Ali Yildiz
Some of the asymmetric three qubit $W$ states are used for perfect teleportation, superdense coding and quantum information splitting. We present the protocols for the optimal distillation of the asymmetric as well as the symmetric $W$ states from a single copy of any three qubit $W$ class pure state.
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The aim of this work is to examine the exponential rates at which entanglement distillation occur in three-qubits systems. The approach we will follow to elucidate the entanglement concentration is based on the Schur-Weyl decomposition and the Keyl-Werner theorem. In order to clearly state the main results of this work we will have to introduce the notion of SLOCC equivalence and the covariant algebra which will allow us to classify states in different \emph{entanglement classes}. Our main results comprehend the asymptotic rates for the probability of being in an invariant subspace in the Wedd…
We propose a scheme for both distilling and quantifying entanglement, applicable to individual copies of an arbitrary unknown two-qubit state. It is realized in a usual two-qubit interferometry with local filtering. Proper filtering operation for the maximal distillation of the state is achieved, by erasing single-qubit interference, and then the concurrence of the state is determined directly from the visibilities of two-qubit interference. We compare the scheme with full state tomography.
Entanglement distillation is a procedure for extracting from one or more pairs of entangled qubits a smaller number of pairs with a higher degree of entanglement that is essential for many applications in quantum information science. Schmidt projection is a unique distillation method that can be applied to more than two pairs of entangled qubits at the same time with high efficiency. We implement the Schmidt projection protocol by applying single-photon two-qubit quantum logic to a partially hyperentangled four-qubit input state. The basic elements of the procedure are characterized and we con…
Logic-qubit entanglement has attracted much attention in both quantum communication and quantum computation. Here, we present an efficient protocol to distill the logic-qubit entanglement with the help of cross-Kerr nonlinearity. This protocol not only can purify the logic bit-flip error and logic phase-flip error, but also can correct the physical bit-flip error completely. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors. Our distillation protocol for logic-qubit entanglement may be useful for the practical applications in quantum information, especially in long-di…
Magic state distillation with permutation-invariant codes and a two-qubit example
本文提出了一种基于排列不变码的双量子比特魔态蒸馏协议，实现了0.5误差阈值和1/2蒸馏率，通过允许非克利夫顿门和改变输出态形式，提升了魔态蒸馏性能。
The distillation of magic states is an often-cited technique for enabling universal quantum computing once the error probability for a special subset of gates has been made negligible by other means. We present a routine for magic-state distillation that reduces the required overhead for a range of parameters of practical interest. Each iteration of the routine uses a four-qubit error-detecting code to distill the +1 eigenstate of the Hadamard gate at a cost of ten input states per two improved output states. Use of this routine in combination with the 15-to-1 distillation routine described by…
Many proposals for fault-tolerant quantum computation require injection of 'magic states' to achieve a universal set of operations. Some qubit states are above a threshold fidelity, allowing them to be converted into magic states via 'magic state distillation', a process based on stabilizer codes from quantum error correction. We define quantum weight enumerators that take into account the sign of the stabilizer operators. These enumerators completely describe the magic state distillation behavior when distilling T-type magic states. While it is straightforward to calculate them directly by co…
We experimentally demonstrate optimal entanglement distillation from two forms of two-qubit mixed states under local filtering operations according to the constructive method intruduced by F. Verstraete et al. [Phys. Rev. A 64, 010101(R) (2001)]. In principle, our set-up can be easily applied to distilling entanglement from arbitrary two-qubit partially mixed states. We also test the violation of the Clauser-Horne-Shinmony-Holt (CHSH) inequality for the distilled state from the first form of mixed state to show its "hidden non-locality".
