F. Buscemi, G. M. D'Ariano, M. F. Sacchi
We explicitly construct a large class of unitary transformations that allow to perform the ideal estimation of the phase-shift on a single-mode radiation field. The ideal phase distribution is obtained by heterodyne detection on two radiation modes after the interaction.
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Recent quantum reconstruction projects demand pure unitary time evolution which seems to contradict the collapse postulate. Inspired by Zurek's environment assisted invariance idea, a natural unitary realization of wavefunction collapse is proposed using Grothendieck group construction for the tensor product commutative monoid.
In this paper we obtained for the Higgs algebra three kinds of single-mode realizations such as the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-like realization and the unitary realization based upon Villain-like realization. The corresponding similarity transformations between the Holstein-Primakoff-like realizations and the Dyson-like realizations are revealed.
Our last experimental results on the realization of a measurement-conditional unitary operation at single photon level are presented. This gate operates by rotating by $90^o$ the polarization of a photon produced by means of Type-II Parametric Down Conversion conditional to a polarization measurement on the correlated photon. We then propose a new scheme for measuring the quantum efficiency of a single photon detection apparatus by using this set-up. We present experimental results obtained with this scheme compared with {\it traditional} biphoton calibration. Our results show the interesting …
The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a controlled-U gate can be realized with two controlled-not gates and four single qubit gates. We prove that this implementation is optimal if and only if the matrix U satisfies the conditions tr U != 0, tr UX != 0, and det U != 1. We also derive optimal implementations in the non-generic cases.
Any lossless transformation on $n_{s}$ spatial and $n_{p}$ internal modes of light can be described by an $n_{s}n_{p}\times n_{s}n_{p}$ unitary matrix, but there is no known procedure to effect an arbitrary $n_{s}n_{p}\times n_{s}n_{p}$ unitary matrix on light in $n_{s}$ spatial and $n_{p}$ internal modes. We devise an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. Our realization uses beamsplitters and operations on internal modes to effect arbitrary linear transformations. The number of beamsplitters require…
Atomic Interferometer has two quantum unitary gates that must be realized for quantum sensing purposes from atomic gravimeter and atomic interferometer gyroscope. An optimal cost function which define the distance between two unitary operator is defines and based on it a pulse based stochastic gradient descent algorithm is derived for implementation of atomic mirror and atomic beam-splitter gates. By using numerical optimal control for those gate realization, we achieved to gate fidelity of 0.995 and 0.998 for mirror and beam-splitter gates, respectively. For this research, a two-level atomic …
Quantum operations (QO) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables can be used to achieve a QO with generally different input and output Hilbert spaces. We classify all unitary extensions of a QO, and give explicit realizations in terms of free-evolution direct-sum dilations and interacting tensor-product dilations. In terms of Hilbert space dimensionality the free-evolution dilations minimize the physical resources needed …
Realization of high-fidelity unitary operations on up to 64 frequency bins
本文在多达64个频率箱模式上实现了高保真度可编程酉运算，通过量子行走基准测试验证了系统性能，相似度最高达98%，为Gaussian玻子采样等复杂光子量子任务奠定了基础。
Distilling Qubit Unitary Operations: A No-Go Theorem and Minimal Realization
本文研究通用酉净化任务，证明在不定因果序框架下无平凡2槽高阶操作可通用净化单比特酉，并发现3槽并行架构是实现非平凡净化的最小方案，通过辅助量子比特吸收误差达到最优平均保真度。
The ability to control and hence to realize a given number of photons is of major interest from a fundamental point of view, e.g. Bell inequalities, photons bunching. In recent years this interest has grown by the so-called the "Second Quantum Revolution" where such an ability is needed for quantum computers, etc. In this paper, we show that such a realization can not be done by a unitary process. Therefore, a non-unitary interferometer is given to build a full realization of the tensor product space for two photons at two states. Finally, by modifying the previous interferometer, the full ton…
Eigenstate-assisted realization of general quantum controlled unitaries with a fixed cost
本文提出了一种利用特征态实现通用量子受控单元的固定成本方法，通过固定电路实现常深度的量子门操作，适用于变分和量子机器学习算法。
We show how Bell observables on a bipartite quantum system can be obtained by local observables via a controlled-unitary transformation. For continuous variables this result holds for the Bell observable corresponding to the non-conventional heterodyne measurement on two radiation modes, which is connected through a 50-50 beam-splitter to two local observables given by single-mode homodyne measurements. A simple scheme for a controlled-unitary transformation of continuous variables is also presented, which needs only two squeezers, a parametric downconverter and two beam splitters.
