Ben W. Reichardt
We demonstrate an improved concatenated encoded ancilla preparation procedure. Simulations show that this procedure significantly increases the error threshold beneath which arbitrarily long quantum computations are possible.
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I describe a procedure for calculating thresholds for quantum computation as a function of error model given the availability of ancillae prepared in logical states with independent, identically distributed errors. The thresholds are determined via a simple counting argument performed on a single qubit of an infinitely large CSS code. I give concrete examples of thresholds thus achievable for both Steane and Knill style fault-tolerant implementations and investigate their relation to threshold estimates in the literature.
A critical component of any quantum error-correcting scheme is detection of errors by using an ancilla system. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information. We demonstrate a fault-tolerant error-detection scheme that suppresses spreading of ancilla errors by a factor of 5, while maintaining the assignment fidelity. The same method is used to prevent propagation of ancilla excitations, increasing the logical qubit dephasing time by an order of magnitude. Our approach is hardware-efficient, as it uses a single mult…
In fault-tolerant quantum computing schemes, the overhead is often dominated by the cost of preparing codewords reliably. This cost generally increases quadratically with the block size of the underlying quantum error-correcting code. In consequence, large codes that are otherwise very efficient have found limited fault-tolerance applications. Fault-tolerant preparation circuits therefore are an important target for optimization. We study the Golay code, a 23-qubit quantum error-correcting code that protects the logical qubit to a distance of seven. In simulations, even using a naive ancilla p…
Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae
本文提出一种基于广义路径无关量子控制的混合容错框架，仅用色散耦合和分束器耦合即可为四腿猫态量子比特构造通用纠错器件，并通过级联外部编码展示了利用现有硬件实现容错量子计算的可行性。
Efficient Fault-Tolerant Ancilla Preparation for Quantum BCH codes via Cyclic Symmetry
本文提出一种利用量子BCH码的循环对称性设计低开销提取方法，通过非容错制备与纠缠提取两阶段方法，实现更高效的容错辅助制备，降低空间开销和逻辑错误率，为实用化容错量子计算机的实现提供支持。
We schedule the Steane [[7,1,3]] error correction on a model ion trap architecture with ballistic transport. We compare the level one error rates for syndrome extraction using the Shor method of ancilla prepared in verified cat states to the DiVincenzo-Aliferis method without verification. The study examines how the quantum error correction circuit latency and error vary with the number of available ancilla and the choice of protocol for ancilla preparation and measurement. We find that with few exceptions the DiVincenzo-Aliferis method without cat state verification outperforms the standard S…
Fault-tolerant quantum computation using quantum error-correcting codes requires fault-tolerant constructions of nontransversal gates. Shor proposed a fault-tolerant construction of a nontransversal gate, i.e., the Toffoli gate for a family of the Calderbank-Shor-Steane codes which has even-weight stabilizer generators and odd-weight logical operators. In fact, as shown in this paper, error propagations in the ancilla preparation of Shor's construction lead to logical errors. This work provides a solution to this problem through the insertion of bit flip error correction. Finally, error rates …
Fault-tolerant quantum computation (FTQC) schemes that use multi-qubit large block codes can potentially reduce the resource overhead to a great extent. A major obstacle is the requirement of a large number of clean ancilla states of different types without correlated errors inside each block. These ancilla states are usually logical stabilizer states of the data code blocks, which are generally difficult to prepare if the code size is large. Previously we have proposed an ancilla distillation protocol for Calderbank-Shor-Steane (CSS) codes by classical error-correcting codes. It was assumed t…
