Related papers: Measurement-Assisted Clifford Synthesis
We propose protocols to implement non-Clifford logical gates between stabilizer codes by entangling into a non-Abelian topological order as an intermediate step. Generalizing previous approaches, we provide a framework that generates a…
The leading paradigm for performing computation on quantum memories can be encapsulated as distill-then-synthesize. Initially, one performs several rounds of distillation to create high-fidelity magic states that provide one good T gate, an…
We introduce an open-source software library Graphix, which optimizes and simulates measurement-based quantum computation (MBQC). By combining the measurement calculus with an efficient graph state simulator, Graphix allows the classical…
Magic states are a scarce resource for two-dimensional qubit stabilizer codes. Magic state cultivation was recently proposed to reduce the cost of magic state preparation by measuring the transversal Clifford operator of the color code.…
The standard approach to fault-tolerant quantum computation is to store information in a quantum error correction code, such as the surface code, and process information using a strategy that can be summarized as distill-then-synthesize. In…
We study measurements of the unitary generalization of Pauli operators. First, an analytical (constructive) solution to the eigenproblem of these operators is presented. Next, in the case of two subsystems, the Schmidt form of the…
We consider four-dimensional qudits as qubit pairs and their qudit Pauli operators as qubit Clifford operators. This introduces a nesting, $C_1^2 \subset C_2^4 \subset C_3^2$, where $C_n^m$ is the $n$th level of the $m$-dimensional qudit…
We propose a measurement scheme that validates the preparation of an $n$-qubit stabilizer state. The scheme involves a measurement of $n$ Pauli observables, a priori determined from the stabilizer state and which can be realized using…
Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the…
We propose a systematic framework to construct a (d+1)-dimensional stabilizer model from an initial generic d-dimensional abelian symmetry. Our approach builds upon the iterative gauging procedure, developed by one of the authors in [J.…
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…
We prepare two dimensional states generated by shallow circuits composed of (1) one layer of two-qubit CZ gate or (2) a few layers of two-qubit random Clifford gate. After measuring all of the bulk qubits, we study the entanglement…
We propose a theoretical control protocol designed for the dynamic synthesis of single qubit and four-level qudit quantum gates using external parameters, such as photonic Gaussian pulses and magnetic fields, in a microcavity quantum well…
A protocol is proposed to generate Bell states in two non-directly interacting qubits by means of repeated measurements of the state of a central ancilla connected to both qubits. An optimal measurement rate is found that minimizes the time…
Circuit synthesis is the task of decomposing a given logical functionality into a sequence of elementary gates. It is (depth-)optimal if it is impossible to achieve the desired functionality with even shorter circuits. Optimal synthesis is…
Stabilizer circuits arise in almost every area of quantum computation and communication, so there is interest in studying them from an information-theoretic perspective, i.e. as quantum channels. We consider several natural approaches to…
Measurement-based quantum computation (MBQC) is a paradigm for quantum computation where computation is driven by local measurements on a suitably entangled resource state. In this work we show that MBQC is related to a model of quantum…
Entanglement distillation is a well-studied problem in quantum information, where one typically starts with $n$ noisy Bell pairs and distills $k$ Bell pairs of higher fidelity. While distilling Bell pairs is the canonical setting, it is…
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…
Stabilizer states admit compact classical descriptions, but many downstream tasks still require their full amplitude vectors. Since the output itself has size $2^n$, the main algorithmic question is whether one can materialize an $n$-qubit…