Research interest: Quantum error correction Quantum devices

**Quantum Bespoke** error correction codes

**Quantum Bespoke**error correction codes

A quantum code describes how quantum data is spread among several quantum systems. In practical settings, quantum codes must perform in the context of an explicit physical system. I am interested in **quantum bespoke **codes, where quantum codes are studied with constraints that must imposed by the physical system. Customized quantum error correction potentially greatly improves the fidelity of quantum devices.

# From linear algebra to bespoke quantum codes

Often we want to design a quantum code to satisfy constraints imposed by the physical system. To obtain feasible quantum codes, we often need to go beyond conventional quantum error correction frameworks to seek new codes. In a series of papers, I investigate using linear algebraic techniques to systematically construct tailor-made quantum codes.

**Related Papers:**

2020 Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians

Ramis Movassagh, Yingkai Ouyang

http://arxiv.org/abs/1912.09218

2019 *Permutation-invariant constant-excitation quantum codes for amplitude damping *

Yingkai Ouyang, R. Chao IEEE Transactions on Information Theory 66 (5), 2921 - 2933

# Permutation-invariant quantum codes

Permutation-invariant quantum codes, which are invariant under any permutation of the underlying physical systems, are one important family of **quantum bespoke **codes. Apart from the symmetry they exhibit, permutation-invariant quantum codes are also naturally immune against permutation errors that may occur during quantum communication. Moerover, permutation-invariant qubit codes lie in the ground space of any spin-1/2 Heisenberg ferromagnet, and are immune from the dynamics induced by any such quantum ferromagnet.

**Related Papers:**

2019 *Tight bounds on the simultaneous estimation of incompatible parameters*

J. S. Sidhu, Yingkai Ouyang, E. T. Campbell, P. Kok Physical Review X 11, 011028

2019 *Robust quantum metrology with explicit symmetric states *

Yingkai Ouyang, N. Shettell, D. Markham http://arxiv.org/abs/1908.02378

2019 *Permutation-invariant constant-excitation quantum codes for amplitude damping *

Yingkai Ouyang, R. Chao IEEE Transactions on Information Theory 66 (5), 2921 - 2933

2019 *Quantum storage in quantum ferromagnets*

Yingkai Ouyang Physical Review B 103, 14417

2019 *Initializing a permutation-invariant quantum error correction code*

C. Wu, Y. Wang, C. Guo, Yingkai Ouyang, G. Wang, XL Feng Physical Review A 99 (1), 012335

2017 *Permutation-invariant qudit codes from polynomials*

Yingkai Ouyang Linear Algebra and its Applications 532, Pages 43â€“59

2016 *Permutation-invariant codes encoding more than one qubit*

Yingkai Ouyang, J. Fitzsimons Physical Review A 93, 042340

2014 *Permutation-invariant quantum codes *

Yingkai Ouyang Physical Review A 90, 062317

# Bosonic quantum codes

Many physical systems can be described as bosonic systems. I am interested in designing **quantum bespoke **bosonic codes, which are for example naturally leave invariant by the Hamiltonian of a quantum bus. This makes such codes suitable for transmission in quantum buses.

**Related Papers:**

2019 *Permutation-invariant constant-excitation quantum codes for amplitude damping *

Yingkai Ouyang, R. Chao IEEE Transactions on Information Theory 66 (5), 2921 - 2933

# Quantum linear programming bounds

We introduce quantum weight enumerators for amplitude damping (AD) errors and work within the framework of approximate quantum error correction. In particular, we introduce an auxiliary exact weight enumerator that is intrinsic to a code space and moreover, we establish a linear relationship between the quantum weight enumerators for AD errors and this auxiliary exact weight enumerator. This allows us to establish a linear program that is infeasible only when AQEC AD codes with corresponding parameters do not exist.

**Related Papers:**

2020 *Linear programming bounds for quantum amplitude damping codes *

Yingkai Ouyang, C.Y. Lai 2020 IEEE International Symposium on Information Theory (ISIT), 1875-1879

# Asymptotics of quantum codes

**Related Papers:**

2019 *Causal limit on quantum communication*

R. Pisarczyk, Z. Zhao, Yingkai Ouyang, J. Fitzsimons, V. Vedral Physical Review Letters 123, 150502

2014 *Channel covariance, twirling, contraction, and some upper bounds on the quantum capacity*

Yingkai Ouyang Quantum Information and Computation, 14, Number 11\&12, 0917-0936

2014 *Concatenated codes can attain the Quantum Gilbert-Varshamov bound*

Yingkai Ouyang IEEE Transactions on Information Theory, 60, Issue 6, Pages: 1-6

# Error Avoiding quantum codes

Permutation-invariant quantum codes can avoid exchange errors. There are other forms of errors apart from exchange errors that is advantageous to avoid, such as coherent phase errors. Coherent phase errors can be avoided using constant-excitation (CE) codes.

**Related Papers:**

Avoiding coherent errors with rotated concatenated stabilizer codes, Yingkai Ouyang, npj Quantum Information 7 (87)

Faster quantum computation with permutations and resonant couplings ,Yingkai Ouyang, Y Shen, L Chen, Linear Algebra and its Applications 592, 270-286

Permutation-invariant constant-excitation quantum codes for amplitude damping , Yingkai Ouyang, R Chao, IEEE Transactions on Information Theory 66 (5), 2921 - 2933