Frank Verstraete, Henri Verschelde
We consider a single copy of a mixed state of two qubits and show how its fidelity or maximal singlet fraction is related to the entanglement measures concurrence and negativity. We characterize the extreme points of the convex set of states with constant fidelity, and use this to prove tight lower and upper bounds on the fidelity for a given amount of entanglement.
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We demonstrate high-fidelity Zeeman qubit state detection in a single trapped 88 Sr+ ion. Qubit readout is performed by shelving one of the qubit states to a metastable level using a narrow linewidth diode laser at 674 nm followed by state-selective fluorescence detection. The average fidelity reached for the readout of the qubit state is 0.9989(1). We then measure the fidelity of state tomography, averaged over all possible single-qubit states, which is 0.9979(2). We also fully characterize the detection process using quantum process tomography. This readout fidelity is compatible with recent…
Qubit state detection is an important part of a quantum computation. As number of qubits in a quantum register increases, it is necessary to maintain high fidelity detection to accurately measure the multi-qubit state. Here we present experimental demonstration of high-fidelity detection of a multi-qubit trapped ion register with average single qubit detection error of 4.2(1.5) ppm and a 4-qubit state detection error of 17(2) ppm, limited by the decay lifetime of the qubit, using a novel single-photon-sensitive camera with fast data collection, excellent temporal and spatial resolution, and lo…
In this Brief Report, we present a geometric observation for the Bures fidelity between two states of a qubit.
We give a simple way of characterising the average fidelity between a unitary and a general operation on a single qubit which only involves calculating the fidelities for a few pure input states.
We demonstrate single-shot qubit readout with fidelity sufficient for fault-tolerant quantum computation, for two types of qubit stored in single trapped calcium ions. For an optical qubit stored in the (4S_1/2, 3D_5/2) levels of 40Ca+ we achieve 99.991(1)% average readout fidelity in one million trials, using time-resolved photon counting. An adaptive measurement technique allows 99.99% fidelity to be reached in 145us average detection time. For a hyperfine qubit stored in the long-lived 4S_1/2 (F=3, F=4) sub-levels of 43Ca+ we propose and implement a simple and robust optical pumping scheme …
We analyzed the fidelity of the quantum state transfer (QST) from a photon-polarization qubit to an electron-spin-polarization qubit in a semiconductor quantum dot, with special attention to the exchange interaction between the electron and the simultaneously created hole. In order to realize a high-fidelity QST we had to separate the electron and hole as soon as possible, since the electron-hole exchange interaction modifies the orientation of the electron spin. Thus, we propose a double-dot structure to separate the electron and hole quickly, and show that the fidelity of the QST can reach a…
High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces crosstalk effect, simplifies calibration procedures, yet produces a controlled-Z gate in 30ns with a high fidelity of 99.5%, der…
We describe an efficient protocol to perform quantum state transfer using Hamiltonian dynamics with long-range interactions. The time to transfer $n$ qubits a sufficiently large distance is proportional to $\sqrt{n}$. Even without error correction, the fidelity of this multi-qubit state transfer process remains finite for arbitrarily well-separated qubits in the presence of uncorrelated random errors in coupling constants.
We demonstrate a quantum error correction scheme that protects against accidental measurement, using an encoding where the logical state of a single qubit is encoded into two physical qubits using a non-deterministic photonic CNOT gate. For the single qubit input states |0>, |1>, |0>+|1>, |0>-|1>, |0>+i|1>, and |0>-i|1> our encoder produces the appropriate 2-qubit encoded state with an average fidelity of 0.88(3) and the single qubit decoded states have an average fidelity of 0.93(5) with the original state. We are able to decode the 2-qubit state (up to a bit flip) by performing a measurement…
We study the convergence properties of state estimates of an oscillating qubit being monitored by a sequence of \textit{discrete}, unsharp measurements. Our method derives a differential equation determining the evolution of the estimation fidelity from a single incremental step. When the oscillation frequency $Ω$ is precisely known, the estimation fidelity converges exponentially fast to unity. For imprecise knowledge of $Ω$ we derive the asypmtotic estimation fidelity.
