Hoshang Heydari
We construct a quantum gate entangler based on selective phase rotation transform. In particular, we established a relation between quantum integral transform and quantum gates entangler in terms of universal controlled gates for multi-qubit states. Our construction is also related to the geometrical structure of multipartite quantum systems.
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We construct quantum gates entanglers for different classes of multipartite states. In particular we construct entangler operators for W and GHZ classes of multipartite states based on the construction of the concurrence classes. We also in detail discuss these two classes of the quantum gates entanglers for three-partite states.
We construct quantum gate entangler for general multipartite states based on topological unitary operators. We show that these operators can entangle quantum states if they satisfy the separability condition that is given by the complex multi-projective Segre variety. We also in detail discuss the construction of quantum gate entangler for higher dimensional bipartite and three-partite quantum systems.
We construct quantum gate entanglers for different classes of multipartite states based on definition of W and GHZ concurrence classes. First, we review the basic construction of concurrence classes based on orthogonal complement of a positive operator valued measure (POVM) on quantum phase. Then, we construct quantum gates entanglers for different classes of multi-qubit states. In particular, we show that these operators can entangle multipartite state if they satisfy some conditions for W and GHZ classes of states. Finally, we explicitly give the W class and GHZ classes of quantum gate entan…
Here we consider perfect entanglers from another perspective. It is shown that there are some {\em special} perfect entanglers which can maximally entangle a {\em full} product basis. We have explicitly constructed a one-parameter family of such entanglers together with the proper product basis that they maximally entangle. This special family of perfect entanglers contains some well-known operators such as {\textsc{cnot}} and {\textsc{dcnot}}, but {\em not} ${\small{\sqrt{\rm{\textsc{swap}}}}}$. In addition, it is shown that all perfect entanglers with entangling power equal to the maximal va…
A gate is called entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for generating entanglements, and thus provides important physical resources for accomplishing many tasks in quantum computing and quantum information. This Letter demonstrates that a universal entangler always exists except for a degenerated case. Nevertheless, the problem how to find a universal entangler remains open.
We derive expressions for the invariant length element and measure for the simple compact Lie group SU(4) in a coordinate system particularly suitable for treating entanglement in quantum information processing. Using this metric, we compute the invariant volume of the space of two-qubit perfect entanglers. We find that this volume corresponds to more than 84% of the total invariant volume of the space of two-qubit gates. This same metric is also used to determine the effective target sizes that selected gates will present in any quantum-control procedure designed to implement them.
We establish a relation between topological and quantum entanglement for a multi-qubit state by considering the unitary representations of the Artin braid group. We construct topological operators that can entangle multi-qubit state. In particular we construct operators that create quantum entanglement for multi-qubit states based on the Segre ideal of complex multi-projective space. We also in detail discuss and construct these operators for two-qubit and three-qubit states.
Characteristics, Implementation and Applications of Special Perfect Entangler Circuits
本文构造了与特殊完美纠缠门局部等价的单参数双比特电路，利用交叉共振相互作用和脉冲级编程进行实现，并验证了其在生成通用双比特门及多比特完美W态中的高保真度应用。
The perfect entangler spectrum as a tool to analyze crosstalk
本文提出利用完美纠缠光谱检测量子系统中的动态串扰，通过分析光谱峰揭示串扰机制，为量子计算中的串扰分析提供新工具。
We construct the general gate operator for 2-players 3-strategies ELW games. It is shown that such a gate, implementing classical strategies, can be constructed out of the elements of Cartan subalgebra of $SU(3)$. The relation between the degree of entanglement and the structure of stability subgroup of initial state is analyzed.
Non-local properties of ensembles of quantum gates induced by the Haar measure on the unitary group are investigated. We analyze the entropy of entanglement of a unitary matrix U equal to the Shannon entropy of the vector of singular values of the reshuffled matrix. Averaging the entropy over the Haar measure on U(N^2) we find its asymptotic behaviour. For two--qubit quantum gates we derive the induced probability distribution of the interaction content and show that the relative volume of the set of perfect entanglers reads 8/3 π\approx 0.85. We establish explicit conditions under which a giv…
We study the entangling power and perfect entangler nature of (SWAP)1/m, for m>=1, and controlled unitary (CU) gates. It is shown that (SWAP)1/2 is the only perfect entangler in the family. On the other hand, a subset of CU which is locally equivalent to CNOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally-entangled state out of some initial product state. The functional depends on easily-computable local invariants and uniquely determines when a gate evolves into a perfect entangler. Optimization with our functional is most usefu…
The difficulty of an optimization task in quantum information science depends on the proper mathematical expression of the physical target. Here we demonstrate the power of optimization functionals targeting an arbitrary perfect two-qubit entangler, creating a maximally-entangled state out of some initial product state. For two quantum information platforms of current interest, nitrogen vacancy centers in diamond and superconducting Josephson junctions, we show that an arbitrary perfect entangler can be reached faster and with higher fidelity than specific two-qubit gates or local equivalence …
The ability to reach a maximally entangled state from a separable one through the use of a two-qubit unitary operator is analyzed for mixed states. This extension from the known case of pure states shows that there are at least two families of gates which are able to give maximum entangling power for all values of purity. It is notable that one of this gates coincides with a maximum discording one. We give analytical proof that such gate is indeed perfect entangler at all purities and give numerical evidence for the existence of the second one. Further, we find that there are other gates, many…
A fundamental requirement in the circuit model of quantum information processing is the realization of fault-tolerant multi-qubit quantum gates with entangling capabilities. A key step towards this end is to achieve control of qubit states through geometric phases at very small spatial scales in an effective and feasible way. A spin-electric coupling present in antiferromagnetic triangular single-molecule magnets (SMMs) allows for manipulation of the spin (qubit) states with a great flexibility. Here, we establish an all-electrical two-qubit geometric phase shift gate acting on the four-fold g…
We construct a generalized controlled phased gate entangler for a multi-qubit state based on the geometrical structure of quantum systems. We also investigate relation between the generalized controlled phase construction of a quantum gate entangler and graph state for two-qubit and three-qubit states.
Numerical search for universal entanglers in C3xC4 and C4xC4
针对高维空间中量子门是否为通用纠缠门难以验证的问题，本研究采用基于差分进化的算法在C3×C4和C4×C4空间中搜索通用纠缠门，各得到两个优质候选，并证伪了文献中的一个候选门。
We present the first experimental demonstration of the ''optimal'' and ''universal'' quantum entangling process involving qubits encoded in the polarization of single photons. The structure of the ''quantum entangling machine'' consists of the quantum injected optical parametric amplifier by which the contextual realization of the 1->2 universal quantum cloning and of the universal NOT (U-NOT) gate has also been achieved.
We study non-local two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of non-local gates is a 3-Torus. We derive the invariants for local transformations, and connect these local invariants to the coordinates of the 3-Torus. Since different points on the 3-Torus may correspond to the same local equivalence class, we use the Weyl group theory to reduce the symmetry. We show that the local equivalence classes of two-qubit gates are in one-to-one correspondence with the points in a tetrahedron except on the base. We…
Semiconductor quantum dots (known as artificial atoms) hold great promise for solid-state quantum networks and quantum computers. To realize a quantum network, it is crucial to achieve light-matter entanglement and coherent quantum-state transfer between light and matter. Here we present a robust photon-spin entangling gate with high fidelity and high efficiency (up to 50 percent) using a charged quantum dot in a double-sided microcavity. This gate is based on giant circular birefringence induced by a single electron spin, and functions as an optical circular polariser which allows only one ci…
Realization of high-fidelity perfect entangler between remote superconducting quantum processors
本文利用同轴电缆驻波模式在30厘米距离的远程超导量子处理器间实现了CNOT和CZ高保真完美纠缠门，保真度分别达99.15%和98.04%，为大规模分布式量子计算奠定了基础。
We propose a setup that transforms a photon pair in arbitrary rank-four mixed state, which could also be unknown, to a Bell state. The setup involves two linear optical circuits processing the individual photons and a parity gate working with weak cross-Kerr nonlinearity. By the photon number resolving detection on one of the output quantum bus or communication beams, the setup will realize a near deterministic transformation to a Bell state for every entangling attempt. With the simple threshold detectors, on the other hand, the system can still reach a considerable success probability of 0.5…
Nonstabilizerness of the entangling layer in quantum circuit Born machines
本文证明量子电路Born机的纠缠层可为Clifford电路，不提供非稳定子性，其性能与近Haar纠缠器相当，且训练态的非稳定子性来自旋转，并给出最小稳定子Rényi熵的计算方法。
We study the conditions for a double quantum dot system to work as a reliable electron spin entangler, and the efficiency of a beam splitter as a detector for the resulting entangled electron pairs. In particular, we focus on the relative strengths of the tunneling matrix elements, the applied bias and gate voltage, the necessity of time-dependent input/output barriers, and the consequence of considering wavepacket states for the electrons as they leave the double dot to enter the beam splitter. We show that a double quantum dot turnstile is, in principle, an efficient electron spin entangler …
Optimal implementation of quantum gates is crucial for designing a quantum computer. The necessary condition for optimal construction of a two-qubit unitary operation is obtained. It can be proved that the B gate is the unique gate that can construct a two-qubit universal circuit with only two applications, i.e. this condition is also sufficient in the case of two applications of the elementary two-qubit gate. It is also shown that one half of perfect entanglers can not simulate an arbitrary two-qubit gate with only 3 applications.
We propose a realization of a charge parity meter based on two double quantum dots alongside a quantum point contact. Such a device is a specific example of the general class of mesoscopic quadratic quantum measurement detectors previously investigated by Mao et al. [Phys. Rev. Lett. 93, 056803 (2004)]. Our setup accomplishes entangled state preparation by a current measurement alone, and allows the qubits to be effectively decoupled by pinching off the parity meter. Two applications of the parity meter are discussed: the measurement of Bell's inequality in charge qubits and the realization of…
We present a Superconducting Planar ARchitecture for Quantum Simulations (SPARQS) intended to implement a scalable qubit layout for quantum simulators. To this end, we describe the iFREDKIN gate as a controlled entangler for the simulation of Fermionic systems that is advantageous if it can be directly implemented. Using optimal control, we show that and how this gate can be efficiently implemented in the SPARQS circuit, making it a promising platform and control scheme for quantum simulations. Such a quantum simulator can be built with current quantum technologies to advance the design of mol…
Producing and maintaining entanglement reside at the heart of the optimal construction of quan- tum operations and are fundamental issues in the realization of universal quantum computation. We here introduce a setup of spin qubits that allows for geometric implementation of entangling gates between the register qubits with any arbitrary entangling power. We show this by demon- strating a circuit through a spin chain, which performs universal nonadiabatic holonomic two-qubit entanglers. The proposed gates are all electric and geometric, which would help to realize fast and robust entangling ga…
As a class of multipartite entangled states, the multipartite concatenated GHZ (C-GHZ) states remain superior stability under the influence of decoherence. We propose two scalable experimental realization of the multiphoton C-GHZ states based on the entanglers of multiphoton GHZ state. Given a $km$-photon GHZ state as an input state, if $m$ is odd, one can create a $km$-photon C-GHZ state. Also, generally, we design a scheme to prepare $km$-photon C-GHZ states from $km$ single-photon states by using $k$ entanglers of $m$-photon GHZ state and $k$ $m$-control Toffoli gates.
Qudit entanglers using quantum optimal control
本文利用连续Lie代数控制与数字Lie群控制两种量子最优控制方法，在碱土金属原子核自旋编码的qudit中借助Rydberg阻塞效应高效生成高保真纠缠门，并展示了$d=2$到$d=10$范围内的可行性及具体保真度结果。
The two-players $N$ strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme (Phys. Rev. Lett. 83 (1999), 3077) are considered. Group theoretical methods are applied to the problem of finding a general form of gate operators (entanglers) under the assumption that the set of classical pure strategies is contained in the set of pure quantum ones. The role of the stability group of the initial state of the game is stressed. As an example, it is shown that the maximally entangled games do not admit nontrivial pure Nash strategies. The general arguments are supported by explicit…
We present a proposal for implementing quantum phase gates using selective interactions. We analize selectivity and the possibility to implement these gates in two particular systems, namely, trapped ions and Cavity QED.
Experimental realization of quantum information processing in the field of nuclear magnetic resonance (NMR) has been well established. Implementation of conditional phase shift gate has been a significant step, which has lead to realization of important algorithms such as Grover's search algorithm and quantum Fourier transform. This gate has so far been implemented in NMR by using coupling evolution method. We demonstrate here the implementation of the conditional phase shift gate using transition selective pulses. As an application of the gate, we demonstrate Grover's search algorithm and qua…
We generalize an efficient decomposition method for diagonal operators by Welch et al. to qudit systems. The phase-context aware method focusses on cascaded entanglers whose decomposition into multi-controlled INC-gates can be optimized by the choice of a proper signed base-$d$ representation for the natural numbers. While the gate count of the best known decomposition method for general diagonal operators on qubit systems scales with $\mathcal{O}(2^n)$, the circuits synthesized by the Welch algorithm for diagonal operators with $k$ distinct phases are upper-bounded by $\mathcal{O}(n^2k)$, whi…
In this paper, we propose a scheme to implement two-qubit logic gates with a controllable and selective interaction in a scalable superconducting circuit of charge qubits. A nanomechanical resonator is used as a data bus to connect qubits. It is indicated that a controllable interaction between qubits can be obtained by making use of the data bus. It is shown that a selective interaction between qubits can be realized when many qubits are involved in the system under our consideration.
Quantum computing using two-dimensional NMR has recently been described using scalar coupling evolution technique [J. Chem. Phys.,109,10603 (1998)]. In the present paper, we describe two-dimensional NMR quantum computing with the help of selective pulses. A number of logic gates are implemented using two and three qubits with one extra observer spin. Some many-in-one gates (or Portmanteau gates) are implemented. Toffoli gate (or AND/NAND gate) and OR/NOR gates are implemented on three qubits. Deutsch-Jozsa quantum algorithm for one and two qubits, using one extra work qubit, has also been impl…
We consider quantum gates for trapped ions using state-selective displacement of the ions. We generalize earlier work in order to treat arbitrary separations between the traps. This requires the impact of anharmonicity arising from the Coulomb interaction to be estimated. We show that its effects are always small enough to allow high fidelity. In particular, the method can be applied to two ions in the same trap. We also show that gates between non-neighbour ions, and hence a Toffoli (three-qubit controlled-NOT) gate, can be achieved. We discuss how the gate can be applied to logical qubits en…
We discuss the implementation of frequency selective rotations using sequences of hard pulses and delays. These rotations are suitable for implementing single qubit gates in Nuclear Magnetic Resonance (NMR) quantum computers, but can also be used in other related implementations of quantum computing. We also derive methods for implementing hard pulses in the presence of moderate off-resonance effects, and describe a simple procedure for implementing a hard 180 degree rotation in a two spin system. Finally we show how these two approaches can be combined to produce more accurate frequency selec…
We propose two potentially practical schemes to carry out two-qubit quantum gates on endohedral fullerenes $N@C_{60}$ or $P@C_{60}$. The qubits are stored in electronic spin degrees of freedom of the doped atom $N$ or $P$. By means of the magnetic dipolar coupling between two neighboring fullerenes, the two-qubit controlled-NOT gate and the two-qubit conditional phase gate are performed by selective microwave pulses assisted by refocusing technique. We will discuss the necessary additional steps for the universality of our proposal. We will also show that our proposal is useful for both quantu…
The capacity of a quantum gate to produce entangled states on a bipartite system is quantified in terms of the entangling power. This quantity is defined as the average of the linear entropy of entanglement of the states produced after applying a quantum gate over the whole set of separable states. Here we focus on symmetric two-qubit quantum gates, acting on the symmetric two-qubit space, and calculate the entangling power in terms of the appropriate local-invariant. A geometric description of the local equivalence classes of gates is given in terms of the $\mathfrak{su}(3)$ Lie algebra root …
Due to their long coherence times, nuclear spins have gained considerable attention as physical qubits. Two-qubit gates between nuclear spins of distinct resonance frequencies can be mediated by electron spins, usually employing a sequence of electron-nuclear gates. Here we present a different approach inspired by, but not limited to, NV centers in diamond and discuss possible applications. To this end we generalize external electron spin control sequences for nuclear spin initialization and hyperpolarization to achieve the simultaneous control of distinct nuclear spins via an electron spin. T…
The experimental implementation of selective quantum process tomography (SQPT) involves computing individual elements of the process matrix with the help of a special set of states called quantum 2-design states. However, the number of experimental settings required to prepare input states from quantum 2-design states to selectively and precisely compute a desired element of the process matrix is still high, and hence constructing the corresponding unitary operations in the lab is a daunting task. In order to reduce the experimental complexity, we mathematically reformulated the standard SQPT …
We present an error-detected hyperparallel Toffoli (hyper-Toffoli) gate for a three-photon system based on the interface between polarized photon and cavity-nitrogen-vacancy(NV) center system. This hyper-Toffoli gate can be used to perform double Toffoli gate operations simultaneously on both the polarization and spatial-mode degrees of freedom (DoFs) of a three-photon system with a low decoherence, shorten operation time, and less quantum resources required, in compared with those on two independent three-photon systems in one DoF only. As the imperfect cavity-NV-center interactions are trans…
Realizing individual control on single qubits in a spin-based quantum register is an ever-increasing challenge due to the close proximity of the qubits resonance frequencies. Current schemes typically suffer from an inherent trade-off between fidelity and qubits selectivity. Here, we report on a new scheme which combines noise protection by dynamical decoupling and magnetic gradient based selectivity, to enhance both the fidelity and the selectivity. With a single nitrogen-vacancy center in diamond, we experimentally demonstrate quantum gates with fidelity = 0.9 $\pm$ 0.02 and a 50 kHz spectra…
Holonomic swap and controlled-swap gates of neutral atoms via selective Rydberg pumping
提出基于选择性里德伯泵浦和含时软控制的中性原子完整交换门快速实现方案，并扩展至三量子比特受控交换门，以抑制失谐与退相干。
We study the quantum brachistochrone evolution for a system of two spins-$\frac{1}{2}$ described by an anisotropic Heisenberg Hamiltonian without $zx$, $zy$ interacting couplings in magnetic field directed along the z-axis. This Hamiltonian realizes quantum evolution in two subspaces spanned by $\|\uparrow\uparrow\rangle$, $\|\downarrow\downarrow\rangle$ and $\|\uparrow\downarrow\rangle$, $\|\downarrow\uparrow\rangle$ separately and allows to consider the brachistochrone problem on each subspace separately. Using the evolution operator for this Hamiltonian we generate quantum gates, namely an …
We propose a method to construct composite two-qubit gates with narrowband profiles with respect to the spin-spin coupling. The composite sequences are selective to the variations in the amplitude and duration of the spin-spin coupling, and can be used for highly-selective qubit addressing with greatly reduced cross talk, quantum logic spectroscopy, and quantum sensing.
Co-designing Transmon devices for control with simple pulses
本文在NISQ背景下，利用最优控制工具和完美纠缠子理论，协同设计Transmon超导量子器件，通过探索模型空间并采用简单脉冲，最大化门保真度并推导门集。
Current typical methods to realize nuclear-nuclear quantum gates require a sequence of electronnuclear quantum gates by using dynamical decoupling techniques, which are implemented at low temperature because of short decoherence and relaxation time of the NV spin at room temperature. This limitation could be overcome by using periodical resets of an NV spin as a mediator of interaction between two nuclear spins [Chen, Schwarz, and Plenio, 119, 010801 (2017)]. However, this method works under stringent coupling strengths condition, which makes it not applicable to heteronuclear quantum gate ope…
An embedded selective recoupling method is proposed which is based on the idea of embedding the recently proposed deterministic selective recoupling scheme of Yamaguchi et al. [quant-ph/0411099] into a stochastic dynamical decoupling method, such as the recently proposed Pauli-random-error-correction-(PAREC) scheme [Eur. Phys. J. D 32, 153, quant-ph/0407262]. The recoupling scheme enables the implementation of elementary quantum gates in a quantum information processor by partial suppression of the unwanted interactions. The random dynamical decoupling method cancels a significant part of the …
We present a fast quantum entangling operation on superconducting qubits assisted by a resonator in the quasi-dispersive regime with a new effect --- the selective resonance coming from the amplified qubit-state-dependent resonator transition frequency and the tunable period relation between a wanted quantum Rabi oscillation and an unwanted one. This operation does not require any kind of drive fields and the interaction between qubits. More interesting, the non-computational third excitation states of the charge qubits can play an important role in shortening largely the operation time of the…
We analyze the cross-resonance effect for fluxonium circuits and investigate a two-qubit gate scheme based on selective darkening of a transition. In this approach, two microwave pulses at the frequency of the target qubit are applied simultaneously with a proper ratio between their amplitudes to achieve a controlled-NOT operation. We study in detail coherent gate dynamics and calculate gate error. With nonunitary effects accounted for, we demonstrate that gate error below $10^{-4}$ is possible for realistic hardware parameters. This number is facilitated by long coherence times of computation…
Distributed Variational Quantum Optimisation by Entanglement-Selective Transport
提出QESTO分布式变分量子算法，利用预共享Bell对实现图优化问题的分布式求解，无需非局域门，在瓦片匹配问题中优于分区QAOA。
Fourier-Geometric Circuit Design for Gate and Entanglement Placement in Quantum Neural Networks
本文提出一种傅里叶-几何电路设计准则，通过分解算子空间为频率平面，指导局部旋转与纠缠层放置，使目标傅里叶系数可达，并经消融实验和物理建模验证其有效性。
We propose a scalable neutral atom quantum computer with an on-demand interaction through a selective two-qubit gate operation. Atoms are trapped by a lattice of near field Fresnel diffraction lights so that each trap captures a single atom. One-qubit gate operation is implemented by a gate control laser beam which is applied to an individual atom. Two-qubit gate operation between an arbitrary pair of atoms is implemented by sending these atoms to a state-dependent optical lattice and making them collide so that a particular two-qubit state acquires a dynamical phase. We give numerical evaluat…
The large available Hilbert space and high coherence of cavity resonators makes these systems an interesting resource for storing encoded quantum bits. To perform a quantum gate on this encoded information, however, complex nonlinear operations must be applied to the many levels of the oscillator simultaneously. In this work, we introduce the Selective Number-dependent Arbitrary Phase (SNAP) gate, which imparts a different phase to each Fock state component using an off-resonantly coupled qubit. We show that the SNAP gate allows control over the quantum phases by correcting the unwanted phase …
This study examines the possibility of finding perfect entanglers for a Hamiltonian which corresponds to several quantum information platforms of interest at the present time. However, in this study, we use a superconducting circuit that stands out from other quantum-computing devices, especially because Transmon qubits can be coupled via capacitors or microwave cavities, which enable us to combine high coherence, fast gates, and high flexibility in its design parameters. There are currently two factors limiting the performance of superconducting processors: timing mismatch and the limitation …
We demonstrate experimentally the usefulness of selective pulses in NMR to perform quantum computation. Three different techniques based on selective pulse excitations have been proposed to prepare a spin system in a pseudo-pure state. We describe the design of novel ``portmanteau'' gates using the selective manipulation of level populations. A selective pulse implementation of the Deutsch-Jozsa algorithm for a two-qubit and a three-qubit quantum computer is demonstrated.
We consider the problem of time-optimal control of quadrupole nucleus with the spin I=1 by NMR. In contrast to the conventional methods based on selective pulses, the control is implemented using nonselective pulses separated by free evolution intervals. Using the Cartan decomposition, the system of equations is obtained for finding parameters of a control field. Partial time-optimal solutions for the important single-qutrit gates (selective rotations and quantum Fourier transform) are found. The strong dependence of minimum gate implementation times on global phase of the gate is observed. Th…
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