave cavity QED system.

Measuring quantum coherence using the interference fringes

[8] Y.T. Wang, J.S. Tang, ZYW, S. Yu, Z.J. Ke, X.Y. Xu, C.F. Li, G.C. Guo, "Directly measuring the degree of quantum coherence using interference fringes." PRL(2017)

In [8], we develop a method to measure quantum coherence directly using its most essential behavior—the interference fringes. The ancilla states are mixed into the target state with various ratios, and the minimal ratio that makes the interference fringes of the “mixed state” vanish is taken as the quantity of coherence. We also use the witness observable to witness coherence, and the optimal witness constitutes another direct method to measure coherence. For comparison, we perform tomography and calculate the L1 norm of coherence, which coincides with the results of the other two methods in our situation and shows the effectiveness of our method.

Fig. Experimental setup.