Quantum control for error correction is critical for the practical use of quantum computers. We address quantum optimal control for single-shot multi-qubit gates by framing as a feasibility problem for the Hamiltonian model and then solving with standard global-optimization software. Our approach yields faster high-fidelity ($>$99.99\%) single-shot three-qubit-gate control than obtained previously, and our method has enabled us to solve the quantum-control problem for a fast high-fidelity four-qubit gate.
An approach to the construction of the CNOT quantum logic gate for a 4-dimensional coupled-qubit model with weak but otherwise arbitrary coupling has been given recently [M. R. Geller et al., Phys. Rev. A, 012320 (2010)]. How does the resulting fidelity depend on the form of qubit-qubit coupling? In this paper we calculate intrinsic fidelity curves (fidelity in the absence of decoherence versus total gate time) for a variety of qubit-qubit interactions, including the commonly occurring isotropic Heisenberg and XY models, as well as randomly generated ones. For interactions not too close to tha…
Suppose, we are given two finite ensembles of pure qubit states, so that the qubits in each ensemble are prepared in identical (but unknown for us) states lying on the equator of the Bloch sphere. What is the best strategy to estimate fidelity between these two finite ensembles of qubit states? We discuss three possible strategies for the fidelity estimation. We show that the best strategy includes two stages: a specific unitary transformation on two ensembles and state estimation of the output states of this transformation.
Exploring the Fidelity of Flux Qubit Measurement in Different Bases via the Quantum Flux Parametron
本文通过理论建模和数值模拟，探讨了不同测量基底对单量子比特和耦合双量子比特系统测量保真度的影响，发现能量基底在单量子比特系统中保真度更高，同时测量基底在双量子比特系统中更优。
We describe and characterize an equal-fidelity surface in Bloch space targeted for a qubit state by means of equal-distance concept. The distance is generalized and defined as the Euclidean distance between extended Bloch vectors for arbitrary dimensional states. The distance is a genuine distance according to the definition and is related to other distances between quantum states and super-fidelity.
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…
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 explicitly calculate information, fidelity, and reversibility of an arbitrary single-qubit measurement on a completely unknown state. These quantities are expressed as functions of a single parameter, which is the ratio of the two singular values of the measurement operator corresponding to the obtained outcome. Thus, our results give information tradeoff relations to the fidelity and to the reversibility at the level of a single outcome rather than that of an overall outcome average.
We analyze a system of fermionic $^{6}$Li atoms in an optical trap, and show that an atom "on demand" can be prepared with ultra-high fidelity, exceeding 0.99998. This process can be scaled to many sites in parallel, providing a realistic method to initialize N qubits at ultra-high fidelity for quantum computing. We also show how efficient quantum gate operation can be implemented in this system, and how spatially resolved single-atom detection can be performed.
We describe single-shot readout of a trapped-ion multi-qubit register using space and time-resolved camera detection. For a single qubit we measure 0.9(3)x10^{-4} readout error in 400us exposure time, limited by the qubit's decay lifetime. For a four-qubit register (a "qunybble") we measure an additional error of only 0.1(1)x10^{-4} per qubit, despite the presence of 4% optical cross-talk between neighbouring qubits. A study of the cross-talk indicates that the method would scale with negligible loss of fidelity to ~10000 qubits at a density <~1 qubit/um^2, with a readout time ~1us/qubit.
When a harmonic oscillator is under the influence of a Gaussian process such as linear damping, parametric gain, and linear coupling to a thermal environment, its coherent states are transformed into states with Gaussian Wigner function. Qubit states can be encoded in the |0> and |1> Fock states of a quantum harmonic oscillator, and it is relevant to know the fidelity of the output qubit state after a Gaussian process on the oscillator. In this paper we present a general expression for the average qubit fidelity in terms of the first and second moments of the output from input coherent states …
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…
We study the evolution of qubit-environment entanglement, quantified using Negativity, for NV-center spin qubits interacting with an environment of $^{13}$C isotope partially polarized nuclear spins in the diamond lattice. We compare it with the evolution of the Fidelity of environmental states conditional on the pointer states of the qubit, which can serve as a tool to distinguish between entangling and non-entangling decoherence in pure-dephasing scenarios. The two quantities show remarkable agreement during the evolution in a wide range of system parameters, leading to the conclusion that t…
Single-qubit operations on singlet-triplet qubits in GaAs double quantum dots have not yet reached the fidelities required for fault-tolerant quantum information processing. Considering experimentally important constraints and using measured noise spectra, we numerically minimize the effect of decoherence (including high-frequency 1/f-like noise) and show theoretically that quantum gates with fidelities higher than 99.9% are achievable. We also present a self-consistent tuning protocol which should allow the elimination of individual systematic gate errors directly in an experiment.
We propose a linear-optical setup for heralded qubit amplification with tunable output qubit fidelity. We study its success probability as a function of output qubit fidelity showing that at the expense of lower fidelity, the setup can considerably increase probability of successful operation. These results are subsequently applied in a proposal for state dependent qubit amplification. Similarly to state-dependent quantum cloning, the a priori information about the input state allows to optimize the qubit amplification procedure to obtain better fidelity versus success probability trade-off.
Superconducting fluxonium qubits provide a promising alternative to transmons on the path toward large-scale superconductor-based quantum computing due to their better coherence and larger anharmonicity. A major challenge for multi-qubit fluxonium devices is the experimental demonstration of a scalable crosstalk-free multi-qubit architecture with high fidelity single-qubit and two-qubit gates, single-shot readout and state initialization. Here, we present a two-qubit fluxonium-based quantum processor with a tunable coupler element following our theoretical proposal [DOI: 10.1063/5.0064800]. We…
Superconducting circuits with coupler architecture receive considerable attention due to their advantages in tunability and scalability. Although single-qubit gates with low error have been achieved, high-fidelity two-qubit gates in coupler architecture are still challenging. This paper pays special attention to examining the gate error sources and primarily concentrates on the related physical mechanism of ZZ parasitic couplings using a systematic effective Hamiltonian approach. Benefiting from the effective Hamiltonian, we provide simple and straightforward insight into the ZZ parasitic coup…
Using two trapped ion species ($\rm{^{27}Al^+}$ and $\rm{^9Be^+}$) as primary and ancillary systems, we implement qubit measurements based on the repetitive transfer of information and quantum nondemolition detection. The repetition provides a natural mechanism for an adaptive measurement strategy, which leads to exponentially lower error rates compared to using a fixed number of detection cycles. For a single qubit we demonstrate 99.94 % measurement fidelity. We also demonstrate a technique for adaptively measuring multiple qubit states using a single ancilla, and apply the technique to spect…
Non-demolition fluorescence readout and high-fidelity unconditional reset of a fluxonium qubit via dissipation engineering
本文提出无谐振器的耗散工程方案，利用平面滤波器和读出跃迁选择，实现 fluxonium 量子比特的非破坏荧光读出及快速、高保真、全微波无条件重置。
We describe a simple way of characterizing the average fidelity between a unitary (or anti-unitary) operator and a general operation on a single qubit, which only involves calculating the fidelities for a few pure input states, and discuss possible applications to experimental techniques including Nuclear Magnetic Resonance (NMR).
The duration and fidelity of qubit readout is a critical factor for applications in quantum information processing as it limits the fidelity of algorithms which reuse qubits after measurement or apply feedback based on the measurement result. Here we present fast multiplexed readout of five qubits in a single 1.2 GHz wide readout channel. Using a readout pulse length of 80 ns and populating readout resonators for less than 250 ns we find an average correct assignment probability for the five measured qubits to be $97\%$. The differences between the individual readout errors and those found whe…
In this paper we calculate the loss of fidelity due to quantum leakage for the Josephson charge qubit (JCQ) in virtue of the Mathieu functions. It is shown that for an present typical parameters of JCQ E_{J}/E_{ch}~0.02, the loss of the fidelity per elementary operation is about 10^(-4) which satisfy the DiVincenzo's low decoherence criterion. By appropriately improving the design of the Josephson junction, namely, decreasing E_{J}/E_{ch} to 0.01, the loss of fidelity per elementary operation can decrease to 10^(-6) even smaller.
Quantum teleportation with an arbitrary two-qubit state can be appropriately characterized in terms of maximal fidelity and fidelity deviation. The former quantifies optimality of the process and is defined as the maximal average fidelity achievable within the standard protocol and local unitary strategies, whereas the latter, defined as the standard deviation of fidelity over all input states, is a measure of fidelity fluctuations. The maximal fidelity for a two-qubit state is known and is given by a simple formula that can be exactly computed, but no such formula is known for the fidelity de…
I explore the entanglement evolution of a four qubit cluster state in a dephasing environment concentrating on the phenomenon of entanglement sudden death (ESD). Specifically, I ask whether the onset of ESD has an effect on the utilization of this cluster state as a means of implementing a single qubit rotation in the measurement based cluster state model of quantum computation. To do this I compare the evolution of the entanglement to the fidelity, a measure of how accurately the desired state (after the measurement based operations) is achieved. I find that ESD does not cause a change of beh…
This letter generalizes the expression for the average fidelity of single qubits, as found by Bowdrey et al., to the case of n qubits. We use a simple algebraic approach with basis elements for the density-matrix expansion expressed as Kronecker products of n Pauli spin matrices. An explicit integration over initial states is avoided by invoking the invariance of the state average under unitary transformations of the initial density matrix. The results have applications to measurements of quantum information, for example in ion-trap and NMR experiments.
We study the two qubits Heisenberg XX chain with magnetic impurity in the presence of the external magnetic field and calculate the optimal fidelity of standard teleportation via the thermal equilibrium state. It is found that the combined influence of magnetic impurity and external magnetic field can increase the critical temperatures of entanglement and quantum teleportation without limit. The relation between two kinds of critical temperatures is revealed.
The prospect of computational hardware with quantum advantage relies critically on the quality of quantum gate operations. Imperfect two-qubit gates is a major bottleneck for achieving scalable quantum information processors. Here, we propose a generalizable and extensible scheme for a two-qubit coupler switch that controls the qubit-qubit coupling by modulating the coupler frequency. Two-qubit gate operations can be implemented by operating the coupler in the dispersive regime, which is non-invasive to the qubit states. We investigate the performance of the scheme by simulating a universal tw…
The speed of quantum gates and measurements is a decisive factor for the overall fidelity of quantum protocols when performed on physical qubits with finite coherence time. Reducing the time required to distinguish qubit states with high fidelity is therefore a critical goal in quantum information science. The state-of-the-art readout of superconducting qubits is based on the dispersive interaction with a readout resonator. Here, we bring this technique to its current limit and demonstrate how the careful design of system parameters leads to fast and high-fidelity measurements without affectin…
Based on a `shortcut-to-adiabaticity' (STA) scheme, we theoretically design and experimentally realize a set of high-fidelity single-qubit quantum gates in a superconducting Xmon qubit system. Through a precise microwave control, the qubit is driven to follow a fast `adiabatic' trajectory with the assistance of a counter-diabatic field and the correction of derivative removal by adiabatic gates. The experimental measurements of quantum process tomography and interleaved randomized benchmarking show that the process fidelities of our STA quantum gates are higher than 94.9% and the gate fideliti…
A Simulation Methodology for Superconducting Qubit Readout Fidelity
本文提出一种基于Matlab和Ansys HFSS的超导量子比特读取保真度仿真方法，实现读取路径协同优化，预测结果与实验吻合，发现降低7dB功率或缩窄40%脉冲宽度仍能保持高保真度。
Remote state preparation (RSP) is the act of preparing a quantum state at a remote location without actually transmitting the state itself. Using at most two classical bits and a single shared maximally entangled state, one can in theory remotely prepare any qubit state with certainty and with perfect fidelity. However, in any experimental implementation the average fidelity between the target and output states cannot be perfect. In order for an RSP experiment to demonstrate genuine quantum advantages, it must surpass the optimal threshold of a comparable classical protocol. Here we study the …
We demonstrate coherent control of two logical qubits encoded in a decoherence free subspace (DFS) of four dipolar-coupled protons in an NMR quantum information processor. A pseudo-pure fiducial state is created in the DFS, and a unitary logical qubit entangling operator evolves the system to a logical Bell state. The four-spin molecule is partially aligned by a liquid crystal solvent, which introduces strong dipolar couplings among the spins. Although the system Hamiltonian is never fully specified, we demonstrate high fidelity control over the logical degrees of freedom. In fact, the DFS enc…
Recent investigations show that conservation laws limit the accuracy of gate operations in quantum computing. The inevitable error under the angular momentum conservation law has been evaluated so far for the CNOT, Hadamard, and NOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, we extend the above results to general single-qubit gates. We obtain an upper bound of the gate fidelity of arbitrary single-qubit gates implemented under arbitrary conservation laws, determined by the geometry of the conservation law and the gate operation on the Bloch sphere as well as the si…
Enhancing qubit readout fidelity with two-mode squeezing of the coherent measurement signal
本文提出通过同时测量双模压缩态和相干组合提升量子比特读取保真度，适用于高频放大器和噪声抑制场景。
We address the problem of optimal estimation of the relative phase for two-dimensional quantum systems in mixed states. In particular, we derive the optimal measurement procedures for an arbitrary number of qubits prepared in the same mixed state.
Quantum computers based on silicon are promising candidates for long term universal quantum computation due to the long coherence times of electron and nuclear spin states. Furthermore, the continuous progress of micro- and nano- electronics, also related to the scaling of Metal-Oxide-Semiconductor (MOS) systems, makes possible to control the displacement of single dopants thus suggesting their exploitation as qubit holders. Flip-flop qubit is a donor based qubit (DQ) where interactions between qubits are achievable for distance up to several hundred nanometers. In this work, a linear array of…
Quantum cloning of two identical mixed qubits $ρ\otimes ρ$ is studied. We propose the quantum cloning transformations not only for the triplet (symmetric) states but also for the singlet (antisymmetric) state. We can copy these two identical mixed qubits to M (M>2) copies. This quantum cloning machine is optimal in the sense that the shrinking factor between the input and the output single qubit achieves the upper bound. The result shows that we can copy two identical mixed qubits with the same quality as that of two identical pure states.
Robust, fast and high-fidelity composite single-qubit gates for superconducting transmon qubits
针对超导 transmon 量子比特的相干误差问题，提出基于复合脉冲的控制方法，实现鲁棒快速的高保真单量子比特门，并经仿真和四种独立技术验证。
We calculate the trade-off between the quality of estimating the quantum state of an ensemble of identically prepared qubits and the minimum level of disturbance that has to be introduced by this procedure in quantum mechanics. The trade-off is quantified using two mean fidelities: the operation fidelity which characterizes the average resemblance of the final qubit state to the initial one, and the estimation fidelity describing the quality of the obtained estimate. We analyze properties of quantum operations saturating the achievability bound for the operation fidelity versus the estimation …
In this paper, we discuss the partial separability and its criteria problems of multipartite qubit mixed-states. First we strictly define what is the partial separability of a multipartite qubit system. Next we give a reduction way from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that a N-partite qubit mixed-state to be partially separable is its reduction to satisfy the PPT condition. PACC numbers: 03.67.Mn; 03.65.Ud; 03.67.Hk
Transmon qubit readout fidelity at the threshold for quantum error correction without a quantum-limited amplifier
提出一种无量子极限放大器的超导量子比特读出方案，结合shelving技术与双音激发，并利用机器学习后处理，在140ns读出时间内实现了99.5%的双态和96.9%的三态分配保真度，达到量子纠错阈值。
We analyze the class of single qubit channels with the environment modeled by a one-qubit mixed state. The set of affine transformations for this class of channels is computed analytically, employing the canonical form for the two-qubit unitary operator. We demonstrate that, 3/8 of the generalized depolarizing channels can be simulated by the one-qubit mixed state environment by explicitly obtaining the shape of the volume occupied by this class of channels within the tetrahedron representing the generalized depolarizing channels. Further, as a special case, we show that the two-Pauli Channel …
Simulation of Two-qubit Gate Variability and Fidelity of Spin Qubits Built on Nanosheet Technology
使用QTCAD模拟套件研究基于纳米片技术的硅自旋量子比特双量子点，评估工艺和偏置变化对交换能的影响，并通过主方程求解两量子比特门保真度，发现毫伏级偏置变化可将保真度降至99%以下。
Systematic errors in spin rotation operations using simple RF pulses place severe limitations on the usefulness of the pulsed magnetic resonance methods in quantum computing applications. In particular, the fidelity of quantum logic operations performed on electron spin qubits falls well below the threshold for the application of quantum algorithms. Using three independent techniques, we demonstrate the use of composite pulses to improve this fidelity by several orders of magnitude. The observed high-fidelity operations are limited by pulse phase errors, but nevertheless fall within the limits…
We propose a practical, scalable, and efficient scheme for quantum computation using spatially separated matter qubits and single photon interference effects. The qubit systems can be NV-centers in diamond, Pauli-blockade quantum dots with an excess electron or trapped ions with optical transitions, which are each placed in a cavity and subsequently entangled using a double-heralded single-photon detection scheme. The fidelity of the resulting entanglement is extremely robust against the most important errors such as detector loss, spontaneous emission, and mismatch of cavity parameters. We de…
The separable mixed 2-qubit X-states are classified in accordance with degeneracies in the spectrum of density matrices. It is shown that there are four classes of separable X-states, among them: one 4D family, a pair of 2D family and a single, zero-dimensional maximally mixed state.
We report high-fidelity, quantum nondemolition, single-shot readout of a superconducting transmon qubit using a DC-biased superconducting low-inductance undulatory galvanometer(SLUG) amplifier. The SLUG improves the system signal-to-noise ratio by 7 dB in a 20 MHz window compared with a bare HEMT amplifier. An optimal cavity drive pulse is chosen using a genetic search algorithm, leading to a maximum combined readout and preparation fidelity of 91.9% with a measurement time of Tmeas = 200ns. Using post-selection to remove preparation errors caused by heating, we realize a combined preparation …
We demonstrate laser-driven two-qubit and single-qubit logic gates with fidelities 99.9(1)% and 99.9934(3)% respectively, significantly above the approximately 99% minimum threshold level required for fault-tolerant quantum computation, using qubits stored in hyperfine ground states of calcium-43 ions held in a room-temperature trap. We study the speed/fidelity trade-off for the two-qubit gate, for gate times between 3.8$μ$s and 520$μ$s, and develop a theoretical error model which is consistent with the data and which allows us to identify the principal technical sources of infidelity.
It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an arbitrary mixed state is sufficient to implement Shor's factorization algorithm efficiently.
High-fidelity QND readout and measurement back-action in a Tantalum-based high-coherence fluxonium qubit
本文探索了基于钽的高相干fluxonium量子比特的测量特性，实现了高达97.8%的单次测量保真度和99.6%的QND保真度，发现态混合误差限制了其性能，为优化读取提供了方向。
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