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 $|ψ_v\rangle$ in depth $\tilde O\left(\frac{2^n}{m+n}+n\right)$and size $O(2^n)$, achieving the optimal value for both measures simultaneously. These results also imply a depth complexity of $Θ(4^n/(m+n))$ for quantum circuits implementing a general $n$-qubit unitary using $m = O(2^n/n)$ ancillary qubits. This resolves the depth complexity for circuits without ancillary qubits, and for circuits with exponentially many ancillary qubits, this gives a quadratic saving from $O(4^n)$ to $\tilde Θ(2^n)$. Our circuits are deterministic, prepare the state and carry out the unitary precisely, utilize the ancillary qubits tightly and the depths are optimal in a wide range of parameter regime. The results can be viewed as (optimal) time-space tradeoff bounds, which is not only theoretically interesting, but also practically relevant in the current trend that the number of qubits starts to take off, by showing a way to use a large number of qubits to compensate the short qubit lifetime.
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 …
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…
Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based algorithm to simulate non-unitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal non-unitary operator, which we show can be implemented by a diagonal unitary operator in a 1-qubit dil…
Imaginary time evolution and ground state preparation using unitary multi-copy protocols
ITAMP, Center for Astrophysics | Harvard & Smithsonian（哈佛大学与史密森尼天体物理中心）；Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）
Unitary fault-tolerant encoding of Pauli states in surface codes
Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich（于利希研究中心）；Institute for Quantum Information, RWTH Aachen University（亚琛工业大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；School of Physics and Astronomy, Monash University（蒙纳士大学）；NVIDIA Corporation（英伟达公司）；Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）
TARE: Block Encoding Linear Combinations of Pauli Strings Without Ancilla State Preparation
Fraunhofer-Institut für Arbeitswirtschaft und Organisation IAO（弗劳恩霍夫工作经济与组织研究所）；Universität Stuttgart, Institut für Arbeitswissenschaft und Technologiemanagement IAT（斯图加特大学劳动科学与技术管理研究所）；Fraunhofer-Institut für Angewandte Festkörperphysik IAF（弗劳恩霍夫应用固体物理研究所）；Albert-Ludwigs-Universität Freiburg（弗赖堡阿尔伯特·路德维希大学）
Characterizing 3-qubit UPB states: violations of LHV models, preparation via nonlocal unitaries and PPT entangled nonlocal orbits
对于3量子位UPB状态，即，从Bennett等人的不可扩展的乘积基（Phys. Rev. Lett. 82：5385，1999），我们基于在该状态中编码的特定类型的反射对称性提供了一组局部隐藏变量（LHV）模型的违反。给出了从纯态的反射可分混合态中制备态所需的显式非局域幺正操作，以及一个具有正部分转置（PPT）的非局域单参数态轨道，该轨道在一个周期内将一个态与其反射之间的纠缠交换两次。
We report a scheme for deterministic preparation of non-Gaussian quantum states on-demand. In contrast to probabilistic approaches for preparation of non-Gaussian quantum states, conditioned on photon subtraction or addition, we present a scheme that can prepare non-Gaussian quantum states on-demand, by applying a unitary transformation which removes the Gaussianity of measurement statistics of field quadratures, namely a quadrature rotation via transmission through a beam-splitter, using a two-mode photon-number squeezed state as input. The resulting state exhibits a quantum vortex structure …
Faster matrix product state preparation by exploiting symmetry-induced block-sparsity
Institute of Quantum Technologies, German Aerospace Center（量子技术研究所，德国航空航天中心）；Center for Integrated Quantum Science and Technology (IQST), Ulm University（乌尔姆大学集成量子科学与技术中心）
The preparation of a quantum superposition is the key to the success of many quantum algorithms and quantum machine learning techniques. The preparation of an incomplete or a non-uniform quantum superposition with certain properties is a non-trivial task. In this paper, an $n$-qubits variational quantum circuit using partial negation and controlled partial negation operators will be proposed to prepare an arbitrary quantum superposition. The proposed quantum circuit follows the symmetries of the unitary Lie group. The speed of the preparation process and the accuracy of the prepared superposit…
