Related papers: Fast stabilizer state preparation via AI-optimized…
We show how to prepare any graph state of up to 12 qubits with: (a) the minimum number of controlled-Z gates, and (b) the minimum preparation depth. We assume only one-qubit and controlled-Z gates. The method exploits the fact that any…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
Highly entangled quantum states are an ingredient in numerous applications in quantum computing. However, preparing these highly entangled quantum states on currently available quantum computers at high fidelity is limited by ubiquitous…
Quantum state preparation is a crucial process within numerous quantum algorithms, and the need for efficient initialization of quantum registers is ever increasing as demand for useful quantum computing grows. The problem arises as the…
We start by studying the subgroup structures underlying stabilizer circuits and we use our results to propose a new normal form for stabilizer circuits. This normal form is computed by induction using simple conjugation rules in the…
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of…
We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…
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…
Recent work has explored using the stabilizer formalism to classically simulate quantum circuits containing a few non-Clifford gates. The computational cost of such methods is directly related to the notion of stabilizer rank, which for a…
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…
Graph states are a key resource for measurement-based quantum computation and quantum networking, but state-preparation costs limit their practical use. Graph states related by local complement (LC) operations are equivalent up to…
We study the complexity of learning quantum states in various models with respect to the stabilizer formalism and obtain the following results: - We prove that $\Omega(n)$ $T$-gates are necessary for any Clifford+$T$ circuit to prepare…
One of the primary objectives in the field of quantum state learning is to develop algorithms that are time-efficient for learning states generated from quantum circuits. Earlier investigations have demonstrated time-efficient algorithms…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
Stabilizer circuits play an important role in quantum error correction protocols, and will be vital for ensuring fault tolerance in future quantum hardware. While stabilizer circuits are defined on the Clifford generating set, {H, S, CX},…
Stabilizer states form an important class of states in quantum information, and are of central importance in quantum error correction. Here, we provide an algorithm for deciding whether one stabilizer (target) state can be obtained from…
Minimizing the use of CNOT gates in quantum state preparation is a crucial step in quantum compilation, as they introduce coupling constraints and more noise than single-qubit gates. Reducing the number of CNOT gates can lead to more…
We tackle the problem of Clifford isometry compilation, i.e, how to synthesize a Clifford isometry into an executable quantum circuit. We propose a simple framework for synthesis that only exploits the elementary properties of the Clifford…
Since quantum computing is currently in the NISQ-Era, compilation strategies to reduce the number of gates executed on specific hardware are required. In this work, we utilize the concept of synthesis of a data structure called Clifford…
Graph states are generalized from qubits to collections of $n$ qudits of arbitrary dimension $D$, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2…