Related papers: Fast generation of Pauli transfer matrices utilizi…
This paper considers two frequently used matrix representations -- what we call the $\chi$- and $\mathcal{S}$-matrices -- of a quantum operation and their applications. The matrices defined with respect to an arbitrary operator basis, that…
Simulating quantum physical processes has been one of the major motivations for quantum information science. Quantum channels, which are completely positive and trace preserving processes, are the standard mathematical language to describe…
Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…
We employ the compressed sensing (CS) algorithm and a heavily reduced data set to experimentally perform true quantum process tomography (QPT) on an NMR quantum processor. We obtain the estimate of the process matrix $\chi$ corresponding to…
We introduce a notion of commutativity between operators on a tensor product space, nominally Pauli strings on qubits, that interpolates between qubit-wise commutativity and (full) commutativity. We apply this notion, which we call…
Non-Markovian noise, arising from the memory effect in the environment, poses substantial challenges to conventional quantum noise suppression protocols, including quantum error correction and mitigation. We introduce a channel…
It is well-known that simulating quantum circuits with low but non-zero hardware noise is more difficult than without noise. It requires either to perform density matrix simulations (coming with a space overhead) or to sample over "quantum…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system. First we consider sparse quantum circuits such that each qubit…
Decomposing a matrix into a weighted sum of Pauli strings is a common chore of the quantum computer scientist, whom is not easily discouraged by exponential scaling. But beware, a naive decomposition can be cubically more expensive than…
This work presents an optimization-based scalable quantum neural network framework for approximating $n$-qubit unitaries through generic parametric representation of unitaries, which are obtained as product of exponential of basis elements…
The design and optimization of realistic architectures for fault-tolerant quantum computation requires error models that are both reliable and amenable to large-scale classical simulation. Perhaps the simplest and most practical…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, non-destructive measurements of Pauli observables. Any quantum circuit written in terms of the Clifford+$T$ gate set and having $t$ $T$ gates can be compiled into a…
Cross-platform verification is the task of comparing the output states produced by different physical platforms using solely local quantum operations and classical communication. While protocols have previously been suggested for this task,…
With continuing improvements on the quality of fabricated quantum devices, it becomes increasingly crucial to analyze noisy quantum process in greater details such as characterizing the non-Markovianity in a quantitative manner. In this…
Decomposing Pauli exponentials efficiently to quantum circuits has been the subject of intense research in recent years. Pauli exponentials are an essential component of many different quantum algorithms. Due to the error-prone nature of…
Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications. Recently, as a new approach to this problem, the task of agnostic state…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation,…