Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is intractably difficult to construct an arbitrary quantum state to high precision. Many quantum algorithms rely instead upon initializing the machine in a simple state, and evolving the state through an efficient (i.e. at most polynomial-depth) quantum algorithm. In this work, we show that there exist families of quantum states that can be prepared to high precision with circuits of linear size and depth. We focus on real-valued, smooth, differentiable functions with bounded derivatives on a domain of interest, exemplified by commonly used probability distributions. We further develop an algorithm that requires only linear classical computation time to generate accurate linear-depth circuits to prepare these states, and apply this to well-known and heavily-utilized functions including Gaussian and lognormal distributions. Our procedure rests upon the quantum state representation tool known as the matrix product state (MPS). By efficiently and scalably encoding an explicit amplitude function into an MPS, a high fidelity, linear-depth circuit can directly be generated. These results enable the execution of many quantum algorithms that, aside from initialization, are otherwise depth-efficient.
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
Constructing quantum circuits for efficient state preparation belongs to the central topics in the field of quantum information and computation. As the number of qubits grows fast, methods to derive large-scale quantum circuits are strongly desired. In this work, we propose the automatically differentiable quantum circuit (ADQC) approach to efficiently prepare arbitrary quantum many-qubit states. A key ingredient is to introduce the latent gates whose decompositions give the unitary gates that form the quantum circuit. The circuit is optimized by updating the latent gates using back propagatio…
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…
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）
State preparation with parallel-sequential circuits
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与工程中心）；Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（联合量子研究所与联合量子信息与计算机科学中心，美国国家标准与技术研究院/马里兰大学）；University of Basel（巴塞尔大学）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）
Quantum architecture search (QAS) is the process of automating architecture engineering of quantum circuits. It has been desired to construct a powerful and general QAS platform which can significantly accelerate current efforts to identify quantum advantages of error-prone and depth-limited quantum circuits in the NISQ era. Hereby, we propose a general framework of differentiable quantum architecture search (DQAS), which enables automated designs of quantum circuits in an end-to-end differentiable fashion. We present several examples of circuit design problems to demonstrate the power of DQAS…
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…
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）
The theory of quantum algorithms promises unprecedented benefits of harnessing the laws of quantum mechanics for solving certain computational problems. A persistent obstacle to using such algorithms for solving a wide range of real-world problems is the cost of loading classical data to a quantum state. Several quantum circuit-based methods have been proposed for encoding classical data as probability amplitudes of a quantum state. However, they require either quantum circuit depth or width to grow linearly with the data size, even though the other dimension of the quantum circuit grows logar…
Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code
在容错量子计算方案中，开销通常由可靠地准备码字的成本决定。该成本通常与底层量子纠错码的块大小成二次方地增加。因此，大的代码，否则是非常有效的发现有限的容错应用。因此，容错准备电路是优化的重要目标。我们研究了Golay码，这是一种23量子比特的量子纠错码，可以保护逻辑量子比特的距离为7。在模拟中，即使使用一个天真的辅助准备过程中，Golay码是竞争力与其他代码的开销和可容忍的噪声阈值。我们提供了两个简化的电路容错准备戈莱码编码的辅助。新电路最大限度地减少了错误传播，与标准编码电路相比，开销大约减少了四分之一。通过将恶性集计数技术应用于去极化噪声，我们进一步证明了每个门的阈值高于1.32 x 10^{-3}噪声。
The efficient preparation of quantum states is an important step in the execution of many quantum algorithms. In the noisy intermediate-scale quantum (NISQ) computing era, this is a significant challenge given quantum resources are scarce and typically only low-depth quantum circuits can be implemented on physical devices. We present a genetic algorithm for state preparation (GASP) which generates relatively low-depth quantum circuits for initialising a quantum computer in a specified quantum state. The method uses a basis set of R_x, R_y, R_z, and CNOT gates and a genetic algorithm to systema…
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 …
