Success-or-Draw: A Strategy Allowing Repeat-Until-Success in Quantum Computation

Repeat-Until-Success circuits with fixed-point oblivious amplitude amplification

Certain quantum operations can be built more efficiently through a procedure known as Repeat-Until-Success. Differently from other non-deterministic quantum operations, this procedure provides a classical flag which certifies the success or failure of the procedure and, in the latter case, a recovery step allows the restoration of the quantum state to its original condition. The procedure can then be repeated until success is achieved. After success is certified, the RUS procedure can be equated to a coherent gate. However, this is not the case when the operation needs to be conditioned on the…

Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries

We present a decomposition technique that uses non-deterministic circuits to approximate an arbitrary single-qubit unitary to within distance $ε$ and requires significantly fewer non-Clifford gates than existing techniques. We develop "Repeat-Until-Success" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit $Z$-axis rota…

Repeat-Until-Success quantum computing using stationary and flying qubits

We introduce an architecture for robust and scalable quantum computation using both stationary qubits (e.g. single photon sources made out of trapped atoms, molecules, ions, quantum dots, or defect centers in solids) and flying qubits (e.g. photons). Our scheme solves some of the most pressing problems in existing non-hybrid proposals, which include the difficulty of scaling conventional stationary qubit approaches, and the lack of practical means for storing single photons in linear optics setups. We combine elements of two previous proposals for distributed quantum computing, namely the effi…

在超导量子处理器中利用 repeat-until-success 电路实现量子神经网络

Realization of a quantum neural network using repeat-until-success circuits in a superconducting quantum processor

本文在超导量子处理器上利用实时反馈的 repeat-until-success 电路构建非线性量子神经元，并以最小前馈网络实现对所有 2 到 1 比特 Boolean 函数的学习与非线性分类。

通过重复直至成功的正算子值测量在量子计算中节省资源

Saving resources through repeat-until-success positive-operator-valued-measure measurements in quantum computation

提出一种基于POVM测量的量子计算方法，通过辅助比特的中间测量实现重复直至成功，可多项式减少量子比特和酉操作数量，节省计算资源。

Efficient synthesis of universal Repeat-Until-Success circuits

Recently, it was shown that Repeat-Until-Success (RUS) circuits can achieve a $2.5$ times reduction in expected $T$-count over ancilla-free techniques for single-qubit unitary decomposition. However, the previously best known algorithm to synthesize RUS circuits requires exponential classical runtime. In this paper we present an algorithm to synthesize an RUS circuit to approximate any given single-qubit unitary within precision $\varepsilon$ in probabilistically polynomial classical runtime. Our synthesis approach uses the Clifford+$T$ basis, plus one ancilla qubit and measurement. We provide…

量子硬件编译的进展——魔态蒸馏与重复直至成功协议的演示

Advances in compilation for quantum hardware -- A demonstration of magic state distillation and repeat-until-success protocols

本文探讨容错量子子程序的控制结构表示，利用量子中间表示（QIR）与LLVM工具链在量子硬件上首次实现实时魔态蒸馏协议，并分析重复直至成功算法的四种实现，证明QIR能高效扩展容错协议复杂性且性能媲美手写量子汇编。

利用重复直至成功电路的量子算术与数值分析

Quantum arithmetic and numerical analysis using Repeat-Until-Success circuits

本文提出了一种基于重复直至成功框架的量子电路合成方法，用于近似合成单量子比特旋转，通过两个基本原语合成光滑可计算函数，并展示其在量子计算中所需量子比特更少的优势。

Probabilistic Quantum Teleportation via 3-Qubit Non-Maximally Entangled GHZ State by Repeated Generalized Measurements

We propose a scheme of repeated generalized Bell state measurement (GBSM) for probabilistic quantum teleportation of single qubit state of a particle (say, 0) using 3-qubit non-maximally entangled (NME) GHZ state as a quantum channel. Alice keeps two qubits (say, 1 and 2) of the 3-qubit resource and the third qubit (say, 3) goes to Bob. Initially, Alice performs GBSM on qubits 0 and 1 which may lead to either success or failure. On obtaining success, Alice performs projective measurement on qubit 2 in the eigen basis of $σ_{x}$. Both these measurement outcomes are communicated to Bob classical…

Measuring the entangled Bell and GHZ aspects using a single-qubit shuttle

A complete, non-demolition procedure is established for measuring multi-qubit entangled states, such as the Bell-states and the GHZ-states, which is essential in certain processes of quantum communication, computation, and teleportation. No interaction between the individual parts of the entangled system, nor with any environment is required. A small probe (e.g. a single qubit) takes care of all interaction with the system, and is used repeatedly. The probe-qubit interaction is of the simplest form, and only this one type of interaction is required to perform a complete measurement. The proces…

Ancilla Driven Quantum Computation with arbitrary entangling strength

We extend the model of Ancilla Driven Quantum Computation (ADQC) by considering gates with arbitrary entangling power. By giving up stepwise determinism, universal QC can still be achieved through a variable length sequence of single qubit gates and probabilistic "repeat-until-success" entangling operations. This opens up a new range of possible physical implementations as well as shedding light on the sets of resources sufficient for universal QC.

Quantum Bayesian Neural Networks

Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from posterior distributions than on point estimation, thus it might be more forgiving in the face of additional quantum noise. We propose a quantum algorithm for Bayesian neural network inference, drawing on recent advances in quantum deep learning, and simulate its empirical performance on several tasks. We find that already for small numbers of qubits, our algorithm a…