In quantum error correction, information is encoded in a high-dimensional system to protect it from the environment. A crucial step is to use natural, low-weight operations with an ancilla to extract information about errors without causing backaction on the encoded system. Essentially, ancilla errors must not propagate to the encoded system and induce errors beyond those which can be corrected. The current schemes for achieving this fault-tolerance to ancilla errors come at the cost of increased overhead requirements. An efficient way to extract error syndromes in a fault-tolerant manner is b…
The overhead cost of performing universal fault-tolerant quantum computation for large scale quantum algorithms is very high. Despite several attempts at alternative schemes, magic state distillation remains one of the most efficient schemes for simulating non-Clifford gates in a fault-tolerant way. However, since magic state distillation circuits are not fault-tolerant, all Clifford operations must be encoded in a large distance code in order to have comparable failure rates with the magic states being distilled. In this work, we introduce a new concept which we call redundant ancilla encodin…
Synthesis of Fault-tolerant State Preparation Circuits using Steane-type Error Detection
本文提出了一种通用方法，用于合成Steane型容错状态制备电路，适用于任意CSS码，无需依赖代码对称性，以实现低开销的容错初始化。
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting storage errors, but applications require not just storing information; we must accurately compute even with faulty operations. The theory of fault-tolerant quantum computing illuminates a way forward by providing a foundation and collection of techniques for limiting the spread of errors. Here we implement one of the smallest quantum codes in a five-qubit super…
Quantum error correction and fault-tolerant quantum computation are two fundamental concepts which make quantum computing feasible. While providing a theoretical means with which to ensure the arbitrary accuracy of any quantum circuit, fault-tolerant error correction is predicated upon the robust preparation of logical states. An optimal direct circuit and a more complex fault-tolerant circuit for the preparation of the [[7,1,3]] Steane logical-zero are simulated in the presence of discrete quantum errors to quantify the regime within which fault-tolerant preparation of logical states is prefe…
Flexible Fault Tolerant Gate Gadgets
本研究设计出可让数据与辅助比特采用不同编码的灵活容错门构件，通过为辅助比特选用稳定子码，实现了通用量子码上的Clifford与非Clifford门容错操作，首次提出非加性码的通用容错门集合，并验证了其在两类信道下的容错性。
State Preparation on Quantum Computers via Quantum Steering
提出一种基于测量诱导导引的量子状态制备方法，通过辅助量子比特的纠缠、测量与主动重置，将系统量子比特导引至目标状态，并验证了其在NISQ及未来纠错码中的关键价值。
Single-ancilla ground state preparation via Lindbladians
提出一种基于 Lindbladian 的单辅助量子比特基态制备量子算法，克服初始零重叠限制，并设计出具有近最优模拟成本的离散时间变体，数值模拟验证了其有效性。
Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning
针对基于标记协议的容错量子电路缺乏明确设计方法的问题，提出用强化学习自动发现紧凑且适配硬件的电路，在逻辑态制备任务中门和辅助量子比特更少，还支持探索连通性与迁移学习，为多类容错电路发现提供新路径。
SpiderCSS: Scalable Fault-Tolerant CSS State Preparation
本文提出SpiderCSS，一种基于ZX-演算和故障等价重写的可扩展编译流水线，用于生成任意CSS码的容错态制备电路，实现CNOT最小化并显著降低深度和量子比特占用，同时平均逻辑错误率降低33.7%、接受率提高9.5%。
Fault-tolerant quantum error correction requires the measurement of error syndromes in a way that minimizes correlated errors on the quantum data. Steane and Shor ancilla are two well-known methods for fault-tolerant syndrome extraction. In this paper, we find a unifying construction that generates a family of ancilla blocks that interpolate between Shor and Steane. This family increases the complexity of ancilla construction in exchange for reducing the rounds of measurement required to fault-tolerantly measure the error. We then apply this construction to the toric code of size $L\times L$ a…
Gate-Based Quantum Simulation of Finite-Temperature Open-System Dynamics: A Post-Processing Reconstruction Approach for Collision Models
本文提出一种后处理重构方法，利用纯辅助量子比特模拟有限温度开放系统动力学，避免热态制备开销，适用于$U(1)$对称碰撞模型，可重用数据于不同温度。
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…
Quantum state preparation via engineered ancilla resetting
本研究提出一种结合周期性量子重置的协议，通过引导哈密顿量实现系统与辅助系统耦合，以制备无阻挫母哈密顿量基态，发现辅助系统纠缠能加速收敛且存在最优重置时间，并对噪声具有鲁棒性。
Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors arising from a few faults can be detected by a few ancillas and distinguished using subsequent syndrome measurements. The technique can be further improved using the fact that for some families of codes, errors of any weight are logically equivalent if they have the same syndrome and weight parity, as previously shown in [Phys. Rev. A 104, 042410 (2021)]. In…
Deterministic Fault-Tolerant State Preparation for Near-Term Quantum Error Correction: Automatic Synthesis Using Boolean Satisfiability
本文提出利用布尔可满足性等经典电路设计技术，为当前及近期硬件可实现的一类量子码自动综合确定性、最优容错态制备电路，并通过电路级噪声模拟验证。
In principle, quantum key distribution (QKD) offers unconditional security based on the laws of physics. In practice, flaws in the state preparation undermine the security of QKD systems, as standard theoretical approaches to deal with state preparation flaws are not loss-tolerant. An eavesdropper can enhance and exploit such imperfections through quantum channel loss, thus dramatically lowering the key generation rate. Crucially, the security analyses of most existing QKD experiments are rather unrealistic as they typically neglect this effect. Here, we propose a novel and general approach th…
Fault-tolerant preparation of arbitrary logical states in the cat code
本文提出在四腿猫码中实现容错制备任意逻辑态的框架，通过抑制非相干误差，实现高保真度并支持扩展和硬件兼容性。
Flag qubits have recently been proposed in syndrome extraction circuits to detect high-weight errors arising from fewer faults. The use of flag qubits allows the construction of fault-tolerant protocols with the fewest number of ancillas known to-date. In this work, we prove some critical properties of CSS codes constructed from classical cyclic codes that enable the construction of a flag fault-tolerant error correction scheme. We then develop fault-tolerant protocols as well as a family of circuits for flag fault-tolerant error correction and operator measurement, requiring only four ancilla…
This dissertation treats the topics of threshold calculation, ancilla construction, and non-standard error models. Chapter 2 introduces background material ranging from quantum mechanics to classical coding to thresholds for quantum computation. In Chapter 3 numerical and analytical means are used to generate estimates of and bounds on the threshold given an error model described by a restricted stochastic Pauli channel. Chapter 4 develops a simple, flexible means of estimating the threshold and applies it to some cases of interest. Finally, a novel method of ancilla construction is proposed i…
Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit depth, as well as the ability to perform inverse quantum Fourier transform, making it expensive to implement on an early fault-tolerant quantum computer. We propose an alternative method to estimate the ground state energy of a Hamiltonian with Heisenberg-limited precision scaling, which employs a simple quantum circuit with one ancilla qubit, and a classic…
Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant quantum computation (FTQC). However, how to fault-tolerantly prepare arbitrary CSS stabilizer states for general CSS stabilizer codes is still unknown, and their preparation can be highly costly in computational resources. In this paper, we show how to prepare a large class of CSS stabilizer states useful for FTQC. We propose distillation protocols using syndrome …
Automated Flag-based Fault-Tolerant State Preparation using Integer Linear Programming
研究如何优化容错态制备电路，利用电路规范算子形式将标志电路构建表示为整数线性规划，能构建门数等于或低于现有技术的电路，还能检测多达三个错误，并推导了Steane纠错器件，测试得到较低错误率。
Transferring quantum information between distant nodes of a network is a key capability. This transfer can be realized via remote state preparation where two parties share entanglement and the sender has full knowledge of the state to be communicated. Here we demonstrate such a process between heterogeneous nodes functioning with different information encodings, i.e., particle-like discrete-variable optical qubits and wave-like continuous-variable ones. Using hybrid entanglement of light as a shared resource, we prepare arbitrary coherent-state superpositions controlled by measurements on the …
