P. Campanale, D. Picca
In this paper we present the complete simulation of the quantum logic CNOT gate in the one-way model, that consists entirely of one-qubit measurements on a particular class of entangled states.
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We investigate the counterparts of random walk in universal quantum computing and their implementation using standard quantum circuits. Quantum walk have been recently well investigated for traversing graphs with certain oracles. We focus our study on traversing a 1-D graph, namely a circle, and show how to implement discrete circular quantum walk in quantum circuits built with universal CNOT and single quit gates. We review elementary quantum gates and circuit decomposition and propose a a generalized version of the all CNOT based quantum discrete circular walk. We simulated these circuits on…
Single qubit rotation gate and the controlled-NOT (CNOT) gate constitute a complete set of gates for universal quantum computation. In general the CNOT gate are only for two nearby qubits. For two qubits which are remote from each other, we need a series of swap gates to transfer these two qubits to the nearest neighboring sites, and then after the CNOT gate we should transfer them to their original sites again. However, a series of swap gates are resource for quantum information processing. One economy way which does not consume so much resource is to implement CNOT gate remotely. The remote …
In this paper we discuss an efficient technique that can implement any given Boolean function as a quantum circuit. The method converts a truth table of a Boolean function to the corresponding quantum circuit using a minimal number of auxiliary qubits. We give examples of some circuits synthesized with this technique. A direct result that follows from the technique is a new way to convert any classical digital circuit to its classical reversible form.
Depth optimization of CNOT ladder circuits
本文研究了CNOT阶梯电路的深度优化，通过交换线性增加的深度为常数深度，采用更宽的电路依赖于中间电路测量和经典控制操作，从而降低误差率。
We propose a deterministic and scalable scheme to construct a two-qubit controlled-NOT (CNOT) gate and realize entanglement swapping between photonic qubits using a quantum-dot (QD) spin in a double-sided optical microcavity. The scheme is based on spin selective photon reflection from the cavity and can be achieved in a nondestructive and heralded way. We assess the feasibility of the scheme and show that the scheme can work in both the weak coupling and the strong coupling regimes. The scheme opens promising perspectives for long-distance photonic quantum communication and distributed quantu…
A quantum compiler is a software program for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). The author of this paper is also the author of a quantum compiler called Qubiter. Qubiter uses a matrix decomposition called the Cosine-Sine Decomposition (CSD) that is well known in the field of Computational Linear Algebra. One way of measuring the efficiency of a quantum compiler is to measure the number of CNOTs it uses to express an unstructured unitary matrix (a unitary matrix with no special symmetries). We will henceforth refer to this numbe…
Controlled-NOT (CNOT) gates are commonly included in the standard gate set of quantum processors and provide an important way to entangle qubits. For fixed-frequency qubits using the cross-resonance entangling technique, using the higher-frequency qubit to control the lower-frequency qubit enables much shorter entangling times than using the lower-frequency qubit as the control. Consequently, when implementing a CNOT gate where logical control by the lower-frequency qubit is needed, compilers may implement this functionality by using an equivalent circuit such as placing Hadamard gates on both…
The exact lower bound of CNOT-complexity for fault-tolerant quantum Fourier transform
本文研究容错量子傅里叶变换的CNOT门复杂度精确下界，提出数值与解析结合的算法精确计算T门最小数量，证明T门复杂度下界问题为NP完全，并给出横向实现方案及在精度10^{-2}下的CNOT精确下界。
Quantum Compiling Algorithms decompose (exactly, without approximations) an arbitrary $2^\nb$ unitary matrix acting on $\nb$ qubits, into a sequence of elementary operations (SEO). There are many possible ways of decomposing a unitary matrix into a SEO, and some of these decompositions have shorter length (are more efficient) than others. Finding an optimum (shortest) decomposition is a very hard task, and is not our intention here. A less ambitious, more doable task is to find methods for optimizing small segments of a SEO. Call these methods piecewise optimizations. Piecewise optimizations i…
