Sigmund Kohler, Peter Hänggi
We investigate the influence of AC driving fields on the coherence properties of one- and two-qubit gate operations. In both cases, we find that for suitable driving parameters, the gate purity improves significantly. A mapping of the time-dependent system-bath model to an effective static model provides analytical results. The resulting purity loss compares favorably with numerical results.
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To explore the properties of a two-qubit mixed state, we consider quantum teleportation. The fidelity of a teleported state depends on the resource state purity and entanglement, as characterized by concurrence. Concurrence and purity are functions of state parameters. However, it turns out that a state with larger purity and concurrence, may have comparatively smaller fidelity. By computing teleportation fidelity, concurrence and purity for two-qubit X-states, we show it explicitly. We further show that fidelity changes monotonically with respect to functions of parameters - other than concur…
A scheme for measuring the purity of a quantum system with a finite number of levels is presented. The method makes use of two square root of SWAP gates and only hinges on measurements performed on a reference system, prepared in a certain pure state and coupled with the target system. Neither tomographic methods, with the complete reconstruction of the state, nor interferometric setups is needed.
In this paper we study the decoherence and purity of a driven solid-state qubit in the Ohmic bath by using the method based on the master equation. At first, instead of solving the master equation we investigate the coefficients of the equation which describe the shift in frequency, diffusive, decoherence, and so on. It is shown that one of the coefficients (we called it decoherence coefficient) is crucial to the decoherence of the qubit in the model. Then we investigate the evolution of the purity of the state in the model. From the analysis of the purity we see that the decoherence time of t…
We show the existence of dynamical purity swapping phenomena in the Jaynes-Cummings model. Moreover we show that purity swapping between a qubit and a generic quantum system is possible, provided they are coupled via non-unitary matrix elements interaction. We particularize to the case of a quantum optical Ramsey interferometer. We show that using purity swapping, a perfect interference pattern can be obtained at the output port of the interferometer even if we start from totally unpolarized sources. This feature is shown to be associated with the phenomena of recreation of the state vector at…
The entanglement, purity and energy of two isolated two-level atoms which are initially prepared in Bell state and each interacts with a thermal cavity field are investigated by considering the atomic motion and the field-mode structure. We achieve the analytical solutions of the atomic qubits by using the algebraic dynamical approach and the influences of the field-mode structure parameter, the strength of the thermal field and the detuning on the entanglement, purity and energy are discussed. We also investigate the state evolution of the atomic qubits based on the entanglement-purity-energy…
Qubit-State Purity Oscillations from Anisotropic Transverse Noise
本研究通过拉姆齐实验和低频磁通量子比特，揭示了各向异性横向噪声导致量子比特纯度在拉莫尔频率两倍处振荡，并阐明其对退相干的影响，有助于区分电荷与磁通噪声。
In this article, we investigate the purity dynamics of entangled 2 two-level atoms interacting with a single quantized electromagnetic field. We show that the purity of the qubit pairs depends on the initial state of the atomic system. It is found that the superposition case is the best choice to generate entangled states with high purity and hence high entanglement. It is clear that the purity of one qubit can be purified at the expense of the other pair through the phenomena of purity swapping. The mean photon number plays an important role in increasing the purity. The robustness of the qua…
We analyze and show experimental results of the conditional purity, the quantum discord and other related measures of quantum correlation in mixed two-qubit states constructed from a pair of photons in identical polarization states. The considered states are relevant for the description of spin pair states in interacting spin chains in a transverse magnetic field. We derive clean analytical expressions for the conditional local purity and other correlation measures obtained as a result of a remote local projective measurement, which are fully verified by the experimental results. A simple exac…
Given a finite number $N$ of copies of a qubit state we compute the maximum fidelity that can be attained using joint-measurement protocols for estimating its purity. We prove that in the asymptotic $N\to\infty$ limit, separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This in turn shows that the optimal estimation of the entanglement of a two-qubit state can also be achieved asymptotically with fully separable measurements. The relationship between our global Bayesian approach and the quantum Cramer-Rao bound is also di…
The dynamical map of entanglement and mixedness in four-qubit maximally entangled GHZ state paired with classical channels driven by fractional Gaussian noise is investigated. The qubit-channel coupling is assumed in four distinct ways: common, bipartite, tripartite, and independent local channel-qubit configurations comprising single, double, triple, or independent noisy sources. Using entanglement witness, negativity, purity and von Neumann entropy, except for the independent configuration, we show that indefinite entanglement and purity preservation may be simulated in multipartite GHZ-like…
The success of quantum information processing applications relies on accurate and efficient characterization of quantum states, especially nearly-pure states. In this work, we investigate a procedure for adaptive qubit state tomography which achieves $O(1/N)$ scaling in accuracy for large $N$. We analyze the performance of the adaptive protocol on the characterization of pure, mixed and nearly-pure states, and clarify the interplay between the purity of the state and the statistical fluctuations of the measurement results. Our results highlight the subtle difference between the characterizatio…
We analyze how a maximally entangled state of two-qubits (e.g., the singlet $ψ_s$) is affected by action of local channels described by completely positive maps $\cE$ . We analyze the concurrence and the purity of states $\varrho_\cE=\cE\otimes\cI[ψ_s]$.Using the concurrence-{\it vs}-purity phase diagram we characterize local channels $\cE$ by their action on the singlet state $ψ_s$. We specify a region of the concurrence-{\it vs.}-purity diagram that is achievable from the singlet state via the action of unital channels. We show that even most general (including non-unital) local channels act…
The Uhlmann-Jozsa fidelity (or, equivalently, the Bures distance) is a basic concept of quantum communication and quantum information, which however is very difficult to measure efficiently without recourse to quantum tomography. Here we propose a direct experimental method to estimate the fidelity between two unknown two-qubit mixed states via the measurement of the upper and lower bounds of the fidelity, which are referred to as the superfidelity and subfidelity, respectively. Our method enables a direct measurement of the first- and second-order overlaps between two arbitrary two-qubit stat…
We study the relationship between the entanglement, mixedness and energy of two-qubit and two-mode Gaussian quantum states. We parametrize the set of allowed states of these two fundamentally different physical systems using measures of entanglement, mixedness and energy that allow us to compare and contrast the two systems using a phase diagram. This phase diagram enables one to clearly identify not only the physically allowed states, but the set of states connected under an arbitrary quantum operation. We pay particular attention to the maximally entangled mixed states (MEMS) of each system.…
Quantum state tomography and other measures of the global properties of a quantum state are indispensable tools in understanding many body physics through quantum simulators. Unfortunately, the number of experimental measurements of the system required to estimate these global quantities scales exponentially with system size. Here, we consider the use of random-axis measurements for quantum state tomography and state purity estimation. We perform a general analysis of the statistical deviation in such methods for any given algorithm. We then propose a simple protocol which relies on single-pul…
Knowledge of the relationships among different features of quantumness, like entanglement and state purity, is important from both fundamental and practical viewpoints. Yet, this issue remains little explored in dynamical contexts for open quantum systems. We address this problem by studying the dynamics of entanglement and purity for two-qubit systems using paradigmatic models of radiation-matter interaction, with a qubit being isolated from the environment (spectator configuration). We show the effects of the corresponding local quantum channels on an initial two-qubit pure entangled state i…
We consider an arbitrary qubit channel depending on a single parameter, which is to be estimated by a physical process. Using the quantum Fisher information per channel invocation to quantify the estimation accuracy, we consider various estimation protocols when the available initial states are mixed with very low purity. We compare a protocol using a single channel invocation on one out of $n$ qubits prepared in a particular correlated input state to the optimal protocol using uncorrelated input states, with the same initial state purity. We show that, to lowest order in initial-state purity,…
High Success Probability, Fidelity, and Purity Nonlinear Optical Two-Qubit Gates on Chip
提出基于薄膜铌酸锂平台的两比特门方案，通过解耦光子相互作用与量子比特翻转操作及光谱相位预补偿，实现高成功概率、纯度及保真度。
We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank-deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically-motivated assumptions, we provide strong numerical evidence that three-fold degenerate X states of purity $P$ reach the highest entangle…
A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum value of the purity one can get at the output of a channel by varying over all physical input states, when purity is measured by the Schatten $q$-norm, and is denoted by $ν_q$. The multiplicativity problem is the question whether two channels used in parallel have a combined $ν_q$ that is the product of the $ν_q$ of the two channels. A positive answer would …
We provide a general method to calculate and maximize the purity of a qubit interacting with an anisotropic non-Markovian environment. Counter to intuition, we find that the purity is often maximized by preparing and storing the qubit in a superposition of non-interacting eigenstates. For a model relevant to decoherence of a heavy-hole spin qubit in a quantum dot or for a singlet-triplet qubit for two electrons in a double quantum dot, we show that preparation of the qubit in its non-interacting ground state can actually be the worst choice to maximize purity. We further give analytical result…
Quantum channels depending on a number of classical control parameters are considered. Assuming the stochastic fluctuations of the control parameters in the small errors limit it is shown that the channel fidelity is equal to the average value of the channel purities calculated in the cases of the control errors presence and absence respectively. The result validity is demonstrated on two particular examples, namely, one-qubit quantum gates implemented in the framework of the ion trap setup and the single qubit anisotropic depolarizing quantum channel.
Given a large number N of copies of a qubit state of which we wish to estimate its purity, we prove that separable-measurement protocols can be as efficient as the optimal joint-measurement one if classical communication is used. This shows that the optimal estimation of the entanglement of a two-qubit state can also be achieved asymptotically with fully separable measurements. Thus, quantum memories provide no advantage in this situation. The relationship between our global Bayesian approach and the quantum Cramer-Rao bound is discussed.
We present an all-fibre source of high-purity heralded single photons with an integrated conditional optical gate that reduces uncorrelated noise by almost an order of magnitude. Generating photon pairs by four-wave mixing in photonic crystal fibre, we observe with the noise gate active a factor of 7 reduction in the rate of single counts in the heralded channel with no measurable drop in coincidence count rate. In contrast to electronic post-selection of coincidence events, the real reduction in the flux of unwanted photons is beneficial for example to avoid bleaching light-sensitive samples …
The quantum correlations, including entanglement and discord with its geometric measure, and classical correlation are studied for a bipartite partition of a open or closed quantum system. It is found that the purity of the initial state plays an important role in the dynamics of quantum and classical correlations. In the dephasing model, the quantum correlations loss and the classical correlation gain are instantaneously happen. While, the purity of the initial state destroys the quantum correlations which is resulted by the unitary interaction. Therefore, with the purity parameter, a particu…
We study decoherence induced by stochastic squeezing control errors considering the particular implementation of Hadamard gate on optical and ion trap holonomic quantum computers. We analytically obtain both the purity of the final state and the fidelity for Hadamard gate when the control noise is modeled by Ornstein-Uhlenbeck stochastic process. We demonstrate the purity and the fidelity oscillations depending on the choice of the initial superimposed state. We derive a linear formulae connecting the gate fidelity and the purity of the final state.
Trapped atomic ions are an ideal candidate for quantum network nodes, with long-lived identical qubit memories that can be locally entangled through their Coulomb interaction and remotely entangled through photonic channels. The integrity of this photonic interface is generally reliant on purity of single photons produced by the quantum memory. Here we demonstrate a single-photon source for quantum networking based on a trapped $^{138}\mbox{Ba}^+$ ion with a single photon purity of $ g^{2}(0)=(8.1\pm2.3)\times 10^{-5} $ without background subtraction. We further optimize the tradeoff between t…
Phonon-Coupled Hole-Spin Qubits in High-Purity Germanium: Design and Modeling of a Scalable Architecture
本研究设计并建模了基于高纯锗栅控量子点空穴自旋量子位的可扩展量子架构，通过集成声子晶体腔与电调自旋轨道耦合，结合同位素富集材料，实现了长自旋相干、快门控与长程耦合，提供了CMOS兼容的高保真可扩展量子计算路径。
High-fidelity two-qubits gates are essential for the realization of large-scale quantum computation and simulation. Tunable coupler design is used to reduce the problem of parasitic coupling and frequency crowding in many-qubit systems and thus thought to be advantageous. Here we design a extensible 5-qubit system in which center transmon qubit can couple to every four near-neighbor qubit via a capacitive tunable coupler and experimentally demonstrate high-fidelity controlled-phase (CZ) gate by manipulating center qubit and one near-neighbor qubit. Speckle purity benchmarking (SPB) and cross e…
In two-qubit gate simulations an entangling gate is used several times together with single qubit gates to simulate another two-qubit gate. We show how a two-qubit gate's simulation power is related to the simulation power of its mirror gate. And we show that an arbitrary two-qubit gate can be simulated by three applications of a super controlled gate together with single qubit gates. We also give the gates set that can be simulated by n applications of a controlled gate in a constructive way. In addition we give some gates which can be used four times to simulate an arbitrary two-qubit gate.
We explore a dynamic signature of quantum phase transition (QPT) in an isotropic Lipkin-Meshkov-Glick (LMG) model by studying the time evolution of a central qubit coupled to it. We evaluate exactly the time-dependent purity, which can be used to measure quantum coherence, of the central qubit. It is found that distinctly different behaviors of the purity as a function of the parameter reveal clearly the QPT point in the system. It is also clarified that the present model is equivalent to an anti Jaynes-Cummings model under certain conditions.
The decomposition of matrices associated to two-qubit and three-qubit orthogonal gates is studied, and based on the decomposition the synthesis of these gates is investigated. The optimal synthesis of general two-qubit orthogonal gate is obtained. For two-qubit unimodular orthogonal gate, it requires at most 2 CNOT gates and 6 one-qubit Ry gates. For the general three-qubit unimodular orthogonal gate, it can be synthesized by 16 CNOT gates and 36 one-qubit Ry and Rz gates in the worst case.
Near-term quantum computers are limited by the decoherence of qubits to only being able to run low-depth quantum circuits with acceptable fidelity. This severely restricts what quantum algorithms can be compiled and implemented on such devices. One way to overcome these limitations is to expand the available gate set from single- and two-qubit gates to multi-qubit gates, which entangle three or more qubits in a single step. Here, we show that such multi-qubit gates can be realized by the simultaneous application of multiple two-qubit gates to a group of qubits where at least one qubit is invol…
In this work we investigate that whether one can construct single and two qubit gates for arbitrary quantum states from the principle of no signalling. We considered the problem for Pauli gates, Hadamard gate, C-Not gate.
We introduce the discording power of a unitary transformation, which assesses its capability to produce quantum discord, and analyze in detail the generation of discord by relevant classes of two-qubit gates. Our measure is based on the Cartan decomposition of two-qubit unitaries and on evaluating the maximum discord achievable by a unitary upon acting on classical-classical states at fixed purity. We found that there exist gates which are perfect discorders for any value of purity, and that they belong to a class of operators that includes the $\sqrt{SWAP}. Other gates, even those universal f…
In this paper, we propose a scheme to realize three-qubit controlled phase gate and multiqubit controlled-NOT gate of one qubit simultaneously controlling n target qubit with four level quantum system in a cavity. Adjustment of level spacing during the gates implementation is not required. Implementation time for multiqubit controlled NOT gate is independent of number of qubit. Three-qubit phase gate is generalized to n-qubit phase gate with multiple control qubit and the number of steps (complexity) reduces linearly as compare to conventional gate decomposition method. Our scheme can be appli…
In this paper, we study the optimal simulation of three-qubit unitary by using two-qubit gates. First, we give a lower bound on the two-qubit gates cost of simulating a multi-qubit gate. Secondly, we completely characterize the two-qubit gate cost of simulating a three-qubit controlled controlled gate by generalizing our result on the cost of Toffoli gate. The function of controlled controlled gate is simply a three-qubit controlled unitary gate and can be intuitively explained as follows: the gate will output the states of the two control qubit directly, and apply the given one-qubit unitary …
Purity decay rate in random circuits with different configurations of gates
本文利用多项式维转移矩阵的马尔可夫链描述，研究不同随机两体幺正门几何下 n 量子位链的纯度衰减，揭示多数电路的两阶段衰减机制及 λ_eff 对二分边界和门几何的依赖。
We propose how to realize a three-step controlled-phase gate of one superconducting qubit simultaneously controlling n qubits selected from N qubits in a cavity (1<n<N). The operation time of this gate is independent of the number n of qubits involved in the gate operation. This phase gate controlling at once n qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on n qubits.
We propose how to realize a three-step controlled-phase gate of one qubit simultaneously controlling $n$ qubits in a cavity or coupled to a resonator. The $n$ two-qubit controlled-phase gates, forming this multiqubit phase gate, can be performed simultaneously. The operation time of this phase gate is independent of the number $n$ of qubits. This phase gate controlling at once $n$ qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on $n$ qubits. We present two alternative approaches to implement this gate. One a…
We demonstrate an on-demand source of microwave single photons with 71--99\% intrinsic quantum efficiency. The source is narrowband (300\unite{kHz}) and tuneable over a 600 MHz range around 5.2 GHz. Such a device is an important element in numerous quantum technologies and applications. The device consists of a superconducting transmon qubit coupled to the open end of a transmission line. A $π$-pulse excites the qubit, which subsequently rapidly emits a single photon into the transmission line. A cancellation pulse then suppresses the reflected $π$-pulse by 33.5 dB, resulting in 0.005 photons …
We present improved circuits for the control-control-phase (Toffoli) gate and the control-swap (Fredkin) gate using three and four global two-qubit gates, respectively. This is a nearly double speed-up compared to the conventional circuits, which require five (for Toffoli) and seven (for Fredkin) conditional two-qubit gates. We apply the same approach to construct the conditional four-qubit phase gate by seven global two-qubit gates. We also present construction of the Toffoli and the Fredkin gates with five nearest-neighbour interactions. Our constructions do not employ ancilla qubits or anci…
Quantum algorithms often benefit from the ability to execute multi-qubit (>2) gates. To date such multi-qubit gates are typically decomposed into single- and two-qubit gates, particularly in superconducting qubit architectures. The ability to perform multi-qubit operations in a single step could vastly improve the fidelity and execution time of many algorithms. Here, we propose a single shot method for executing an i-Toffoli gate, a three-qubit gate gate with two control and one target qubit, using currently existing superconducting hardware. We show numerical evidence for a process fidelity o…
We explore the dynamics of two atoms interacting with a cavity field via deformed operators. Properties of the asymptotic regularization of entanglement measures proving, for example, purity cost, regularized fidelity and accuracy of information transfer are analyzed. We show that the robustness of a bipartite system having a finite number of quantum states vanishes at finite photon numbers, for arbitrary interactions between its constituents and with cavity field. Finally it is shown that the stability of the purity and the fidelity is improved in the absence of the deformation parameters.
Uncertainty equality for SU(N) observables enabling the experimentally friendly detection of k-inseparability via purity measurements
论文推导了有限维希尔伯特空间量子态的精确不确定性关系，并展示了纯度与不确定性之间的关系，为通过纯度测量检测k不可分性提供了新的方法。
Modifying $n$-qubit controlled-$ZX$ gate to be $n$-qubit Toffoli gate
本文修改受控-$ZX$门的分解方法，仅用$2n-3$个附加单量子比特门实现$n$-量子比特Toffoli门，保持原电路深度$8n-20$且无需辅助比特，并证明其在现有物理系统中易于构建。
High-fidelity three-qubit iToffoli gate for fixed-frequency superconducting qubits
研究固定频率超导量子比特中高保真三比特 iToffoli 门的实现，基于交叉共振效应并同步施加微波脉冲，达到 98.26% 的过程保真度，为多比特门开发开辟了新路径。
We demonstrate that in a coupled two-qubit system any single-qubit gate can be decomposed into two conditional two-qubit gates and that any conditional two-qubit gate can be implemented by a manipulation analogous to that used for a controlled two-qubit gate. Based on this we present a unified approach to implement universal single-qubit and two-qubit gates in a coupled two-qubit system with fixed always-on coupling. This approach requires neither supplementary circuit or additional physical qubits to control the coupling nor extra hardware to adjust the energy level structure. The feasibility…
We prove that a generic three-qubit quantum logic gate can be implemented using at most 98 one-qubit rotations about the $y$- and $z$-axes and 40 CNOT gates, beating an earlier bound of 64 CNOT gates.
In this paper, we settle the long-standing open problem of the minimum cost of two-qubit gates for simulating a Toffoli gate. More precisely, we show that five two-qubit gates are necessary. Before our work, it is known that five gates are sufficient and only numerical evidences have been gathered, indicating that the five-gate implementation is necessary. The idea introduced here can also be used to solve the problem of optimal simulation of three-qubit control phase introduced by Deutsch in 1989.
Experimental demonstration of a high-fidelity virtual two-qubit gate
本研究实验演示虚拟双量子比特门，通过电路中间测量实现投影门、确定性采样减少评估次数并结合量子误差缓解，将虚拟CZ门平均保真度提至0.9938±0.0002，为少比特量子模拟及远距双比特门实现提供实用方案。
In some quantum computing (QC) architectures, entanglement of an arbitrary number of qubits can be generated in a single operation. This property has many potential applications, and may specifically be useful for quantum error correction (QEC). Stabilizer measurements can then be implemented using a single multi-qubit gate instead of several two-qubit gates, thus reducing circuit depth. In this study, the toric code is used as a benchmark to compare the performance of two-qubit and five-qubit gates within parity-check circuits. We consider trapped ion qubits that are controlled via Raman tran…
We consider the implementation of two-qubit unitary transformations by means of CNOT gates and single-qubit unitary gates. We show, by means of an explicit quantum circuit, that together with local gates three CNOT gates are necessary and sufficient in order to implement an arbitrary unitary transformation of two qubits. We also identify the subset of two-qubit gates that can be performed with only two CNOT gates.
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. …
Two-qubit gates for the soft 0-π qubit
针对软0-π量子比特，提出一种无保护CZ门，利用计算态与高非计算态直接跃迁，在约160纳秒内实现约99.9%保真度，填补了双量子比特门空白。
Two-qubit gates are important components of quantum computing. However, unwanted interactions between qubits (so-called parasitic gates) can be particularly problematic and degrade the performance of quantum applications. In this work, we present two software methods to mitigate parasitic two-qubit gate errors. The first approach is built upon the KAK decomposition and keeps the original unitary decomposition for the error-free native two-qubit gate. It counteracts a parasitic two-qubit gate by only applying single-qubit rotations and therefore has no two-qubit gate overhead. We show the optim…
Time-optimal multi-qubit gates: Complexity, efficient heuristic and gate-time bounds
本研究证明时间最优多量子比特门合成是NP难的，给出特殊时间最优门的显式构造，提出多项式时间启发式合成算法，推导GZZ门时间上下界并推测其为O(n)标度，可实现更快更鲁棒的量子算法执行。
Optimal Construction of Two-Qubit Gates using the Symmetries of B Gate Equivalence Class
本文利用B门等价类的对称性，发现仅该等价类具有逆和镜像两种对称性，并找到一参数族可构造通用两比特量子电路，仅需两个非局部门。
Fast microwave-driven two-qubit gates between fluxonium qubits with a transmon coupler
本研究通过精心设计的微波驱动脉冲，实现了一个高保真度的回旋子量子比特间两个量子比特门，展示了快速频率选择性纠缠门的实现方法。
We construct a minimal robust controlled-NOT gate with an Ising-type interaction by which elementary two-qubit gates are implemented. It is robust against inaccuracy of the coupling strength and the obtained quantum circuits are constructed with the minimal number (N=3) of elementary two-qubit gates and several one-qubit gates. It is noteworthy that all the robust circuits can be mapped to one-qubit circuits robust against a pulse length error. We also prove that a minimal robust SWAP gate cannot be constructed with N=3, but requires N=6 elementary two-qubit gates.
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