Related papers: Optimal algorithms for materializing stabilizer st…
Stabilizer states along with Clifford manipulations (unitary transformations and measurements) thereof -- despite being efficiently simulable on a classical computer -- are an important tool in quantum information processing, with…
Efficient simulation of quantum computers relies on understanding and exploiting the properties of quantum states. This is the case for methods such as tensor networks, based on entanglement, and the tableau formalism, which represents…
We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding…
We give a simple description of rectangular matrices that can be implemented by a post-selected stabilizer circuit. Given a matrix with entries in dyadic cyclotomic number fields $\mathbb{Q}(\exp(i\frac{2\pi}{2^m}))$, we show that it can be…
In this paper, we study the problem of learning an unknown quantum circuit of a certain structure. If the unknown target is an $n$-qubit Clifford circuit, we devise an efficient algorithm to reconstruct its circuit representation by using…
We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a…
In this work, we explore a new approach to designing both algorithms and error detection codes for preparing approximate ground states of molecules. We propose a classical algorithm to find the optimal stabilizer state by using excitations…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground…
We investigate the problem of synthesizing T-depth optimal quantum circuits over the Clifford+T gate set. First we construct a special subset of T-depth 1 unitaries, such that it is possible to express the T-depth-optimal decomposition of…
We investigate the problem of evaluating the output probabilities of Clifford circuits with nonstabilizer product input states. First, we consider the case when the input state is mixed, and give an efficient classical algorithm to…
Stabilizer states are a prime resource for a number of applications in quantum information science, such as secret-sharing and measurement-based quantum computation. This motivates us to study the entanglement of noisy stabilizer states…
In 2024, Kliuchnikov and Sch\"onnenbeck showed a connection between the Barnes Wall lattices, stabilizer states and Clifford operations. In this work, we study their results and relate them to the problem of lower bounding stabilizer ranks.…
Quantum error-correcting codes are used to protect qubits involved in quantum computation. This process requires logical operators, acting on protected qubits, to be translated into physical operators (circuits) acting on physical quantum…
We give a new algorithm for computing the robustness of magic - a measure of the utility of quantum states as a computational resource. Our work is motivated by the magic state model of fault-tolerant quantum computation. In this model, all…
We present novel algorithms to estimate outcomes for qubit quantum circuits. Notably, these methods can simulate a Clifford circuit in linear time without ever writing down stabilizer states explicitly. These algorithms outperform previous…
We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…
How entangled is a randomly chosen bipartite stabilizer state? We show that if the number of qubits each party holds is large the state will be close to maximally entangled with probability exponentially close to one. We provide a similar…
The quantum stabilizer formalism became foundational for understanding error correction soon after the realization of the first useful quantum error correction codes. Stabilizers provide a way to describe sets of quantum states which are…
For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate…