量子态制备是量子计算中的一个重要子程序。我们证明，任意 n 量子比特量子态都可以仅使用单量子比特和双量子比特门，通过深度为 Θ(n) 的电路制备，尽管其代价是需要指数数量的辅助量子比特。另一方面，对于具有 d≥2 个非零项的稀疏量子态，我们可以使用 O(nd log d) 个辅助量子比特，将电路深度降至 Θ(log(nd))。该稀疏态算法比此前已知最佳结果快指数倍，且辅助量子比特数量接近最优，并仅随系统规模多项式增长。我们讨论了这些结果在不同量子计算任务中的应用，例如 Hamiltonian simulation（哈密顿量模拟）、求解线性方程组以及实现 quantum random access memories（量子随机存取存储器），并发现了在所有这三类任务中电路深度均实现指数级降低的情形。特别地，利用我们的算法，我们发现了一类线性方程组求解问题，即使与此前已知最佳的量子算法和经典去量子化算法相比，也享有指数级加速。
英文摘要：
Quantum state preparation is an important subroutine for quantum computing. We show that any $n$-qubit quantum state can be prepared with a $Θ(n)$-depth circuit using only single- and two-qubit gates, although with a cost of an exponential amount of ancillary qubits. On the other hand, for sparse quantum states with $d\geqslant2$ non-zero entries, we can reduce the circuit depth to $Θ(\log(nd))$ with $O(nd\log d)$ ancillary qubits. The algorithm for sparse states is exponentially faster than best-known results and the number of ancillary qubits is nearly optimal and only increases polynomially with the system size. We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories, and find cases with exponential reductions of the circuit depth for all these three tasks. In particular, using our algorithm, we find a family of linear system solving problems enjoying exponential speedups, even compared to the best-known quantum and classical dequantization algorithms.
In this short review I aim to explain how we can construct a circuit implementation of the bucketbrigade qRAM first proposed in [1]. Used with classical data, this qRAM model can be used incombination with the quantum accessible data structure [2] to prepare arbitrary quantum statesquickly and repeatedly, once the data to be prepared is in memory
This work presents a feasible design of an integrated photonic circuit performing as a device for single-qubit preparation and rotations through the third-order nonlinear process of difference frequency generation (DFG) and defined in the temporal mode basis. The first stage of our circuit includes the generation of heralded single photons by spontaneous four-wave mixing in a micro-ring cavity engineered for delivering a single-photon state in a unique temporal mode. The second stage comprises the implementation of DFG in a spiral waveguide with controlled dispersion properties for reaching co…
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wavefunctions that are relevant in the behavior of the system under study. Hamiltonian symmetries are an important instrument, to classify relevant many-particle wavefunctions, and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions ba…
The exact number of CNOT and single qubit gates needed to implement a Quantum Algorithm in a given architecture is one of the central problems of Quantum Computation. In this work we study the importance of concise realizations of Partially defined Unitary Transformations for better circuit construction using the case study of Dicke State Preparation. The Dicke States $(\left|D^n_k \right>)$ are an important class of entangled states with uses in many branches of Quantum Information. In this regard we provide the most efficient Deterministic Dicke State Preparation Circuit in terms of CNOT and…
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…
Scalable Preparation of Matrix Product States with Sequential and Brick Wall Quantum Circuits
Zentrum für Optische Quantentechnologien, Universität Hamburg（汉堡大学光学量子技术中心）；Department of Physics and Astronomy, University of Tennessee, Chattanooga（田纳西大学查塔努加分校物理与天文系）；UTC Quantum Center, University of Tennessee, Chattanooga（田纳西大学查塔努加分校UTC量子中心）；The Hamburg Centre for Ultrafast Imaging, Universität Hamburg（汉堡大学超快成像中心）
Scalable Multi-QPU Circuit Design for Dicke State Preparation: Optimizing Communication Complexity and Local Circuit Costs
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Shandong University（山东大学）
The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that r…
Practical Log-Depth Quantum State Preparation and Circuit Verification via Tree Tensor Network Compilation
University College London（伦敦大学学院）；Centre for Computational Science, Department of Chemistry, University College London（伦敦大学学院化学系计算科学中心）；Advanced Research Computing Centre, University College London（伦敦大学学院高级计算研究中心）；Informatics Institute, University of Amsterdam（阿姆斯特丹大学信息学研究所）
Certain quantum many-body ground states can be prepared by a large-depth quantum circuit consisting of geometrically local gates. In the presence of noise, local expectation values deviate from the correct value at most by an amount comparable to the noise rate. This happens if the action of the noiseless circuit, restricted to certain subsystems, rapidly mixes local observables up to a small correction. The encoding circuit for the surface code is given as an example.
Universal compilation is a training process that compiles a trainable unitary into a target unitary and it serves vast potential applications from quantum dynamic simulations to optimal circuits with deep-compressing, device benchmarking, quantum error mitigation, and so on. Here, we propose a universal compilation-based variational algorithm for the preparation and tomography of quantum states in low-depth quantum circuits. We apply the Fubini-Study distance to be a trainable cost function under various gradient-based optimizers, including the quantum natural gradient approach. We evaluate th…
In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when judging the complexity of the circuit: the total number of CNOT gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitr…
In quantum information and communication, optical schemes provide simple and intuitive experimental implementations. Of particular importance is quantum state preparation. In this thesis, the creation of polarisation entanglement using a particular class of optical circuits is studied. I give a mathematical description of this class of circuits in terms of Hermite polynomials. In this context, single photon resolution and single photon sensitivity detectors are discussed and compared with detector cascading. In addition, I study applications of state preparation such as quantum teleportation a…
We theoretically study operations with a four-level superconducting circuit as a two-qubit system. Using a mapping on a two-qubit system, we show how to implement iSWAP gates and Hadamard gates through pulses on transitions between particular pairs of energy levels. Our approach allows one to prepare pure two-qubit entangled states with desired form of reduced density matrices of the same purity and, in particular, arbitrary identical reduced states of qubits. We propose using schemes for the Hadamard gate and two-qubit entangled states with identical reduced density matrices in order to verif…
Data and code for collision-model Dicke-state preparation: depth-fidelity frontiers, circuit costs, and superconducting-processor measurements
Saint Louis University（圣路易斯大学）；KT One；University of South Florida（南佛罗里达大学）；Koç University（科奇大学）；TÜBİTAK Research Institute for Fundamental Sciences (TBAE)（土耳其科技研究基金会基础科学研究所（TBAE））；Tokyo International University（东京国际大学）；Nanoelectronics Research Center（纳米电子学研究中心）
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…
Efficient explicit circuit for quantum state preparation of piecewise continuous functions
Global College, Shanghai Jiao Tong University（上海交通大学全球学院）；Institute of Natural Sciences, School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院自然科学研究院）；Ministry of Education Key Laboratory in Scientific and Engineering Computing, Shanghai Jiao Tong University（上海交通大学教育部科学与工程计算重点实验室）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）
We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate configurations, we determine the maximum achievable fidelity as a function of quantum circuit size. This information allows us to identify the minimum circuit size needed for a specific target operation and enumerate the different gate configurations that allow a perfect implementation of the operation. We find that there are a large number of configurations that …
Mitigating errors in state preparation and measurement with noncomputational states
IBM Quantum, IBM Research Europe – Zurich（IBM量子，IBM欧洲苏黎世研究部）；Laboratory of Theoretical Physics of Nanosystems, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院纳米系统理论物理实验室）；Theory and Simulation of Materials, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院材料理论与模拟）
Matrix-product entanglement characterizing the optimality of state-preparation quantum circuits
Capital Normal University（首都师范大学）；Artificial intelligence College of Putian University（莆田学院人工智能学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学 Kavli 理论科学研究所）
The Quantum State Preparation problem aims to prepare an $n$-qubit quantum state $|ψ_v\rangle =\sum_{k=0}^{2^n-1}v_k|k\rangle$ from the initial state $|0\rangle^{\otimes n}$, for a given unit vector $v=(v_0,v_1,v_2,\ldots,v_{2^n-1})^T\in \mathbb{C}^{2^n}$ with $\|v\|_2 = 1$. The problem is of fundamental importance in quantum algorithm design, Hamiltonian simulation and quantum machine learning, yet its circuit depth and size complexity remain open when ancillary qubits are available. In this paper, we study efficient constructions of quantum circuits with $m$ ancillary qubits that can prepare…