We study several properties of distillation protocols to purify multilevel qubit states (qudits) when applied to a certain family of initial mixed bipartite states. We find that it is possible to use qudits states to increase the stability region obtained with the flow equations to distill qubits. In particular, for qutrits we get the phase diagram of the distillation process with a rich structure of fixed points. We investigate the large-$D$ limit of qudits protocols and find an analytical solution in the continuum limit. The general solution of the distillation recursion relations is present…
Quantum universality can be achieved using classically controlled stabilizer operations and repeated preparation of certain ancilla states. Which ancilla states suffice for universality? This "magic states distillation" question is closely related to quantum fault tolerance. Lower bounds on the noise tolerable on the ancilla help give lower bounds on the tolerable noise rate threshold for fault-tolerant computation. Upper bounds show the limits of threshold upper-bound arguments based on the Gottesman-Knill theorem. We extend the range of single-qubit mixed states that are known to give univer…
The quantum states corresponding to a secret key are characterized using the so-called private states, where the key part consisting of a secret key is shielded by the additional systems. Based on the construction, it was shown that a secret key can be distilled from bound entangled states. In this work, I consider the shielded two-qubit states in a key-distillation scenario and derive the conditions under which a secret key can be distilled using the recurrence protocol or the two-way classical distillation, advantage distillation together with one-way postprocessing. From the security condit…
We provide generalizations of known two-qubit entanglement distillation protocols for arbitrary Hilbert space dimensions. The protocols, which are analogues of the hashing and breeding procedures, are adapted to bipartite quantum states which are diagonal in a basis of maximally entangled states. We show that the obtained rates are optimal, and thus equal to the distillable entanglement, for a (d-1) parameter family of rank deficient states. Methods to improve the rates for other states are discussed. In particular, for isotropic states it is shown that the rate can be improved such that it ap…
Heuristic Lookahead Distillation Protocol Search
本研究提出启发式前瞻蒸馏协议搜索方法，实现了更高的量子比特Werner态蒸馏速率，提升了量子比特去极化信道双向辅助量子容量的最优下界，推动了量子信息理论问题的解决。
Magic state distillation uses special codes to suppress errors in input states, which are often tailored to a Clifford-twirled error model. We present detailed measurement sequences for magic state distillation protocols which can suppress arbitrary errors on any part of a protocol, assuming the independence of errors across qubits. Provided with input magic states, our protocol operates on a two-dimensional square grid by measurements of $ZZ$ on horizontal pairs of qubits, $XX$ on vertical pairs, and $Z,X$ on single qubits.
Constant sized support state distillation with qubit recycling
本文提出一族利用码加倍和量子比特回收的蒸馏协议，可在Clifford层次各级以固定逻辑量子比特数实现任意高距离，并发现如111到1的紧凑协议。
For certain quantum architectures and algorithms, most of the required resources are consumed during the distillation of one-qubit magic states for use in performing Toffoli gates. I show that the overhead for magic-state distillation can be reduced by merging distillation with the implementation of Toffoli gates. The resulting routine distills 8 one-qubit magic states directly to a Toffoli state, which can be used without further magic to perform a Toffoli gate.
Quantum information processing in a modular architecture requires the distribution, stabilization and distillation of entanglement in a qubit network. We present autonomous entanglement stabilization protocols between two superconducting qubits that are coupled to distant cavities. The coupling between cavities is mediated and controlled via a three-wave mixing device that generates either a two-mode squeezed state or a delocalized mode between the remote cavities depending on the pump applied to the mixer. Local drives on the qubits and the cavities steer and maintain the system to the desire…
Despite significant overhead reductions since its first proposal, magic state distillation is often considered to be a very costly procedure that dominates the resource cost of fault-tolerant quantum computers. The goal of this work is to demonstrate that this is not true. By writing distillation circuits in a form that separates qubits that are capable of error detection from those that are not, most logical qubits used for distillation can be encoded at a very low code distance. This significantly reduces the space-time cost of distillation, as well as the number of qubits. In extreme cases,…
We present a general algorithm to achieve local operators which can produce the GHZ state for an arbitrary given three-qubit state. Thus the distillation process of the state can be realized optimally. The algorithm is shown to be sufficient for the three-qubit state on account of the fact that any state for which this distillation algorithm is invalid cannot be distilled to the GHZ state by any local actions. Moreover, an analytical result of distillation operations is achieved for the general state of three qubits.