Quantum computing is believed to be particularly useful for the simulation of chemistry and materials, among the various applications. In recent years, there have been significant advancements in the development of near-term quantum algorithms for quantum simulation, including VQE and many of its variants. However, for such algorithms to be useful, they need to overcome several critical barriers including the inability to prepare high-quality approximations of the ground state. Current challenges to state preparation, including barren plateaus and the high-dimensionality of the optimization la…
Scalable and fault-tolerant preparation of encoded k-uniform states
提出一种可扩展且容错的编码k-uniform态制备方法，通过直接从稳定子表确定k-uniform性并利用Clifford电路，结合混合物理-逻辑策略降低开销并提升性能。
Fault-tolerant syndrome extraction and cat state preparation with fewer qubits
本文降低了容错量子计算中伴随式测量与猫态制备的量子比特开销，证明在距离为3的容错下开销实现指数级降低，并利用$a$维超立方体最长路径高效复用标志量子比特。
Fault-tolerant resource estimation for ground-state preparation via Lindblad simulation
本研究基于Lindblad模拟，针对费米子Hubbard模型基态制备，推导严格误差界并对比经验参数，发现精确过滤能量跃迁是主要成本，估计需7.7×10^8个T门。
Factory-based Fault-tolerant Preparation of Quantum Polar Codes Encoding One logical Qubit
本文提出基于工厂并行制备 Q1 码态并引入额外调度步骤以避免整体丢弃，从而显著提高制备率，并给出与蒙特卡洛模拟吻合的理论估计方法，展示其在大规模容错量子计算中的优势。
Adaptive Dissipative State Preparation through Reinforcement Learning
本文提出RL-Adapt，一种基于单次强化学习的自适应耗散算法，通过优化辅助量子比特频率和相互作用算子选择，无需系统频谱先验知识即可加速基态制备并提升收敛鲁棒性。
We propose a fault tolerant loading scheme to produce an array of fermions in an optical lattice of the high fidelity required for applications in quantum information processing and the modelling of strongly correlated systems. A cold reservoir of Fermions plays a dual role as a source of atoms to be loaded into the lattice via a Raman process and as a heat bath for sympathetic cooling of lattice atoms. Atoms are initially transferred into an excited motional state in each lattice site, and then decay to the motional ground state, creating particle-hole pairs in the reservoir. Atoms transferre…
Gottesman-Kitaev-Preskill (GKP) states appear to be amongst the leading candidates for correcting errors when encoding qubits into oscillators. However the preparation of GKP states remains a significant theoretical and experimental challenge. Until now, no clear definitions for fault-tolerantly preparing GKP states have been provided. Without careful consideration, a small number of faults can lead to large uncorrectable shift errors. After proposing a metric to compare approximate GKP states, we provide rigorous definitions of fault-tolerance and introduce a fault-tolerant phase estimation p…
Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. We first show that robustness of magic is a well-behaved magic monotone that operationally quantifies the classical simulation overhead for a Gottesman-Knill type scheme using ancillary magic states. Our framework subsequently finds immediate application in the task of synthesizing non-Clifford gates using magic states. When magic states are interspersed with Clifford gates, Pauli measurements and stabilizer ancillas - the most general synthesis scenario - then the…
TARE: Block Encoding Linear Combinations of Pauli Strings Without Ancilla State Preparation
TARE通过将系数幅度整合到由互反交换的Pauli字符串构成的单位ary中，实现Pauli字符串线性组合的块编码，减少T门数量并改善电路深度，适用于多种量子系统。
Quantum error correction is an essential component for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and high-fidelity non-Clifford rotation gates. To address this issue, we propose a postselection-based algorithm to efficiently prepare resource states for gate teleportation. Our algorithm achieves fault tolerance, demonstrating the exponential suppression of logical errors with code distance, and it applies to any stabilizer codes. We provide analytical derivat…
Optimizing sparse quantum state preparation with measurement and feedforward
本文针对稀疏量子态制备问题，提出两种在辅助量子比特有限时降低电路深度的算法，其中一种利用电路中段测量与前馈将深度降至O(n)，在辅助量子比特数m=d时均优于现有最优算法。
Optimal (controlled) quantum state preparation and improved unitary synthesis by quantum circuits with any number of ancillary qubits
本文针对受控量子态制备和酉合成问题，构造了深度与规模最优或接近最优的量子线路，利用任意数量辅助量子比特，实现了时间-空间权衡，并显著缩小了酉合成的复杂度差距。
SpiderCat: Optimal Fault-Tolerant Cat State Preparation
本文提出SpiderCat方法，通过构造最优电路实现容错猫态制备，显著扩展了容错实现的范围并改进了资源计数。
Fault-tolerant $|\sqrt{ \mathrm{T} }\rangle$ state preparation and injection for more efficient fine-grained quantum circuit synthesis
本研究针对3D四面体色码及其变形变体，提出制备|√T⟩魔术态的容错协议，发现该态可降低量子电路综合的时空成本，为通用量子计算拓宽设计空间。
Verifiable blind quantum computing allows a client with poor quantum devices to delegate universal quantum computing to a remote quantum server in such a way that the client's privacy is protected and the honesty of the server is verified. In existing protocols, the client has to send single-qubit states to the server. These states might be decohered by the channel noise. Furthermore, the client hides some "trap" qubits in the server's register so that the client can detect the server's deviation. In reality, however, these trap qubits are disturbed by imperfect operations by the server, which…
We propose a general scheme for dissipatively preparing arbitrary pure quantum states on a multipartite qubit register in a finite number of basic control blocks. Our "splitting-subspace" approach relies on control resources that are available in a number of scalable quantum technologies (complete unitary control on the target system, an ancillary resettable qubit and controlled-not gates between the target and the ancilla), and can be seen as a "quantum-controller" implementation of a sequence of classical feedback loops. We show how a large degree of flexibility exists in engineering the req…
In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error correction procedures, circumventing existing no-go theorems. We then show how to simplify ancilla preparation, reducing the cost of error correction by more than a factor of four. Using this optimized ancilla preparation, we develop improved techniques for proving rigorous lower bounds on the noise threshold. Additional overhead can be incurred because quantu…
Efficient preparation of Dicke states
该研究提出了一种高效制备Dicke态的算法，利用中间电路测量和反馈，实现了多项对数深度和辅助粒子数量，适用于广泛范围的Dicke态。
A scheme for the extraction of entanglement in two noninteracting qubits (spins) is proposed. The idea is to make use of resonant transmission of ancilla qubit through the two fixed qubits, controlled by the entanglement in the scatterers. Repetition of the resonant transmission extracts the singlet state in the target qubits from their arbitrary given state. Neither the preparation nor the post-selection of the ancilla spin is required, in contrast to the previously proposed schemes.
Fast magic state preparation by gauging higher-form transversal gates in parallel
本文提出了一种通过并行化高形式横向门规范来加速魔态制备的方法，实现快速且容错的魔态制备。
To solve classically hard problems, quantum computers need to be resilient to the influence of noise and decoherence. In such a fault-tolerant quantum computer, noise-induced errors must be detected and corrected in real-time to prevent them from propagating between components. This requirement is especially pertinent while applying quantum gates, when the interaction between components can cause errors to quickly spread throughout the system. However, the large overhead involved in most fault-tolerant architectures makes implementing these systems a daunting task, which motivates the search f…
Fault-Tolerant Logical Operations and Efficient State Preparation in Modular Quantum Architectures with Noisy Interfaces
本文针对模块化量子架构，研究带噪声接口的容错逻辑操作，开发高效分布式容错逻辑GHZ态制备协议，为规模化容错量子计算提供定量依据。
Fault-tolerant logical measurements via homological measurement
提出同调测量框架用于测量CSS稳定子码的逻辑Pauli算符，并开发边扩展同调测量协议，仅需线性增长的辅助量子比特即可实现一般qLDPC码的容错测量且保持码距，在光子架构中表现出与高辅助比特方法相当的逻辑错误率。
Automated Synthesis of Fault-Tolerant State Preparation Circuits for Quantum Error Correction Codes
针对CSS码容错逻辑态制备依赖人工、难获最优电路的问题，提出基于SAT的自动综合方法及启发式方案，并验证d=3、d=5码的逻辑错误率缩放。
Flag at origin: a modular fault-tolerant preparation for CSS codes
本文提出了一种模块化方法，用于在CSS码中高效地进行容错逻辑稳定器态的准备，通过添加X和Z检测标志装置，显著提高了资源效率，尤其在大距离码中表现突出。
Fault-tolerant Post-Selection for Low Overhead Magic State Preparation
提出容错后选择（FTPS）框架，利用logical gap等软信息度量在低开销下抑制surface code magic state制备的错误率，并验证其在i.i.d. Pauli和擦除错误模型下的有效性。
Extremely Low-Cost Magic State Preparation toward Fault-Tolerant Quantum Computing
该研究提出一种极低成本魔法态制备协议，通过协同设计稳定子生成元与标志小工具，在15量子比特码上制备逻辑态并规范固定为7量子比特码，以19个量子比特和82个CNOT门实现高保真度，显著降低容错量子计算开销。
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