A behavior of a two qubit system coupled by the electric capacitance has been studied quantum mechanically. We found that the interaction is essentially the same as the one for the dipole-dipole interaction; i.e., qubit-qubit coupling of the NMR quantum gate. Therefore a quantum gate could be constructed by the same operation sequence for the NMR device if the coupling is small enough. The result gives an information to the effort of development of the devices assuming capacitive coupling between qubits.
Here, we propose a scheme to generate a controllable Ising interaction between superconducting flux qubits. Existing schemes rely on inducting couplings to realize Ising interactions between flux qubits, and the interaction strength is controlled by an applied magnetic field On the other hand, we have found a way to generate an interaction between the flux qubits via capacitive couplings. This has an advantage in individual addressability, because we can control the interaction strength by changing an applied voltage that can be easily localized. This is a crucial step toward the realizing sup…
Coulomb blockade effects in capacitively coupled quantum dots can be utilized for constructing an N-qubit system with antiferromagnetic Ising interactions. Starting from the tunneling Hamiltonian, we theoretically show that the Hamiltonian for a weakly coupled quantum-dot array is reduced to that for nuclear magnetic resonance (NMR) spectroscopy. Quantum operations are carried out by applying only electrical pulse sequences. Thus various error-correction methods developed in NMR spectroscopy and NMR quantum computers are applicable without using magnetic fields. A possible measurement scheme i…
It has often been assumed that electrically floating qubits, such as flux qubits, are immune to decoherence due to capacitive coupling. We show that capacitive coupling to bias leads can be a dominant source of dissipation, and therefore of decoherence, for such floating qubits. Classical electrostatic arguments are sufficient to get a good estimate of this source of relaxation for standard superconducting qubit designs. We show that relaxation times can be improved by designing floating qubits so they couple symmetrically to the bias leads. Observed coherence times of flux qubits with varying…
Josephson junctions form the essential non-linearity for almost all superconducting qubits. The junction is formed when two superconducting electrodes come within $\sim$1 nm of each other. Although the capacitance of these electrodes is a small fraction of the total qubit capacitance, the nearby electric fields are more concentrated in dielectric surfaces and can contribute substantially to the total dissipation. We have developed a technique to experimentally investigate the effect of these electrodes on the quality of superconducting devices. We use $λ$/4 coplanar waveguide resonators to emu…
We report the simultaneous operation and two-qubit coupling measurement of a pair of two-electron spin qubits that are actively decoupled from quasistatic nuclear noise in a GaAs quadruple quantum dot array. Coherent Rabi oscillations of both qubits (decay time $\approx$2 μs; frequency few MHz) are achieved by continuously tuning the drive frequency using rapidly converging real-time Hamiltonian estimators. By state conditional exchange oscillation measurements, we also observe strong two-qubit capacitive interaction (> 190 MHz). We show that the scaling of the capacitive interaction with resp…
Decoherence of a tunable capacitively shunted flux qubit
Department of Physics and Astronomy, University of Waterloo（物理与天文学系，滑铁卢大学）；Department of Electrical and Computer Engineering, University of Waterloo（电气与计算机工程系，滑铁卢大学）；Department of Physics and Astronomy, Dartmouth College（物理与天文学系，达特茅斯学院）；Research Laboratory of Electronics, Massachusetts Institute of Technology（电子学研究实验室，麻省理工学院）
The implementation of high fidelity two-qubit gates is a bottleneck in the progress towards universal quantum computation in semiconductor quantum dot qubits. We study capacitive coupling between two triple quantum dot spin qubits encoded in the $S = 1/2$, $S_z = -1/2$ decoherence-free subspace -- the exchange-only (EO) spin qubits. We report exact gate sequences for CPHASE and CNOT gates, and demonstrate theoretically, the existence of multiple two-qubit sweet spots (2QSS) in the parameter space of capacitively coupled EO qubits. Gate operations have the advantage of being all-electrical, but…
Capacitively coupled semiconductor spin qubits hold promise as the building blocks of a scalable quantum computing architecture with long-range coupling between distant qubits. However, the two-qubit gate fidelities achieved in experiments to date have been severely limited by decoherence originating from charge noise and hyperfine interactions with nuclear spins, and are currently unacceptably low for any conceivable multi-qubit gate operations. