A four-level qubit system is applied to realize quantum half-adder operation.The half-adder circuit is obtained in terms of a quantum CPHASE gate realized by the qubits comprised of four energy levels [C.P. Yang, Prog.Theor.Phys.128, 587 (2012)], and such a CPHASE gate is demonstrated using the transmon.Commonly, higher energy levels are very sensitive and are easily perturbed by the noise sources.Compared to other qubit systems, the higher energy levels of the transmon are less prone to noise such as charge noise, flux noise and other noises.Further, the order of the dephasing time of the higher energy levels (third and fourth energy levels) is nearly the same as that of the lower energy levels of the transmon when the ratio between the Josephson energy and the charging energy 1.A system of three transmons coupled to a single high quality-factor superconducting coplanar resonator is demonstrated to obtain two-and three-qubit CPHASE gates which are in turn used to obtain the quantum half-adder operation.The main advantage of this quantum half-adder scheme is the reduction in the number of required elementary gates, leading to a significant increase in operational speed and robustness compared to the other existing half-adder schemes.The operational time of a complete half-adder operation is ∼37 ns.The methods presented in this article can also be implemented for more complicated quantum circuits.. . . . .
A four-level qubit system is applied to realize quantum half-adder operation.The half-adder circuit is obtained in terms of a quantum CPHASE gate realized by the qubits comprised of four energy levels [C.P. Yang, Prog.Theor.Phys.128, 587 (2012)], and such a CPHASE gate is demonstrated using the transmon.Commonly, higher energy levels are very sensitive and are easily perturbed by the noise sources.Compared to other qubit systems, the higher energy levels of the transmon are less prone to noise such as charge noise, flux noise and other noises.Further, the order of the dephasing time of the higher energy levels (third and fourth energy levels) is nearly the same as that of the lower energy levels of the transmon when the ratio between the Josephson energy and the charging energy 1.A system of three transmons coupled to a single high quality-factor superconducting coplanar resonator is demonstrated to obtain two-and three-qubit CPHASE gates which are in turn used to obtain the quantum half-adder operation.The main advantage of this quantum half-adder scheme is the reduction in the number of required elementary gates, leading to a significant increase in operational speed and robustness compared to the other existing half-adder schemes.The operational time of a complete half-adder operation is ∼37 ns.The methods presented in this article can also be implemented for more complicated quantum circuits.. . . . .
Short dephasing times pose one of the main challenges in realizing a quantum computer. Different approaches have been devised to cure this problem for superconducting qubits, a prime example being the operation of such devices at optimal working points, so-called sweet spots. This latter approach led to significant improvement of T2 times in Cooper pair box qubits [D. Vion et al., Science 296, 886 (2002)]. Here, we introduce a new type of superconducting qubit called the transmon. Unlike the charge qubit, the transmon is designed to operate in a regime of significantly increased ratio of Josephson energy and charging energy EJ/EC. The transmon benefits from the fact that its charge dispersion decreases exponentially with EJ/EC, while its loss in anharmonicity is described by a weak power law. As a result, we predict a drastic reduction in sensitivity to charge noise relative to the Cooper pair box and an increase in the qubit-photon coupling, while maintaining sufficient anharmonicity for selective qubit control. Our detailed analysis of the full system shows that this gain is not compromised by increased noise in other known channels.
Short dephasing times pose one of the main challenges in realizing a quantum computer. Different approaches have been devised to cure this problem for superconducting qubits, a prime example being the operation of such devices at optimal working points, so-called ``sweet spots.'' This latter approach led to significant improvement of T2 times in Cooper pair box qubits [D. Vion et al., Science 296, 886 (2002)]. Here, we introduce a new type of superconducting qubit called the ``transmon.'' Unlike the charge qubit, the transmon is designed to operate in a regime of significantly increased ratio of Josephson energy and charging energy EJ∕EC. The transmon benefits from the fact that its charge dispersion decreases exponentially with EJ∕EC, while its loss in anharmonicity is described by a weak power law. As a result, we predict a drastic reduction in sensitivity to charge noise relative to the Cooper pair box and an increase in the qubit-photon coupling, while maintaining sufficient anharmonicity for selective qubit control. Our detailed analysis of the full system shows that this gain is not compromised by increased noise in other known channels.
Superconducting quantum computing is a solid state quantum computing technology based on Josephson junction circuits. It becomes one of the most promising candidates for realizing practical quantum computer/simulator, because of its scalability, easy to coupling and control, compatibility to semiconductor technologies, etc. As the complicated electromagnetic environment in solid state metal and insulator, superconducting quantum bits (qubits) suffered from shot coherence time since its early development. In this review, we described some recently developed superconducting qubit structures, including Transmon/Xmon, Fluxonium and C-shunt flux qubit. Although these new qubit structures have very different circuit parameters and energy scales, they all find their way to effectively suppress environmental noises. As a result, their coherence time were improved significantly. Transmon, a transmission-line shunted plasma oscillation qubit, was now among the most popular structures for building a multi-qubit superconducting quantum circuit. It introduced a relatively large shunt capacitor to remarkably reduce the charge dispersion. Although the non-linearity is also decreased, by operating in a properly chosen EJ/Ec, transmon can greatly reduce the charge noise while only sacrificing a small amount of non-linearity. Xmon can be considered as a modified version of transmon. It is designed and optimized for multi-qubit operation and measurement with separate X/Y and Z control lines for each qubit, and a readout bus (a transmission line or a low-Q bandpass filter) for simultaneous readout of all the qubits. Fluxonium provide another solution for suppressing the charge noise in Cooper-pair box (CPB). It introduces a large shunt inductance to filter low-frequency offset charge in the small capacitor of the phase-slip junction (the small junction). To keep the qubit operating in the charge region, the shunt inductor should be large enough to keep the impedance larger than the superconducting impedance quantum RQ~1 kΩ. As a result, the inductance can only be provided by a large series of Josephson junctions. Fluxonium keeps the advantage of high anharmonicity of CPB. In addition, it introduces another degree of freedom: external flux Φext. Quasiparticles (electrons or holes) tunneling at the small junction add coherently to produce a ″1+cosφ″ term. As a result, when Φext= Φ0/2, dissipation caused by quasiparticle tunneling is suppressed and the energy relaxation time (T1) increases drastically. C-shunt flux qubit (CSFQ) decreases α and EJ to suppress flux noise in the qubit. While the charge noise becomes the dominant noise source, a large shunt capacitor is added to suppress the charge noise, similar to that in a transmon qubit. It is worth to notice that in CSFQ, the α decreases to below but near 1/2. As a result, the double-well potential no longer exists. The energy structure become similar to transmon, with the anharmonicity be opposite. CSFQ can get a much improved coherence time, while its anharmonicity can be larger than that of transmon. Those new superconducting qubit structures provide different solutions to improve the coherence time. Although it looks much different in circuit models and parameters, they have ideas in common, and may act as guides to other novel designs with longer coherence time. We can summarize as below. (1) The qubit circuit should be free of small superconducting islands. Charge fluctuation in small islands is a major source of decoherence. As a result, increase the area of the islands, that is, increase the capacitance becomes a straight forward way to suppress the charge noise. In Fluxonium, the small junction is connected with a large series of large junctions that there is also no small islands in the whole loop. (2) Remove superconducting loops in the qubit circuit, or minimize the loop size and loop current to suppress flux noise. (3) Bias the phase difference of the small junction to π, where dissipation caused by quasiparticle tunneling can be suppressed coherently. (4) Decrease the coupling bandwidth of qubit to the environment. In a circuit-QED readout scheme, a high-Q readout resonator that dispersively coupled to the qubit protects the qubit from exposed to the electromagnetic environment of the readout circuit. A ″Purcell filter″ can also be added to suppress such decoherence further. In conclusion, we overviewed some qubit engineering techniques or ideas to improve the coherence time, which is a very important figure for building practical quantum computer/simulator. We hope that someone can combine and optimize these ideas, while interact with developments in materials and micro-fabrication technologies, to develop novel new generation superconducting qubit structures in the near future.
In quantum information processing, realization of 3-qubit quantum operation is challenging especially when multiple logic operations are required to build non-trivial quantum circuits. Quantum half-adder is a 3-qubit circuit and in this work, a simple realization scheme for quantum half-adder operation is proposed. The 3-qubit quantum circuit is composed of a Toffoli operation and a controlled-NOT operation in succession. These two operations are shown to be achievable only by two transition pulses in nuclear magnetic resonance based quantum computing at room temperature. In our proposed scheme, three weakly coupled spin 1/2 nuclei of a molecule serve as three qubits. The time-independent internal Hamiltonian of the system allows us to obtain the desired multi-qubit operation. The simple structure of the spin 1/2 systems of our scheme make it easy to be implemented in experiments. Simulation on fidelity estimation reveals that more than 96% fidelity is achievable in worst case scenario.
We propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual ZZ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below 100 MHz, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above 99% can be obtained with gate times between 100 and 300 ns. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate.
Quantum computing (Q-computing) is a revolutionary technology that applies quantum mechanics (QM) to implement calculations significantly quicker than traditional computers. Q-computing employs Q-bits (qubits) rather than classical bits, which can take on a superposition state, making it possible to represent both 0 and 1 at once. This distinctive property allows qubits to perform multiple calculations simultaneously, making Q computers exponentially more powerful as more qubits are added, compared to the linear scaling of classical computers. However, challenges such as qubit instability and error rates remain significant obstacles to fully realizing this potential. A vital aspect of this technology is the development of Q arithmetic circuits, which act as the foundational blocks for efficiently executing Q algorithms. Q half-adder and full-adder circuits are integral to performing fundamental arithmetic operations within Q computers. In contrast to classical adders, Q adders rely on Q gates such as Controlled NOT (CNOT) and Toffoli gates. These gates exploit Q phenomena like entanglement and superposition, allowing for more efficient computations. The Q half-adder consists of two qubits and adds two single bits, producing a carry and sum output. It utilizes the CNOT gate to compute the sum and the Toffoli gate (controlled-controlled-NOT [CCNOT]) to compute the carry. The Q full-adder builds on this, adding three qubits to produce a sum and a carry output, further increasing computational capacity. Through the entanglement of qubits, these circuits allow for more parallelism and speed compared to classical adders. Q carry-look-ahead adders (QCLAs) and Q ripple-carry adders (QRCAs) are used to perform more complex arithmetic operations based on these half-adder and full-adder structures. Q arithmetic circuits have broad applications, boosting secure key generation in cryptography, speeding up matrix operations for faster model training in machine learning, and enabling more precise, efficient image transformations in Q image processing, benefiting fields like medical imaging and computer vision.