We show an efficient purification protocol in solid-state qubits by replacing the usual bilateral CNOT gate by the bilateral iSWAP gate. We also show that this replacement can be applied to breeding and hashing protocols, which are useful for quantum state purification. These replacements reduce the number of fragile and cumbersome two-qubit operations, making more feasible quantum-information-processing with solid-state qubits. As examples, we also present quantitative analyses for the required time to perform state purification using either superconducting or semiconducting qubits.
The majority of linear-optical nondestructive implementations of universal quantum gates are based on single-photon resolving detectors. We propose two implementations, which are nondestructive (i.e., destroying only ancilla states) and work with conventional detectors (i.e., which do not resolve number of photons). Moreover, we analyze a recently proposed scheme of Wang et al. [J. Opt. Soc. Am. B \textbf{27}, 27 (2010)] of an optical iSWAP gate based on two ancillae in Bell's states, classical feedforward, and conventional detectors with the total probability of success equal to $η^4/32$, whe…
A current bottleneck for quantum computation is the realization of high-fidelity two-qubit quantum operations between two and more quantum bits in arrays of coupled qubits. Gates based on parametrically driven tunable couplers offer a convenient method to entangle multiple qubits by selectively activating different interaction terms in the effective Hamiltonian. Here, we study theoretically and experimentally a superconducting qubit setup with two transmon qubits connected via a capacitively coupled tunable bus. We develop a time-dependent Schrieffer-Wolff transformation and derive analytic ex…
Expanding the Neutral Atom Gate Set: Native iSWAP and Exchange Gates from Dipolar Rydberg Interactions
Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）；Parity Quantum Computing GmbH（Parity量子计算有限公司）；Parity Quantum Computing Germany GmbH（Parity量子计算德国有限公司）；Parity Quantum Computing France SAS（Parity量子计算法国股份有限公司）
High-fidelity two-qubit gates at scale are a key requirement to realize the full promise of quantum computation and simulation. The advent and use of coupler elements to tunably control two-qubit interactions has improved operational fidelity in many-qubit systems by reducing parasitic coupling and frequency crowding issues. Nonetheless, two-qubit gate errors still limit the capability of near-term quantum applications. The reason, in part, is the existing framework for tunable couplers based on the dispersive approximation does not fully incorporate three-body multi-level dynamics, which is e…
Simple analytical flux-tuned iSWAP pulses for leakage suppression
Institute for Quantum Control (PGI-8), Forschungszentrum Jülich（于利希研究中心量子控制研究所）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；Institute for Functional Quantum System (PGI-13), Forschungszentrum Jülich（于利希研究中心功能量子系统研究所）；Department of Physics, RWTH Aachen University（亚琛工业大学物理系）
The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms. A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity. Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits. Using randomized benchmarking protocols we estimate an error per gate of $0.9\pm0.03\%$ and $1.3\pm0.4\%$ fidelity for…
Significant experimental advances in single-electron silicon spin qubits have opened the possibility of realizing long-range entangling gates mediated by microwave photons. Recently proposed iSWAP gates, however, require tuning qubit energies into resonance and have limited fidelity due to charge noise. We present a novel photon-mediated cross-resonance gate that is consistent with realistic experimental capabilities and requires no resonant tuning. Furthermore, we propose gate sequences capable of suppressing errors due to quasistatic noise for both the cross-resonance and iSWAP gates.
We experimentally demonstrate a parametric iSWAP gate in a superconducting circuit based on a tunable coupler for achieving a continuous tunability to eliminate unwanted qubit interactions. We implement the twoqubit iSWAP gate by applying a fast-flux bias modulation pulse on the coupler to turn on parametric exchange interaction between computational qubits. The controllable interaction can provide an extra degree of freedom to verify the optimal condition for constructing the parametric gate. Aiming to fully investigate error sources of the two-qubit gates, we perform quantum process tomograp…
A generalization of the quantum XOR-gate is presented which operates in arbitrary dimensional Hilbert spaces. Together with one-particle Fourier transforms this gate is capable of performing a variety of tasks which are important for quantum information processing in arbitrary dimensional Hilbert spaces. Among these tasks are the preparation of Bell states, quantum teleportation and quantum state purification. A physical realization of this generalized XOR-gate is proposed which is based on non-linear optical elements.
The first realization of solid state quantum computer was demonstrated recently by using artificial atoms -- transmons in superconducting resonator. Here, we propose a novel architecture of flexible and scalable quantum computer based on a waveguide circuit coupling many quantum nodes of controlled atomic ensembles. For the first time, we found the optimal practically attainable parameters of the atoms and circuit for 100{%} efficiency of quantum memory for multi qubit photon fields and confirmed experimentally the predicted perfect storage. Then we revealed self modes for reversible transfer …
Parasitic crosstalk in superconducting quantum devices is a leading limitation for quantum gates. We demonstrate the suppression of static ZZ crosstalk in a two-qubit, two-coupler superconducting circuit, where the frequency of a tunable coupler can be adjusted such that the ZZ interaction from each coupler destructively interfere. We verify the crosstalk elimination with simultaneous randomized benchmarking, and use a parametrically activated iSWAP interaction to achieve a Bell state preparation fidelity of 98.5% and a $\sqrt{\textrm{iSWAP}}$ gate fidelity of 94.8% obtained via quantum proces…
We consider the effects of gate noise on the operation of an entanglement purification protocol. We characterize the performance of the protocol by two measures, the minimum purifiable input state fidelity, and the maximum output state fidelity. Both these measures are a function of gate error rate. For sufficiently large gate error rate these two measures converge, defining a threshold on gate error rates. Numerically, we estimate this threshold to be $9.2\times 10^{-2}$, which is achievable with many present day experimental architectures. (This paper is written in an experimental rapid comm…
Based on a multimode multilevel Jaynes-Cummings model and multiphoton resonance theory, a set of universal two- and three-qubit gates, namely the iSWAP and the Fredkin gates, has been realized where dual-rail qubits are encoded in cavities. In this way the information has been stored in cavities and the off-resonant atomic levels have been eliminated by the semi-classical theory of an effective two-level Hamiltonian. A further semi-classical model, namely the spin-$J$ model, has been introduced so that a complete population inversion for levels of interest has been achieved and periodic multil…
In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial local, independent, noise. It is found that the gate operations must be subject to less than 5.3% error. An existing proof that purification is equivalent to error correction is used to show that this bound can also be applied to concatenated error correcting codes in the presence of noisy gates, and hence gives a limit to the tolerable error rate for a fault-tolerant quantum computer formed by concatenation. This is shown to ap…
We theoretically analyze a system where two electrons are trapped separately in two quantum dots on a suspended carbon nanotube (CNT), subject to external ac electric driving. An indirect mechanically-induced coupling of two distant single electron spins is induced by the interaction between the spins and the mechanical motion of the CNT. We show that a two-qubit iSWAP gate and arbitrary single-qubit gates can be obtained from the intrinsic spin-orbit coupling. Combining the iSWAP gate and single-qubit gates, maximally entangled states of two spins can be generated in a single step by varying …
iSWAP maximises the second-moment spectral gap in random quantum circuits
College of Mathematics and Informatics, South China Agricultural University（华南农业大学数学与信息学院）；Institute of Advanced Intelligence and Computing (IAIC), Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局高级智能与计算研究所）；Division of Mathematical Sciences, Nanyang Technological University（南洋理工大学数理科学系）
该研究证明 iSWAP 门可最大化随机量子电路中厄米二阶矩算子的谱隙，还证明非对称四点不等式定义的多面锥在 iSWAP 半群转置下不变，解决了 Kong 等人的相关猜想。
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…
We describe and implement a family of entangling gates activated by radio-frequency flux modulation applied to a tunable transmon that is statically coupled to a neighboring transmon. The effect of this modulation is the resonant exchange of photons directly between levels of the two-transmon system, obviating the need for mediating qubits or resonator modes and allowing for the full utilization of all qubits in a scalable architecture. The resonance condition is selective in both the frequency and amplitude of modulation and thus alleviates frequency crowding. We demonstrate the use of three …
We consider the two-step method [A. R. Kuzmak and V. M. Tkachuk, Phys. Lett. A 378 (2014) 1469] for preparation of an arbitrary quantum gate on two spins with anisotropic Heisenberg interaction. At the first step, the system evolves during some period of time. At the second step, we apply pulsed magnetic field individually to each spin. We obtain the conditions for realization of SWAP, iSWAP, $\sqrt{SWAP}$ and entangled gates. Finally, we consider the implementation of this method on the physical system of ultracold atoms in optical lattice.
To achieve the practical applications of near-term noisy quantum devices, low-cost ways to mitigate the noise damages in the devices are essential. In many applications, the noiseless state we want to prepare is often a pure state, which has recently inspired a range of purification-based quantum error mitigation proposals. The existing proposals either are limited to the suppressions of only the leading-order state preparation errors, or require a large number of long-range gates that might be challenging to implement depending on the qubit architecture. This article will provide an overview …
Quantum algorithms offer a dramatic speedup for computational problems in machine learning, material science, and chemistry. However, any near-term realizations of these algorithms will need to be heavily optimized to fit within the finite resources offered by existing noisy quantum hardware. Here, taking advantage of the strong adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a 3x reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an iSWAP-like gate to attain an arbitrary swap angle, $θ$, and a…
The problem of finding efficient decompositions of multi-qubit gates is of importance for quantum computing, especially, in application to existing noisy intermediate-scale quantum devices, whose resources are substantially limited. Here we propose a decomposition scheme for a generalized $N$-qubit Toffoli gate with the use of $2N-3$ two-qutrit gates for arbitrary connectivity. The fixed number of the required additional levels (the choice of qutrits is optimal) and the use of the iSWAP gate as a native operation make our approach directly applicable for ongoing experiments with superconductin…
We describe novel purification protocols for bicolorable graph states. The protocols scale efficiently for large graph states. We introduce a method of analysis that allows us to derive simple recursion relations characterizing their behavior as well as analytical expressions for their thresholds and fixed point behavior. We introduce two purification protocols with high threshold. They can, for graph degree four, tolerate 1% (3%) gate error or 20% (30%) local error.
A key challenge for semiconductor quantum-dot charge qubits is the realization of long-range qubit coupling and performing high-fidelity gates based on it. Here, we describe a new type of charge qubit formed by an electron confined in a triple-quantum-dot system, enabling single and two-qubit gates working in the dipolar and quadrupolar detuning sweet spots. We further present the form for the long-range dipolar coupling between the charge qubit and the superconducting resonator. Based on the hybrid system composed of the qubits and the resonator, we present two types of entangling gates: the …
We propose a strategy for engineering multi-qubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number N of qubits, with specific XX+YY couplings between nearest neighbors. For this so-called Krawtchouk chain, a 2-body dr…
We describe an entanglement purification protocol (EPP) for multipartite three-level atomic entangled pair using photonic Faraday rotation. In this EPP, the multipartite atomic entangled state can be purified with the help of some single photons. This protocol resorts to the photonic Faraday rotation to realize the function of the controlled-Not (CNOT) gate. The purified multipartite atomic entangled state can be retained and to be repeated to reach a higher fidelity.
We present a simple protocol to purify bipartite entanglement in spin-1/2 particles by utilizing only natural spin-spin interactions, i.e. those that can commonly be realized in realistic physical systems, and S_z-measurements on single spins. Even the standard isotropic Heisenberg interaction is shown to be sufficient to purify mixed state entanglement if there are at least three pairs of spins. This approach could be useful for quantum information processing in solid-state-based systems.
A new purification scheme is proposed which applies to arbitrary dimensional bipartite quantum systems. It is based on the repeated application of a special class of nonlinear quantum maps and a single, local unitary operation. This special class of nonlinear quantum maps is generated in a natural way by a hermitian generalized XOR-gate. The proposed purification scheme offers two major advantages, namely it does not require local depolarization operations at each step of the purification procedure and it purifies more efficiently than other know purification schemes.
We investigate entanglement purification protocols based on hashing, where a large number of noisy entangled pairs is jointly processed to obtain a reduced number of perfect, noiseless copies. While hashing and breeding protocols are the only purification protocols that asymptotically obtain a nonzero yield, they are not applicable in a realistic scenario if local gates and measurements are imperfect. We show that such problems can be overcome by a compact measurement-based implementation, yielding entanglement purification schemes with nonzero yield that are applicable also in noisy scenarios…
We demonstrate fast two-qubit gates using a parity-violated superconducting qubit consisting of a capacitively-shunted asymmetric Josephson-junction loop under a finite magnetic flux bias. The second-order nonlinearity manifesting in the qubit enables the interaction with a neighboring single-junction transmon qubit via first-order inter-qubit sideband transitions with Rabi frequencies up to 30~MHz. Simultaneously, the unwanted static longitudinal~(ZZ) interaction is eliminated with ac Stark shifts induced by a continuous microwave drive near-resonant to the sideband transitions. The average f…
We investigate measurement-based quantum communication with noisy resource states that are generated by entanglement purification. We consider the transmission of encoded information via noisy quantum channels using a measurement-based implementation of encoding, error correction and decoding. We show that such an approach offers advantages over direct transmission, gate-based error correction and measurement-based schemes with direct generation of resource states. We analyze the noise structure of resource states generated by entanglement purification and show that a local error model, i.e. n…
Recently, two-photon six-qubit hyperentangled states were produced in experiment and they can improve the channel capacity of quantum communication largely. Here we present a scheme for the hyperentanglement purification of nonlocal two-photon systems in three degrees of freedom (DOFs), including the polarization, the first-longitudinal-momentum, and the second longitudinal momentum DOFs. Our hyperentanglement purification protocol (hyper-EPP) is constructed with two steps resorting to parity-check quantum nondemolition measurement on the three DOFs and SWAP gates, respectively. With these two…
We develop a theory for the interaction of multi-level atoms with multi-mode cavities yielding cavity-enhanced multi-photon resonances. The locations of the resonances are predicted from the use of effective two- and three-level Hamiltonians. As an application we show that quantum gates can be realised when photonic qubits are encoded on the cavity modes in arrangements where ancilla atoms transit the cavity. The fidelity of operations is increased by conditional measurements on the atom and by the use of a selected, dual-rail, Hilbert space. A universal set of gates is proposed, including the…
In the framework of cavity QED, we propose a practical scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid CNOT gates, thus reducing complicated pulse sequences and superfluous qubit operations. Our interaction scheme works in a deterministic way, and together with entanglement distribution and swapping, opens a route towards efficient quantum repeaters for long-distance quantum communication.
We propose a quantum algorithm for the purification of a generic mixed state $ρ$ of a $n$-qudit system by using an ancillary $n$-qudit system. The algorithm is optimal in that (i) the number of ancillary qudits cannot be reduced, (ii) the number of parameters which determine the purification state $|Ψ>$ exactly equals the number of degrees of freedom of $ρ$, and (iii) $|Ψ>$ is easily determined from the density matrix $ρ$. Moreover, we introduce a quantum circuit in which the quantum gates are unitary transformations acting on a $2n$-qudit system. These transformations are determined by parame…