A highly feasible dressed-state scheme, which greatly speeds up the adiabatic population transfer of a quantum system, is applied for implementing a fast CNOT gate in a cavity QED system. The cavity QED system consists of two identical five-level atoms which are respectively trapped in two optical cavities connected by a fiber. With the help of quantum Zeno dynamics, the CNOT gate is constructed by three steps with six pulses. Because the adiabatic condition is not necessary to be considered and all of the pulses are smoothly turned on and off, the scheme is fast and feasible in experiment. Nu…
We give a general method of construting quantum circuit for random \QTR{it}{satisfiability} (SAT) problems with the basic logic gates such as multi-qubit controlled-NOT and NOT gates. The sizes of these circuits are almost the same as the sizes of the SAT formulas. Further, a parallelization scheme is described to solve random SAT problems efficiently through these quantum circuits in \QTR{it}{nuclear magnetic resonance} (NMR) ensemble quantum computing. This scheme exploits truly mixed states as input states rather than pseudo-pure states, and combines with the topological nanture of the NMR …
Efficient quantum circuits are necessary for realizing quantum algorithms on noisy intermediate-scale quantum devices. Fermionic excitations entering unitary coupled-cluster (UCC) ansätze give rise to quantum circuits containing CNOT "staircases" whose number scales exponentially with the excitation rank. Recently, Yordanov et al. [Phys. Rev. A 102, 062612 (2020); Commun. Phys. 4, 228 (2021)] constructed CNOT-efficient quantum circuits for both fermionic- (FEB) and qubit-excitation-based (QEB) singles and doubles and illustrated their usefulness in adaptive derivative-assembled pseudo-Trotteri…
One-way quantum computing is a promising candidate for fault-tolerant quantum computing. Here, we propose new protocols to realize a deterministic one-way CNOT gate and one-way $X$-rotations on quantum-computing platforms. By applying a delayed-choice scheme, we overcome a limit of most currently available quantum computers, which are unable to implement further operations on measured qubits or operations conditioned on measurement results from other qubits. Moreover, we decrease the error rate of the one-way logic gates, compared to the original protocol using local operations and classical c…
We present a way for entanglement purification based on two parametric down-conversion (PDC) sources with cross-Kerr nonlinearities. It is comprised of two processes. The first one is a primary entanglement purification protocol for PDC sources with nondestructive quantum nondemolition (QND) detectors by transferring the spatial entanglement of photon pairs to their polarization. In this time, the QND detectors act as the role of controlled-not (CNot) gates. Also they can distinguish the photon number of the spatial modes, which provides a good way for the next process to purify the entangleme…
Cat-Code-Protected Controlled Quantum Communication via Non-Local CNOT Gates over Star Quantum Networks
该研究提出结合猫态编码与非局域CNOT门的受控量子通信协议，通过密度矩阵模拟证明在50公里距离上显著提升保真度，并验证了抗分束器攻击的安全性，为长距离星型量子网络上的纠错受控通信奠定理论基础。
The anyonic excitations of topological two-body color code model are used to implement a set of gates. Because of two-body interactions, the model can be simulated in optical lattices. The excitations have nontrivial mutual statistics, and are coupled to nontrivial gauge fields. The underlying lattice structure provides various opportunities for encoding the states of a logical qubit in anyonic states. The interactions make the transition between different anyonic states, so being logical operation in the computational bases of the encoded qubit. Two-qubit gates can be performed in a topologic…
Magic state cultivation: growing T states as cheap as CNOT gates
提出魔态培育方法，在表面码补丁内以与 CNOT 门相当的物理门成本高效制备 T 态，显著降低逻辑错误率，使后续魔态蒸馏在实践中不再必要。
Randomized benchmarking of a high-fidelity remote CNOT gate over a meter-scale microwave interconnect
本研究利用可调耦合量子比特和超绝热驱动，在60厘米微波互连上实现高保真远程态传输，并构建远程CNOT门，通过随机基准测试测得传输保真度0.988和门保真度0.933。
Realization of permutation groups by quantum circuit
本文研究使用CNOT门实现由两个以上元素生成的置换群，证明了双量子比特SWAP门需3个CNOT门，n量子比特替换操作最多需3(n-1)个，并确定实现三量子比特置换元素(123)需6个CNOT门，为量子电路优化提供了理论基础。
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…
Efficient fault-tolerant code switching via one-way transversal CNOT gates
本文提出一种仅用横向CNOT门的码切换方案，实现低开销容错逻辑T门，数值模拟显示其优于魔法态注入和物理门，并扩展到高距离码对，简化FT通用量子计算硬件需求。
The Fuchs-Peres-Brandt (FPB) probe realizes the most powerful individual attack on Bennett-Brassard 1984 quantum key distribution (BB84 QKD) by means of a single controlled-NOT (CNOT) gate. This paper describes a complete physical simulation of the FPB-probe attack on polarization-based BB84 QKD using a deterministic CNOT constructed from single-photon two-qubit quantum logic. Adding polarization-preserving quantum nondemolition measurements of photon number to this configuration converts the physical simulation into a true deterministic realization of the FPB attack.