Determining the phase in one arm of a quantum interferometer is discussed taking into account the three non-ideal aspects in real experiments: non-deterministic state preparation, non-unitary state evolution due to losses during state propagation, and imperfect state detection. A general expression is written for the probability of a measurement outcome taking into account these three non-ideal aspects. As an example of applying the formalism, the classical Fisher information and fidelity (Shannon mutual information between phase and measurements) are computed for few-photon Fock and N00N stat…
Unitary Realizations of Synchronizing Automata in Quantum Systems
本文提出量子同步自动机的量子类比，通过引入辅助量子比特编码自动机的规则，利用全局幺正操作实现同步词驱动自动机进入预定纯态，同时生成与初始状态相关的纠缠态。
The phenomenon of degeneracy of an $N-$plet of bound states is studied in the framework of quantum theory of closed (i.e., unitary) systems. For an underlying Hamiltonian $H=H(λ)$ the degeneracy occurs at a Kato's exceptional point $λ^{(EPN)}$ of order $N$ and of the spectral geometric multiplicity $K<N$. In spite of the phenomenological appeal of the concept (tractable as a quantum phase transition, or as a unitary processes of the loss of the observability of the system), the dedicated literature deals, predominantly, just with the models where $N=2$ and $K=1$. In our paper it is shown that …
Neutral atom systems are an appealing platform for the development and testing of quantum control and measurement techniques. This dissertation presents experimental investigations of control and measurement tools using as a testbed the 16-dimensional hyperfine manifold associated with the electronic ground state of $^{133}$Cs atoms. On the control side, we present an experimental realization of a protocol to implement robust unitary transformations in the presence of static and dynamic perturbations. We also present an experimental realization of inhomogeneous quantum control. Specifically, w…
A simple realization of Weyl-Heisenberg covariant measurements
本文提出了一种简单算法，用于实现Weyl-Heisenberg协变信息完备测量的Naimark扩展，通过确定d×d酉算子构造d²×d²酉相互作用，并展示其在qubit、qutrit和ququart系统中的应用。
The atomic Quantum Kicked Rotor is an outstanding "quantum simulator" for the exploration of transport in disordered quantum systems. Here we study experimentally the phase-shifted quantum kicked rotor, which we show to display properties close to an ideal disordered quantum system, opening new windows into the study of Anderson physics.
We study possible realizations of generalized quantum measurements on measurement-assisted programmable quantum processors. We focus our attention on the realization of von Neumann measurements and informationally complete POVMs. It is known that two unitary transformations implementable by the same programmable processor require mutually {\it orthogonal} states. It turns out that the situation with von Neumann measurements is different. Specifically, in order to realize two such measurements one does not have to use orthogonal program states. On the other hand, the number of the implementable…
We consider the unitary and the anti--unitary operator realizations of two important genuine quantum gates that transform elements of the computational basis of into superpositions: the square root of the identity and the square root of the negation.
Two-Unitary Complex Hadamard Matrices of Order $36$
本文构造阶 $36$ 的二酉复 Hadamard 矩阵族，利用等振幅与仅含六个六次单位根相位的结构，给出量子 Euler 问题更简洁且便于实验实现的新解。
A Unitary Weights Based One-Iteration Quantum Perceptron Algorithm for Non-Ideal Training Sets
针对欠完备或过完备训练集，本文提出通过奇异值分解构造酉权重矩阵的单次迭代量子感知机算法，并在多种量子门与复合门上验证其精确性和优势。
Effect of noise on quantum circuit realization of non-Hermitian time crystals
本文研究了非厄米 Ising Floquet 模型在含噪声量子计算机上的实现，发现常见噪声会导致无限长寿命的时间晶体振荡消失，并通过 Qiskit 模拟与 ibmq-lima 实验验证了该结论。
The Weyl semimetals [1-6] are three-dimensional (3D) gapless topological phases with Weyl cones in the bulk band, and host massless quasiparticles known as Weyl fermions which were theorized by Hermann Weyl in the last twenties [7]. The lattice theory constrains that Weyl cones must come in pairs, with the minimal number of cones being two. The semimetal with only two Weyl cones is an ideal Weyl semimetal (IWSM) which is the optimal platform to explore broad Weyl physics but hard to engineer in solids. Here, we report the experimental realization of the IWSM band by synthesising for the first …
We construct quantum evolution operators on the space of states, that realize the metaplectic representation of the modular group SL(2,Z_2^n). This representation acts in a natural way on the coordinates of the non-commutative 2-torus and thus is relevant for noncommutative field theories as well as theories of quantum space-time. The larger class of operators, thus defined, may be useful for the more efficient realization of new quantum algorithms.
Universal Unitary Photonic Circuits by Interlacing Discrete Fractional Fourier Transform and Phase Modulation
提出一种将酉矩阵分解为交错离散分数傅里叶变换与对角相移的通用光子架构，仅用 $N+1$ 个相位层表示任意酉算子，并给出梯度优化与集成光路实现方案。
A thermally isolated quantum system undergoes unitary evolution by interacting with an external work source. The two-point energy measurement (TPM) protocol defines the work exchanged between the system and the work source by performing ideal energy measurements on the system before, and after, the unitary evolution. However, the ideal energy measurements used in the TPM protocol ultimately result from a unitary coupling with a measurement apparatus, which requires an interaction with an external work source. For the TPM protocol to be self-consistent, we must be able to perform the TPM protoc…
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