Exploring the landscape of compact magic-state distillation factories
本文利用经典纠错码框架研究魔法态蒸馏协议，通过SAT求解器推导出关于量子比特数、协议深度、工厂距离和输出错误率预因子的不可行定理，并提出了新的最小量子比特数蒸馏协议。
A mixed quantum state shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of that state into a single shared pair of qubits having high fidelity with a maximally entangled state state. In this paper it is proved that there exist states that are distillable, but for which an arbitrarily large number of copies is required before any distillation procedure can produce a shared pair of qubits with even a small amount of entanglement. Specifically, for…
An important task required to build a scalable, fault-tolerant quantum computer is to efficiently represent an arbitrary single-qubit rotation by fault-tolerant quantum operations. Traditionally, the method for decomposing a single-qubit unitary into a discrete set of gates is Solovay-Kitaev decomposition, which in practice produces a sequence of depth O(\log^c(1/ε)), where c~3.97 is the state-of-the-art. The proven lower bound is c=1, however an efficient algorithm that saturates this bound is unknown. In this paper, we present an alternative to Solovay-Kitaev decomposition employing state di…
Entanglement distillation based on polarization and frequency hyperentanglement
本研究提出一种基于偏振-频率超纠缠光子对的纠缠蒸馏方案，利用偏振相关频率转换器实现CNOT操作，通过牺牲频率自由度提升偏振纠缠保真度，兼具高增益、高产量与易实现性，适配现有光纤通信网络。
Optimal Distillation of Qubit Clocks
该研究针对量子比特系统，在时间平移不变操作下确定了相干性蒸馏的最优渐近保真度，发现最低不保真度与相干性纯度成反比，并给出了高阶修正及数值求解方法。
Unfolded distillation: very low-cost magic state preparation for biased-noise qubits
提出一种针对偏噪声量子比特的展开蒸馏方案，通过利用噪声偏置和展开Hadamard 3D量子Reed-Muller码的X稳定子群，在物理层而非逻辑层实现魔法态蒸馏，显著降低电路体积并保持高保真度。
Indistinguishability-assisted two-qubit entanglement distillation
提出一种基于空间局域操作与经典通信框架的高效纠缠提纯方法，利用全同量子比特空间重叠的不可区分性效应，推导了混合态最大纠缠提纯条件，并分析了热Gibbs态和Werner态下的提纯效果，为复合网络量子中继器铺路。
High-threshold magic state distillation with quantum quadratic residue codes
本文探讨了量子二次剩余码在魔态提纯中的应用，展示了现有提纯魔态的编码与量子二次剩余码等价，并提出新的高阈值提纯编码。
We discuss a specific entanglement distillation scheme under the constraint of finite samples of entangled qubit pairs. It is shown that an iterative process can be explicitly formulated. The average fidelity of this process can be enhanced by introducing conditional storing of entangled qubit pairs in each step of the iteration. We investigate the corresponding limitations on the size and the initial fidelity of the sample.
A key ingredient of quantum repeaters is entanglement distillation, i.e., the generation of high-fidelity entangled qubits from a larger set of pairs with lower fidelity. Here, we present entanglement distillation protocols based on qubit couplings that originate from exchange interaction. First, we make use of asymmetric bilateral two-qubit operations generated from anisotropic exchange interaction and show how to distill entanglement using two input pairs. We furthermore consider the case of three input pairs coupled through isotropic exchange. Here, we characterize a set of protocols which …
A set of stabilizer operations augmented by some special initial states known as 'magic states', gives the possibility of universal fault-tolerant quantum computation. However, magic state preparation inevitably involves nonideal operations that introduce noise. The most common method to eliminate the noise is magic state distillation (MSD) by stabilizer operations. Here we propose a hybrid MSD protocol by connecting a four-qubit H-type MSD with a five-qubit T-type MSD, in order to overcome some disadvantages of the previous MSD protocols. The hybrid MSD protocol further integrates distillable…
Triangle Criterion: a mixed-state magic criterion with applications in distillation and detection
本文提出三角准则，用于衡量混合态魔性，类似正偏置转置准则用于纠缠。通过该准则揭示多量子比特魔性提纯和检测的新特性，并证明多量子比特提纯协议比单量子比特方案更强大。
KLiNQ: Knowledge Distillation-Assisted Lightweight Neural Network for Qubit Readout on FPGA
本文提出 KLiNQ 架构，通过知识蒸馏将量子比特读取神经网络压缩约 99%，在 FPGA 上以 32ns 完成判别并保持 91% 精度，从而支持中电路测量并推动实用量子计算。
Distillation of N-Qubit Stabilizer States on a Star Network Topology
提出一种基于任意稳定子码的纠缠蒸馏协议，在星型网络拓扑上高效地将N量子比特GHZ态转换为高保真逻辑态，并通过数值实验和理论证明其普适性。
Transversal Gates and Magic State Distillation in an Optimally Synthesized Spin-Qubit Shuttling Bus
本研究提出多量子比特自旋量子比特穿梭总线架构，优化布局与辅助量子比特共享方案，结合Quantum Reverse Mapping方法，实现容错量子计算的层间协同设计，验证了自旋量子比特穿梭架构的可行性。
We present an optimal probabilistic protocol to distill quantum coherence. Inspired by a specific entanglement distillation protocol, our main result yields a strictly incoherent operation that produces one of a family of maximally coherent states of variable dimension from any pure quantum state. We also expand this protocol to the case where it is possible, for some initial states, to avert any waste of resources as far as the output states are concerned, by exploiting an additional transformation into a suitable intermediate state. These results provide practical schemes for efficient quant…
We develop a distillation protocol for multilevel qubits (qudits) using generalized beam splitters like in the proposal of Pan et al. for ordinary qubits. We find an acceleration with respect to the scheme of Bennet et al. when extended to qudits. It is also possible to distill entangled pairs of photons carrying orbital angular momenta (OAM) states that conserves the total angular momenta as those produced in recent experiments.
Fourier states are multi-qubit registers that facilitate phase rotations in fault-tolerant quantum computing. We propose distillation protocols for constructing the fundamental, $n$-qubit Fourier state with error $O(2^{-n})$ at a cost of $O(n \log n)$ Toffoli gates and Clifford gates, or any arbitrary Fourier state using $O(n^2)$ gates. We analyze these protocols with methods from digital signal processing. These results suggest that phase kickback, which uses Fourier states, could be the current lowest-overhead method for generating arbitrary phase rotations.
Quantum algorithms for quantum chemistry map the dynamics of electrons in a molecule to the dynamics of a coupled spin system. To reach chemical accuracy for interesting molecules, a large number of quantum gates must be applied which implies the need for quantum error correction and fault-tolerant quantum computation. Arbitrary fault-tolerant operations can be constructed from a small, universal set of fault-tolerant operations by gate compilation. Quantum chemistry algorithms are compiled by decomposing the dynamics of the coupled spin-system using a Trotter formula, synthesizing the decompo…
Low Depth Virtual Distillation of Quantum Circuits by Deterministic Circuit Decomposition
针对多量子比特期望值虚拟蒸馏中B门无法纠正噪声且可能破坏变分原理的问题，提出一种结合多投影的低深度确定性线路分解方法，在真实设备上有效缓解了VQE算法的实验噪声。
Probabilistic Channel Distillation via Indefinite Causal Order
研究高阶量子开关在量子信道蒸馏中的优势，证明其能以非零概率蒸馏任意量子比特泡利信道，并刻画渐近速率及多量子比特推广的不可行性。
Magic state distillation is one of the leading candidates for implementing universal fault-tolerant logical gates. However, the distillation circuits themselves are not fault-tolerant, so there is additional cost to first implement encoded Clifford gates with negligible error. In this paper we present a scheme to fault-tolerantly and directly prepare magic states using flag qubits. One of these schemes uses a single extra ancilla, even with noisy Clifford gates. We compare the physical qubit and gate cost of this scheme to the magic state distillation protocol of Meier, Eastin, and Knill, whic…
Constant-Overhead Magic State Distillation
本文提出利用代数几何码构造量子比特魔法态蒸馏协议，实现恒定开销（指数γ=0），优于此前最佳γ≈0.678，解决了最优指数蒸馏的开放问题。
Qubit Recycling in Entanglement Distillation
针对Gisin局部滤波中保真度与产率的权衡，本文提出利用优化局部算子回收废弃光子的纠缠蒸馏协议，在全滤波和部分滤波配置下均显著提升产率。
Hardware-Tailored Resource Estimation for Magic-State Distillation on Silicon Spin Qubits
针对硅自旋量子比特平台，通过结合自底向上和自顶向下的方法，分析多种架构和纠错码，评估魔法态蒸馏的物理资源需求，并展示优化控制脉冲和偏置纠错码可显著降低开销。
We propose a scheme of multipartite entanglement distillation driven by a complementary pair of stabilizer measurements, to distill directly a wider range of states beyond the stabilizer code states (such as the Greenberger-Horne-Zeilinger states). We make our idea explicit by constructing a recurrence protocol for the 3-qubit W state. Noisy W states resulting from typical decoherence can be directly purified in a few steps, if their initial fidelity is larger than a threshold. For general input mixed states, we observe distillations to hierarchical fixed points, i.e., not only to the W state …
Orchestrating multi-level magic state distillation: a dynamic pipeline architecture
针对多级魔态蒸馏流水线资源开销大的问题，本文提出动态工厂调度与资源分配架构，在大规模应用和蒸馏基准上显著降低量子比特成本及量子比特-时间量。
Magic State Distillation via Codes over Binary Extension Fields
本研究采用代数几何技术构造二元扩展域上的码，提出多量子比特门封装方案与蒸馏协议，其在多数场景下的性能优于现有技术。
Zero-level $CCZ$ Distillation
本文提出了一种零级提纯协议，利用二维正方形晶格中的近邻相互作用，仅用物理量子比特高效生成高保真度的逻辑 $CCZ$ 魔法状态，从而减少空间和时间开销，提升容错量子计算的可行性。
In a recent paper it has been shown that for double extremal static spherically symmetric BPS black hole solutions in the STU model the well-known process of moduli stabilization at the horizon can be recast in a form of a distillation procedure of a three-qubit entangled state of GHZ-type. By studying the full flow in moduli space in this paper we investigate this distillation procedure in more detail. We introduce a three-qubit state with amplitudes depending on the conserved charges the warp factor, and the moduli. We show that for the recently discovered non-BPS solutions it is possible to…
Quantum entanglement serves as a valuable resource for many important quantum operations. A pair of entangled qubits can be shared between two agents by first preparing a maximally entangled qubit pair at one agent, and then sending one of the qubits to the other agent through a quantum channel. In this process, the deterioration of entanglement is inevitable since the noise inherent in the channel contaminates the qubit. To address this challenge, various quantum entanglement distillation (QED) algorithms have been developed. Among them, recurrence algorithms have advantages in terms of imple…
We present the optimal local protocol to distill a Greenberger-Horne-Zeilinger (GHZ) state from a single copy of any pure state of three qubits.
Universal, unambiguous concentration and distillation of Bell pairs
该研究提出了一种能无歧义地提纯贝尔对的方案，通过本地操作和测量实现高效提纯，适用于实际应用。
Distilling Magic States in the Bicycle Architecture
本文提出在双变量自行车码中实现基于泡利测量的克利福德电路，通过联合优化逻辑量子比特映射、门调度、测量本地化和量子比特回收来设计蒸馏工厂，在更小量子比特占用下实现更低目标错误率。
Magic state distillation is a crucial component in the leading approaches to implementing universal fault tolerant quantum computation, with existing protocols for both qubit and higher dimensional systems. Early work focused on determining the region of distillable states for qubit protocols, yet comparatively little is known about which states can be distilled and with what distillable region for d>2. Here we focus on d=3 and present new four-qutrit distillation schemes that improve upon the known distillable region, and achieve distillation tight to the boundary of undistillable states for …
We propose families of protocols for magic state distillation -- important components of fault tolerance schemes --- for systems of odd prime dimension. Our protocols utilize quantum Reed-Muller codes with transversal non-Clifford gates. We find that, in higher dimensions, small and effective codes can be used that have no direct analogue in qubit (two-dimensional) systems. We present several concrete protocols, including schemes for three-dimensional (qutrit) and five-dimensional (ququint) systems. The five-dimensional protocol is, by many measures, the best magic state distillation scheme ye…
Error mitigated shadow estimation based on virtual distillation
本文提出一种基于虚拟蒸馏的误差缓解阴影估计方法，利用量子比特重置技术减少开销，确保资源不依赖精度且避免指数测量开销，支持混合阴影并定量分析权衡，数值模拟验证其有效性。
Quantum networking relies on the management and exploitation of entanglement. Practical sources of entangled qubits are imperfect, producing mixed quantum state with reduced fidelity with respect to ideal Bell pairs. Therefore, an important primitive for quantum networking is entanglement distillation, whose goal is to enhance the fidelity of entangled qubits through local operations and classical communication (LOCC). Existing distillation protocols assume the availability of ideal, noiseless, communication channels. In this paper, we study the case in which communication takes place over noi…
Low Overhead Qutrit Magic State Distillation
本研究构建了适用于魔态蒸馏的三正交qutrit纠错码族，证明其可大幅降低容错量子计算的魔态蒸馏开销，小参数下的码性能已优于同规模的已知qubit三正交码。
Quantum Circuit Distillation and Compression
本文提出量子电路蒸馏方法，利用强化学习生成短且抗噪的电路，应用于IQFT和Shor算法，在IBM量子处理器上实现正确计算，并发现近似n量子比特IQFT的通用规则，提升噪声量子处理器性能。
We show that any incoherent qubit channel could be decomposed into four incoherent Kraus operators. The proof consists in showing existence of four incoherent Kraus operators by decomposing the corresponding Choi-Jamiołkowski-Sudarshan matrix. We mention some applications of this optimal decomposition. We also show that the Kraus rank and incoherent rank are different even for qubit channel.
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