Lattice patch structure for fixed-frequency transmon quantum computer with high-fidelity CNOT gates
提出一种晶格贴片架构，将四个固定频率transmon耦合到一个固定频率总线，直接映射到表面码晶格单元，实现高连通性，CNOT门保真度超过0.98。
In our earlier work we posited that simple quantum gates and quantum algorithms can be designed utilizing the diffraction phenomena of a photon within a multiplexed holographic element. The quantum eigenstates we use are the photon's transverse linear momentum (LM) as measured by the number of waves of tilt across the aperture. Two properties of linear optical quantum computing (LOQC) within the circuit model make this approach attractive. First, any conditional measurement can be commuted in time with any unitary quantum gate; and second, photon entanglement can be encoded as a superposition …
We report the characterization of a universal set of logic gates for one-way quantum computing using a four-photon `star' cluster state generated by fusing photons from two independent photonic crystal fibre sources. We obtain a fidelity for the cluster state of 0.66 +/- 0.01 with respect to the ideal case. We perform quantum process tomography to completely characterize a controlled-NOT, Hadamard and T gate all on the same compact entangled resource. Together, these operations make up a universal set of gates such that arbitrary quantum logic can be efficiently constructed from combinations o…
Parallel implementation of CNOT$^{N}$ and C$_2$NOT$^2$ gates via homonuclear and heteronuclear Förster interactions of Rydberg atoms
本文提出利用异核Förster共振的强偶极-偶极相互作用克服里德堡阻塞多量子比特门保真度限制，优化了CNOT$^N$和C$_2$NOT$^2$门方案，数值模拟显示其保真度分别达99.3%和99.7%。
Digital Quantum Simulation of Scalar Yukawa Coupling
本文在 IBM Q 上研究了标量汤川耦合模型淬火后的动力学，设计了低深度量子电路模拟最多三个玻色子的演化，并通过误差 mitigation 验证了结果与经典基准的一致性。
High fidelity CNOT gates in photonic integrated circuits using composite segmented directional couplers
本文提出了一种基于复合分段方向耦合器的高保真CNOT门设计，通过实验和模拟验证其在提升门保真度和降低误差方面的优势。
Fewer-qubit quantum logic gate, serving as a basic unit for constructing universal multiqubit gates, has been widely applied in quantum computing and quantum information. However, traditional constructions for fewer-qubit gates often utilize a multi-pulse protocol which inevitably suffers from serious intrinsic errors during the gate execution. In this article, we report an optimal model about universal two- and three-qubit CNOT gates mediated by excitation to Rydberg states with easily-accessible van der Waals interactions. This gate depends on a global optimization to implement amplitude and…
It has been proved that surface plasmon polariton (SPP) can well conserve and transmit the quantum nature of entangled photons. Therefore, further utilization and manipulation of such quantum nature of SPP in a plasmonic chip will be the next task for scientists in this field. In quantum logic circuits, the controlled-NOT (CNOT) gate is the key building block. Here, we implement the first plasmonic quantum CNOT gate with several-micrometer footprint by utilizing a single polarization-dependent beam-splitter (PDBS) fabricated on the dielectric-loaded SPP waveguide (DLSPPW). The quantum logic fu…
Environment Alignment and Redundant Record Formation in Imperfect-CNOT Quantum Darwinism
本研究在不完美CNOT模型中探究制备、相互作用角度和场无序对环境记录的影响，揭示对齐参数与条件分支几何决定记录的非单调响应，并证明Z基仍最优，为稳健量子达尔文主义记录提供碎片大小指导。
Molecular quantum simulations with the variational quantum eigensolver (VQE) rely on ansatz states that approximate the molecular ground states. These ansatz states are generally defined by parametrized fermionic excitation operators and an initial reference state. Efficient ways to perform fermionic excitations are vital for the realization of the VQE on noisy intermediate-scale quantum computers. Here, we address this issue by first demonstrating circuits that perform qubit excitations, excitations that do not account for fermionic anticommutation relations. We then extend the functionality …
Efficient and deterministic high-dimensional controlled-swap gates on hybrid linear optical systems with high fidelity
本文提出利用混合线性光系统高效实现高维受控交换门，通过优化光学元件减少数量并提高保真度。
What is the time-optimal way of realizing quantum operations? Here, we show how important instances of this problem can be related to the study of shortest paths on the surface of a sphere under a special metric. Specifically, we provide an efficient synthesis of a controlled NOT (CNOT) gate between qubits coupled indirectly via Ising-type couplings to a third spin. Our implementation of the CNOT gate is more than twice as fast as conventional approaches. The pulse sequences for efficient manipulation of our coupled spin system are obtained by explicit computation of geodesics on a sphere unde…
Universal quantum entangling gates are a crucial building block in the large-scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the implementation of a controlled-NOT (CNOT) gate is constructed by introducing a non-computational quantum state in the auxiliary space. Furthermore, the method is extended to the construction of a general n-control-qubit Toffoli gate with (2n-1) qubit-qudit gates and (2n-2) single-qudit gates. Based on the presented quantum circuits, the polarization CNOT and …
How NOT to build control-target gates in semiconductor quantum dots and beyond
该研究针对半导体量子点器件架构无法高效实现CNOT等非对称控制-目标门的问题，提出异质双量子点器件蓝图，可在同位素纯化硅中实现单脉冲容错的100纳秒CNOT门。
Optimization complexity and resource minimization of emitter-based photonic graph state generation protocols
本研究利用图论优化器最小化基于发射器的光子图态生成中的纠缠门数量，显著降低CNOT资源，并实现中继图态资源的全局最优，同时解析了图的局部等价轨道。
Reversible logic gates were previously implemented in superconducting circuits as adiabatic-reversible gates, which are powered with a sufficiently slow clock. In contrast, we are studying ballistic-reversible gates, where fluxons serve to both encode the information and power the gates. No power is applied to the gate apart from the energy of the input fluxons, and the two possible flux polarities represent the bit states. Undamped long Josephson junctions (LJJs), where fluxons move at practically constant speed from inertia, form the input and output channels of the gates. LJJs are connected…
Multipartite controlled-NOT gates using molecules and Rydberg atoms
本文提出了一种基于非传统里德堡泵浦机制的混合系统，实现高保真度的受控不门，通过分子和里德堡原子的内部结构与强偶极子-偶极子相互作用，实现了二到一和一到二的门配置，展示了高保真度的量子信息处理平台。
Automated reduction of fault-tolerant circuits
本文提出一种基于故障等价重写的自动化方法，通过贝尔对缩减降低容错电路资源，并在Shor和Steane综合征提取中分别实现约21%和15%的逻辑错误率改进。
Scalable quantum circuits for exponential of Pauli strings and Hamiltonian simulations
本研究设计了可在低连接度硬件实现的泡利字符串指数量子电路，验证其可扩展性，将其用于多类哈密顿量演化模拟，18量子比特下精度接近数值Trotter误差，且在NISQ量级噪声下表现稳定。
Further advancement of quantum computing (QC) is contingent on enabling many-body models that avoid deep circuits and excessive use of CNOT gates. To this end, we develop a QC approach employing finite-order connected moment expansions (CMX) and affordable procedures for initial state preparation. We demonstrate the performance of our approach employing several quantum variants of CMX through the classical emulations on the H2 molecule potential energy surface and the Anderson model with a broad range of correlation strength. The results show that our approach is robust and flexible. Good agre…
Scalable long-distance quantum fan-out gates with reduced resource overhead
该研究提出一种高效方案，利用预共享的n量子比特GHZ态等实现空间分离各方的n量子比特扇出门，减少了门资源开销，开发的光学架构提升了成功概率，为长距离量子计算提供实验可行路径。
A two-qubit controlled-NOT (CNOT) gate, realized by a controlled-phase (C-phase) gate combined with single-qubit gates, has been experimentally implemented recently for quantum-dot spin qubits in isotopically enriched silicon, a promising solid-state system for practical quantum computation. In the experiments, the single-qubit gates have been demonstrated with fault-tolerant control-fidelity, but the infidelity of the two-qubit C-phase gate is, primarily due to the electrical noise, still higher than the required error threshold for fault-tolerant quantum computation (FTQC). Here, by taking t…
Circuit optimization of qubit IC-POVMs for shadow estimation
本文针对随机测量阴影估计需频繁调整线路的问题，利用维度扩张框架优化单量子比特 IC-POVM/SIC-POVM 编译，将 CNOT 数分别降至至多 2 个和 1 个，并验证其抗噪性与灵活性。
Optimisation of Pulse Waveforms for Qubit Gates using Deep Learning
提出利用DNN学习脉冲幅度与门保真度关系并以两阶段优化脉冲参数的方法，在Qiskit模拟中实现了高保真度单量子比特门。
Decomposition Algorithm of an Arbitrary Pauli Exponential through a Quantum Circuit
本文回顾阶梯算法并提出两种更高效的递归方法（倒阶梯算法和费米子SWAP门方法），分别减少单比特门和CNOT门数量，并讨论费米子门不可替代性。
Quantum computers promise great improvements in solving problems such as factoring large integers, simulating quantum systems, and database searching. Using a photon as a quantum bit (qubit) is one of the most promising ways to realize a universal quantum computer because the coherent superposition state of a photon is very robust against various sources of decoherence. However, it is too difficult to realize two-qubit (photon) gates because it requires huge nonlinearity between photons. Here we show the realization of a controlled-NOT (CNOT) gate, the most important and elemental two-qubit ga…
The quality of quantum bits (qubits) in silicon is highly vulnerable to charge noise that is omni-present in semiconductor devices and is in principle hard to be suppressed. For a realistically sized quantum dot system based on a silicon-germanium heterostructure whose confinement is manipulated with electrical biases imposed on top electrodes, we computationally explore the noise-robustness of 2-qubit entangling operations with a focus on the controlled-X (CNOT) logic that is essential for designs of gate-based universal quantum logic circuits. With device simulations based on the physics of …
The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. First, by removing the need for Gaussian elimination, we make the simulation algorithm much faster at the cost of a factor-2 increase in the number of bits needed to represent a state. We have implemented the improved algorithm in a freely-available program called CHP (CNOT-Hadamard-Phase), which can handle thousands of qubits easily. Second, …
Enhanced Two-Way Teleportation of Entangled States with Six-Qubit Cluster State
本文提出基于六量子比特簇态的双向隐形传态协议，通过贝尔测量实现两方未知双量子比特态交换，无需CNOT和辅助量子比特，仿真验证了高保真度和资源效率优势。
As an important degree of freedom (DoF) in integrated photonic circuits, the orthogonal transverse mode provides a promising and flexible way to increasing communication capability, for both classical and quantum information processing. To construct large-scale on-chip multimode multi-DoF quantum systems, a transverse mode-encoded controlled-NOT (CNOT) gate is necessary. Here, through design and integrate transverse mode-dependent directional coupler and attenuators on a silicon photonic chip, we demonstrate the first multimode implementation of a two-qubit quantum gate. With the aid of state …
We present an efficient way for measuring the entanglement of the atoms. Through the auxiliary single photons input-output process in cavity quantum electrodynamics (QED), the concurrence of the atomic entanglement can be obtained according to the success probability of picking up the singlet states of the atoms. This protocol has three advantages: First, we do not require the sophisticated controlled-not (CNOT) gates. Second, the distributed atoms are not required to intact with each other. Third, the atomic entanglement can be distributed nonlocally, which provides its important applications…
We simulate the evolution of three-node spin chain on the quantum processor of IBM Quantum Experience using the diagonalization of $XX$-Hamiltonian and representing the evolution operator in terms of CNOT operations and one-qubit rotations. We study the single excitation transfer from the first to the third node and show the significant difference between calculated and theoretical values of state transfer probability. Then we propose a method reducing this difference by applying the two-parameter transformation including the shift and scale of the calculated probabilities. { We demonstrate th…
Rydberg atom parity gate based on dark state resonances
基于暗态共振的瑞利德原子奇偶门通过优化参数和减少电路深度，提高量子计算和模拟的保真度与效率。
Fault-tolerant quantum computation using large spin cat-codes
提出基于大自旋 qudit 的 spin-cat 容错纠错协议，设计保秩 CNOT 等通用门及无测量幅度纠错，并在中性原子方案中验证其更高阈值与更低开销。
Optimizing Encoder Circuits of Entanglement-Assisted Quantum LDPC Codes via Beam Search
提出用束搜索算法优化纠缠辅助量子QC-LDPC码的SKG编码器，通过GF(2)行操作减少CNOT门数量，在测试码族上实现7.3-34.0%的CNOT计数降低。
Hybrid Quantum State Preparation via Data Compression
本研究提出一种无辅助量子的混合经典-量子策略，通过数据压缩降低量子态制备的CNOT门和电路深度，实现高效且可扩展的QSP方法。
From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct a universal quantum circuit. A new analytic construction procedure is presented and shown to be either optimal or close to optimal. This result can be extended to improve the efficiency of universal quantum circuit construction from any entangling gate. Specifically, for both the Controlled-NOT and Double-CNOT gates, we develop simple analytic ways to construct universal quantum circuits with three applications, which is the least possible.
Zero noise extrapolation (ZNE) is a widely used technique for gate error mitigation on near term quantum computers because it can be implemented in software and does not require knowledge of the quantum computer noise parameters. Traditional ZNE requires a significant resource overhead in terms of quantum operations. A recent proposal using a targeted (or random) instead of fixed identity insertion method (RIIM versus FIIM) requires significantly fewer quantum gates for the same formal precision. We start by showing that RIIM can allow for ZNE to be deployed on deeper circuits than FIIM, but r…
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