Quantum feature-map learning with reduced resource overhead
Department of Computer Science and Institute of Applied Mathematics, University of British Columbia (UBC), Vancouver, B.C. V6T 1Z4, Canada（计算机科学系和应用数学研究所，不列颠哥伦比亚大学（UBC），温哥华，B.C. V6T 1Z4，加拿大）；Stewart Blusson Quantum Matter Institute (QMI), Vancouver, B.C. V6T 1Z4, Canada（斯图尔特·布卢森量子物质研究所（QMI），温哥华，B.C. V6T 1Z4，加拿大）；Institute of Physics, University of Freiburg, Freiburg (Breisgau), 79104, Germany（物理研究所，弗赖堡大学，弗赖堡（巴登-符腾堡），79104，德国）；Department of Chemistry, University of British Columbia (UBC), Vancouver, B.C. V6T 1Z1, Canada（化学系，不列颠哥伦比亚大学（UBC），温哥华，B.C. V6T 1Z1，加拿大）
当前的量子计算机需要算法经济地使用有限资源。在量子机器学习中，成功取决于量子特征映射，它将经典数据嵌入到量子比特的状态空间中。我们引入了通过解析迭代重构的量子特征映射学习（Q-FLAIR），这是一种在迭代特征映射电路构建中减少量子资源开销的算法。它通过部分解析重构量子模型，仅使用少量评估就将工作负载转移到经典计算机上。对于每次探测到的门添加到拟设中，数据特征和权重参数的同时选择和优化则完全在经典计算机上进行。集成到量子神经网络和量子核支持向量分类器中，Q-FLAIR展示了最先进的基准性能。由于资源开销与特征维度解耦，我们在真实的IBM设备上仅用四小时就训练了一个量子模型，在完整分辨率MNIST数据集（784个特征，数字3 vs 5）上达到了超过90%的准确率。这样的结果以前是无法实现的，因为特征维度会极大地增加固定拟设的硬件需求以及自适应拟设的搜索成本。此外，Q-FLAIR展示了针对直接经典建模的去量子化鲁棒性，满足了文献中罕见的基准，这是潜在量子优势的必要条件。通过超越黑盒优化重新思考特征映射学习，这项工作为在现实问题和近期量子计算机上实现量子机器学习迈出了具体的一步。
英文摘要：
Current quantum computers require algorithms that use limited resources economically. In quantum machine learning, success hinges on quantum feature-maps, which embed classical data into the state space of qubits. We introduce Quantum Feature-Map Learning via Analytic Iterative Reconstructions (Q-FLAIR), an algorithm that reduces quantum resource overhead in iterative feature-map circuit construction. It shifts workloads to a classical computer via partial analytic reconstructions of the quantum model, using only a few evaluations. For each probed gate addition to the ansatz, the simultaneous selection and optimization of the data feature and weight parameter is then entirely classical. Integrated into quantum neural network and quantum kernel support vector classifiers, Q-FLAIR shows state-of-the-art benchmark performance. Since resource overhead decouples from feature dimension, we train a quantum model on a real IBM device in only four hours, surpassing 90% accuracy on the full-resolution MNIST dataset (784 features, digits 3 vs 5). Such results were previously unattainable, as the feature dimension prohibitively drives hardware demands for fixed and search costs for adaptive ansätze. Furthermore, Q-FLAIR demonstrates de-quantization robustness against direct classical modeling, satisfying a benchmark rare in the literature and a necessary condition for potential quantum advantage. By rethinking feature-map learning beyond black-box optimization, this work takes a concrete step toward enabling quantum machine learning for real-world problems and near-term quantum computers.
Quantum error mitigation techniques can reduce noise on current quantum hardware without the need for fault-tolerant quantum error correction. For instance, the quasiprobability method simulates a noise-free quantum computer using a noisy one, with the caveat of only producing the correct expected values of observables. The cost of this error mitigation technique manifests as a sampling overhead which scales exponentially in the number of corrected gates. In this work, we present a new algorithm based on mathematical optimization that aims to choose the quasiprobability decomposition in a nois…
We estimate and analyze the error rates and the resource overheads of the repetition cat qubit approach to universal and fault-tolerant quantum computation. The cat qubits stabilized by two-photon dissipation exhibit an extremely biased noise where the bit-flip error rate is exponentially suppressed with the mean number of photons. In a recent work, we suggested that the remaining phase-flip error channel could be suppressed using a 1D repetition code. Indeed, using only bias-preserving gates on the cat-qubits, it is possible to build a universal set of fault-tolerant logical gates at the leve…
A non-Clifford gate is required for universal quantum computation, and, typically, this is the most error-prone and resource intensive logical operation on an error-correcting code. Small, single-qubit rotations are popular choices for this non-Clifford gate, but certain three-qubit gates, such as Toffoli or controlled-controlled-Z (CCZ), are equivalent options that are also more suited for implementing some quantum algorithms, for instance those with coherent classical subroutines. Here, we calculate error rates and resource overheads for implementing logical CCZ with pieceable fault-toleranc…
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained, and we introduce a new method for decoding which uses this information to improve performance. Applied to the subsystem toric code with three-qubit check operators, we increase the threshold under circuit-level depolarising noise from $0.67\%$ to $0.81\%$. The threshold increases further under a circuit-level noise model with small finite bias, up to $2.22…
Taming Spacetime Overhead and Design Complexity in Distributed Fault-Tolerant Superconducting Quantum Computation
Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China（中国科学技术大学物理科学学院）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学上海量子科学研究中心与中科院量子信息科学与技术卓越创新中心）
We present two verification protocols where the correctness of a "target" computation is checked by means of "trap" computations that can be efficiently simulated on a classical computer. Our protocols rely on a minimal set of noise-free operations (preparation of eight single-qubit states or measurement of four observables, both on a single plane of the Bloch sphere) and achieve linear overhead. To the best of our knowledge, our protocols are the least demanding techniques able to achieve linear overhead. They represent a step towards further reducing the quantum requirements for verification…
Verifying quantum states is central to certifying the correct operation of various quantum information processing tasks. In particular, in measurement-based quantum computing, checking whether correct graph states are generated is essential for reliable quantum computing. Several verification protocols for graph states have been proposed, but none of these are particularly resource efficient: multiple copies are required to extract a single state that is guaranteed to be close to the ideal one. The best protocol currently known requires $O(n^{15})$ copies of the state, where $n$ is the size of…
Quantum algorithms need to be compiled to respect the constraints imposed by quantum processors, which is known as the mapping problem. The mapping procedure will result in an increase of the number of gates and of the circuit latency, decreasing the algorithm's success rate. It is crucial to minimize mapping overhead, especially for Noisy Intermediate-Scale Quantum (NISQ) processors that have relatively short qubit coherence times and high gate error rates. Most of prior mapping algorithms have only considered constraints such as the primitive gate set and qubit connectivity, but the actual g…
The knowledge and thus characterization of the temporal modes of quantum light fields is important in many areas of quantum physics ranging from experimental setup diagnosis to fundamental-physics investigations. Recent results showed how the auto-correlation function computed from continuous-wave homodyne measurements can be a powerful way to access the temporal mode structure. Here, we push forward this method by providing a deeper understanding and by showing how to extract the amplitude and phase of the temporal mode function with reduced experimental resources. Moreover, a quantitative an…
Remote Entanglement in Lattice Surgery: To Distill, or Not to Distill
Duke University（杜克大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；North Carolina State University（北卡罗来纳州立大学）；University of California, Berkeley（加州大学伯克利分校）
We propose an all-linear-optical scheme to ballistically generate a cluster state for measurement-based topological fault-tolerant quantum computation using hybrid photonic qubits entangled in a continuous-discrete domain. Availability of near-deterministic Bell-state measurements on hybrid qubits is exploited for the purpose. In the presence of photon losses, we show that our scheme leads to a significant enhancement in both tolerable photon-loss rate and resource overheads. More specifically, we report a photon-loss threshold of $\sim3.3\times 10^{-3}$, which is higher than those of known op…
Trade-offs between Quantum and Classical Resources in the Linear Combination of Unitaries
Graduate School of Science and Technology, Keio University（庆应义塾大学理工学研究科）；NTT Computer and Data Science Laboratories, NTT Inc.（日本电信电话株式会社计算机与数据科学实验室）；Department of Applied Physics and Physico-Informatics, Keio University（庆应义塾大学应用物理与理化信息学系）；NTT Research Center for Theoretical Quantum Information, NTT Inc.（日本电信电话株式会社理论量子信息中心）
This work compares the overhead of quantum error correction with concatenated and topological quantum error-correcting codes. To perform a numerical analysis, we use the Quantum Resource Estimator Toolbox (QuRE) that we recently developed. We use QuRE to estimate the number of qubits, quantum gates, and amount of time needed to factor a 1024-bit number on several candidate quantum technologies that differ in their clock speed and reliability. We make several interesting observations. First, topological quantum error correction requires fewer resources when physical gate error rates are high, w…
We analyze the resource overhead of recently proposed methods for universal fault-tolerant quantum computation using concatenated codes. Namely, we examine the concatenation of the 7-qubit Steane code with the 15-qubit Reed-Muller code, which allows for the construction of the 49 and 105-qubit codes that do not require the need for magic state distillation for universality. We compute a lower bound for the adversarial noise threshold of the 105-qubit code and find it to be $8.33\times 10^{-6}.$ We obtain a depolarizing noise threshold for the 49-qubit code of $9.69\times 10^{-4}$ which is comp…
Fault-tolerant Z rotations by pi/2^k are important as they arise in numerous quantum algorithms, most notably those involving quantum Fourier transforms. We describe surface code implementations of two recently described methods of efficiently constructing these rotations. One method uses state distillation to get low-error (|0> + exp(i pi/2^k)|1>)/sqrt(2) states, with each distillation level requiring 2^(k+2)-1 input states to produce a single purer output state, and uses these distilled states to directly implement pi/2^k angle Z rotations. The other method is indirect, using sequences of si…
Magic state distillation is a resource intensive sub-routine for quantum computation. The ratio of noisy input states to output states with error rate at most $ε$ scales as $O(\log^γ(1/ε))$ (Bravyi and Haah, PRA 2012). In a breakthrough paper, Hastings and Haah (PRL 2018) showed that it is possible to construct distillation routines with sub-logarithmic overhead, achieving $γ\approx 0.6779$ and falsifying a conjecture that $γ$ is lower bounded by $1$. They then ask whether $γ$ can be made arbitrarily close to $0$. We answer this question in the affirmative for magic state distillation routines…
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…
Quantum Process Tomography (QPT) is a powerful tool to characterize quantum operations, but it requires considerable resources making it impractical for more than 2-qubit systems. This work proposes an alternative approach that requires significantly fewer resources for unitary process characterization without prior knowledge of the process and provides a built-in method for state preparation and measurement (SPAM) error mitigation. By measuring the quantum process as rotated through the X and Y axes on the Bloch Sphere, we can acquire enough information to reconstruct the quantum process matr…
Entanglement-assisted circuit knitting: Distributed quantum computing using limited entanglement resources
National Tsing Hua University（国立清华大学）；National Cheng Kung University（国立成功大学）；Tamkang University（淡江大学）；Hon Hai Research Institute（鸿海研究院）；National Center for Theoretical Sciences（国家理论科学中心）
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state distillation, code switching, code concatenation and pieceable fault-tolerance are well-known examples of such approaches. However, the overhead of these approaches is one of the main bottlenecks for large-scale quantum computation. In this paper, a hybrid approach is proposed which combines the code concatenation technique with the other mentioned approache…
Fault-tolerant, error-corrected quantum computation is commonly acknowledged to be crucial to the realisation of large-scale quantum algorithms that could lead to extremely impactful scientific or commercial results. Achieving a universal set of quantum gate operations in a fault-tolerant error-corrected framework suffers from a `conservation of unpleasantness'. In general, no matter what error correction technique is employed, there is always one element of a universal gate set that carries a significant resource overhead - either in physical qubits, computational time, or both. Specifically,…
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…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state distillation, code switching, code concatenation and pieceable fault-tolerance are well-known examples of such approaches. However, the overhead of these approaches is one of the main bottlenecks for large-scale quantum computation. In this paper, two approaches for universal fault-tolerant quantum computation, mainly based on code concatenation, are propose…
We consider a model of quantum computation we call "Varying-$Z$" (V$Z$), defined by applying controllable $Z$-diagonal Hamiltonians in the presence of a uniform and constant external $X$-field, and prove that it is universal, even in 1D. Universality is demonstrated by construction of a universal gate set with $O(1)$ depth overhead. We then use this construction to describe a circuit whose output distribution cannot be classically simulated unless the polynomial hierarchy collapses, with the goal of providing a low-resource method of demonstrating quantum supremacy. The V$Z$ model can achieve …
In leading fault-tolerant quantum computing schemes, accurate transformation are obtained by a two-stage process. In a first stage, a discrete, universal set of fault-tolerant operations is obtained by error-correcting noisy transformations and distilling resource states. In a second stage, arbitrary transformations are synthesized to desired accuracy by combining elements of this set into a circuit. Here, we present a scheme which merges these two stages into a single one, directly distilling complex transformations. We find that our scheme can reduce the total overhead to realize certain gat…
The Gottesman-Kitaev-Preskill (GKP) quantum error-correcting code has emerged as a key technique in achieving fault-tolerant quantum computation using photonic systems. Whereas [Baragiola et al., Phys. Rev. Lett. 123, 200502 (2019)] showed that experimentally tractable Gaussian operations combined with preparing a GKP codeword $\lvert 0\rangle$ suffice to implement universal quantum computation, this implementation scheme involves a distillation of a logical magic state $\lvert H\rangle$ of the GKP code, which inevitably imposes a trade-off between implementation cost and fidelity. In contrast…
Logical Resource Estimation for Quantum State Preparation with Compilation
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Los Angeles（加州大学洛杉矶分校）；Duke University（杜克大学）；University of California, Berkeley（加州大学伯克利分校）
Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Focusing on the class of distillation tasks -- which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels --…
