**Title：**Quantum applications based on density matrix vectorization: a polynomial-time quantum algorithm for some hard ground state problems and an unconditionally decoherence-free quantum error mitigation method

**Speaker：** Zhong-Xia Shang University of Science and Technology of China

**Time：** 2024-05-08 19:15-2024-05-08 20:15

**Venue：**RM S327, MMW Building (腾讯会议：155-879-237 (pwd: 1984))

**Abstract: **

In this talk, we will give two quantum applications based on density matrix vectorization. Vectorizing density matrices has been a useful mathematical trick for simplifying many concepts in quantum information science. Here, we generalize the idea of density matrix vectorization by actually treating n-qubit density matrices as 2n-qubit pure states. We will show how this will make sense by introducing a universal and efficient measurement strategy. By doing so, powerful quantum applications emerge for both FTQC and NISQ devices.

For FTQC, we will give a polynomial-time quantum algorithm for solving the ground states of a class of classically hard Hamiltonians by combining the idea of density matrix vectorization and the Lindblad master equation. Unlike ground state quantum algorithms based on quantum phase estimation, this algorithm can solve some ground state problems efficiently even if the overlap between the initial state and the ground state is exponentially small. We will also give concrete constructions that are easy for this algorithm but hard for classical computers.

For the case of NISQ devices, the idea of density matrix vectorization can lead to an unconditionally decoherence-free quantum error mitigation (QEM) method. Different from the ideas of existing QEM methods that try to distill noiseless information from noisy quantum states, density matrix vectorization directly changes the way of encoding information and maps the density matrices of noisy quantum states to noiseless pure states, resulting an unconditionally decoherence-free QEM protocol. From the operational level, our protocol requires no knowledge of the noise model, no knowledge of the symmetry structures of problems, no ability to tune the noise strength, and no ancilla qubits for complicated controlled unitaries but only 2-qubit rotation unitaries before measurements. We will talk about various aspect of our protocol including the sampling complexity, the strong numerical results, and the combinations of our protocol with other QEM methods for further improvements.

**Short Bio: **

Zhong-Xia Shang is a PhD candidate from the University of Science and Technology of China mentored by Prof. Chao-Yang Lu. He received his bachelor's degree from the School of Gifted Young, University of Science and Technology of China. His current interests are mainly quantum algorithms ranging from NISQ to FTQC.