More Like this

1. Pauli spectrum and nonstabilizerness of typical quantum many-body states

   https://doi.org/10.1103/PhysRevB.111.054301  

   Turkeshi, Xhek; Dymarsky, Anatoly; Sierant, Piotr (February 2025, Physical Review B)

   An important question of quantum information is to characterize genuinely quantum (beyond-Clifford) resources necessary for universal quantum computing. Here, we use the Pauli spectrum to quantify how “magic,” beyond Clifford, typical many-qubit states are. We first present a phenomenological picture of the Pauli spectrum based on quantum typicality, and then we confirm it for Haar random states. We then introduce filtered stabilizer entropy, a magic measure that can resolve the difference between typical and atypical states. We proceed with the numerical study of the Pauli spectrum of states created by random circuits as well as for eigenstates of chaotic Hamiltonians. We find that in both cases, the Pauli spectrum approaches the one of Haar random states, up to exponentially suppressed tails. We discuss how the Pauli spectrum changes when ergodicity is broken due to disorder. Our results underscore the difference between typical and atypical states from the point of view of quantum information 

   more » « less
2. Quantum Lego Expansion Pack: Enumerators from Tensor Networks

   https://doi.org/10.1103/PRXQuantum.5.030313  

   Cao, ChunJun; Gullans, Michael J; Lackey, Brad; Wang, Zitao (July 2024, PRX Quantum)

   We provide the first tensor-network method for computing quantum weight enumerator polynomials in the most general form. If a quantum code has a known tensor-network construction of its encoding map, our method is far more efficient, and in some cases exponentially faster than the existing approach. As a corollary, it produces decoders and an algorithm that computes the code distance. For non-(Pauli)-stabilizer codes, this constitutes the current best algorithm for computing the code distance. For degenerate stabilizer codes, it can be substantially faster compared to the current methods. We also introduce novel weight enumerators and their applications. In particular, we show that these enumerators can be used to compute logical error rates exactly and thus construct (optimal) decoders for any independent and identically distributed single qubit or qudit error channels. The enumerators also provide a more efficient method for computing nonstabilizerness in quantum many-body states. As the power for these speedups rely on a quantum Lego decomposition of quantum codes, we further provide systematic methods for decomposing quantum codes and graph states into a modular construction for which our technique applies. As a proof of principle, we perform exact analyses of the deformed surface codes, the holographic pentagon code, and the two-dimensional Bacon-Shor code under (biased) Pauli noise and limited instances of coherent error at sizes that are inaccessible by brute force. Published by the American Physical Society2024 

   more » « less
3. Bounding the forward classical capacity of bipartite quantum channels

   https://doi.org/10.1109/TIT.2022.3233924  

   Ding, Dawei; Khatri, Sumeet; Quek, Yihui; Shor, Peter W.; Wang, Xin; Wilde, Mark M. (January 2023, IEEE Transactions on Information Theory)

   We present a quantum compilation algorithm that maps Clifford encoders, an equivalence class of quantum circuits that arise universally in quantum error correction, into a representation in the ZX calculus. In particular, we develop a canonical form in the ZX calculus and prove canonicity as well as efficient reducibility of any Clifford encoder into the canonical form. The diagrams produced by our compiler explicitly visualize information propagation and entanglement structure of the encoder, revealing properties that may be obscured in the circuit or stabilizer-tableau representation 

   more » « less
4. Extracting Topological Orders of Generalized Pauli Stabilizer Codes in Two Dimensions

   https://doi.org/10.1103/PRXQuantum.5.030328  

   Liang, Zijian; Xu, Yijia; Iosue, Joseph T; Chen, Yu-An (August 2024, PRX Quantum)

   In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The algorithm applies to ${\mathbb{Z}}_d$qudits, including instances where $d$is a nonprime number. This capability allows the identification of topological orders that differ from the ${\mathbb{Z}}_d$toric codes. It extends our understanding beyond the established theorem that Pauli stabilizer codes for ${\mathbb{Z}}_p$qudits (with $p$being a prime) are equivalent to finite copies of ${\mathbb{Z}}_p$toric codes and trivial stabilizers. The algorithm is designed to determine all anyons and their string operators, enabling the computation of their fusion rules, topological spins, and braiding statistics. The method converts the identification of topological orders into computational tasks, including Gaussian elimination, the Hermite normal form, and the Smith normal form of truncated Laurent polynomials. Furthermore, the algorithm provides a systematic approach for studying quantum error-correcting codes. We apply it to various codes, such as self-dual CSS quantum codes modified from the two-dimensional honeycomb color code and non-CSS quantum codes that contain the double semion topological order or the six-semion topological order. Published by the American Physical Society2024 

   more » « less
5. Error-correcting codes for fermionic quantum simulation

   https://doi.org/10.21468/SciPostPhys.16.1.033  

   Chen, Yu-An; Gorshkov, Alexey V.; Xu, Yijia (January 2024, SciPost Physics)

   Utilizing the framework of\mathbb{Z}_2 ${\mathbb{Z}}_2$lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of d=2,3,4,5,6,7, allowing correction of any\lfloor \frac{d-1}{2} \rfloor $\lfloor \frac{d-1}{2}\rfloor$-qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of d=3,4,5. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically. 

   more » « less