In a comprehensive review paper on quantum error mitigation by Cai et al. (arXiv:2210.00921), the authors posed an open problem: what is the full landscape of the “zoo” of QEM techniques? I recently launched a website to help address this: the QEM Zoo. It’s a living catalog of quantum error mitigation and suppression techniques, inspired by the Complexity Zoo and the Error Correction Zoo. The site organizes techniques into protocols, supporting methods, noise models, and applications—all searchable and filterable.

In a previous post, I gave a high-level overview of zero-noise extrapolation (ZNE) and how we can increase the noise of quantum circuits for ZNE using a technique known as quantum circuit unoptimization. In this post, I’ll describe a technique that my colleague Andrea Mari and I came up with called layerwise Richardson extrapolation (LRE), which can be thought of as a generalization of standard ZNE. The paper can be found on arXiv (arXiv:2402.

In the quantum world, things are often weird. One of the classic sources of weirdness is entanglement, the “spooky action at a distance” that connects particles no matter how far apart they are. But there’s a lesser-known, yet equally fascinating, type of weirdness called “quantum nonlocality without entanglement.” This phenomenon occurs when you have a set of unentangled (product) quantum states that are, surprisingly, impossible to tell apart perfectly if you’re restricted to local operations.

While quantum computers have continued to improve over the past few years, it’s a known issue that error rates cannot be made low enough simply by improvements to the hardware. One approach to this problem is the domain of quantum error correction (QEC) which promises fault-tolerant devices that properly deals with the issue of noise. While the theory of QEC is well-established, the implementation of the theory is still a while away from being physically realizable.

I created the toqito software project back in early 2020 as a pet project for delving into some research questions I wanted to pursue in quantum information but felt were lacking in the Python community. When I was a Ph.D. student, having software like toqito would have been indispensible for rapidly prototyping ideas and attacking problems numerically. I’ve been continuing to build my quantum information numerical arsenal that has been a real feather in my cap when probing into particularly thorny research questions and it’s also been a ton of fun to build and to watch grow.

Let \(n\) be an integer, let \(\mathcal{X}\) be a complex Euclidean space, let \(\rho_i \in \text{D}(\mathcal{X})\) be a pure quantum state represented as a density operator, and let $$ \eta = \left\{\left(\frac{1}{n}, \rho_1\right), \ldots, \left(\frac{1}{n}, \rho_n\right)\right\} \subset \mathcal{X} $$ be an ensemble of pure and mutually orthogonal quantum states. Define \(\eta^{\otimes 2}\) as the two-copy ensemble where $$ \eta^{\otimes 2} = \left\{\left(\frac{1}{n}, \rho_1 \otimes \rho_1\right), \ldots, \left(\frac{1}{n}, \rho_n \otimes \rho_n\right)\right\} \subset \mathcal{X} \otimes \mathcal{X}.

I’m going to discuss a conjecture that got me interested in the topic of “quantum state antidistinguishability”. Conjecture [Havlíček-Barret (2020)]: Let \(S = \{|\psi_1\rangle, \ldots, |\psi_n\rangle\} \subset \mathbb{C}^n\) be a set of \(n\) pure quantum states each of dimension \(n\). Then \(S\) is antidistinguishable when $$ |\langle \psi_i | \psi_j \rangle| \leq \frac{n-2}{n-1} $$ for all \(i \neq j\). Before unpacking this statement more formally, I want to mention some points that drew me to it: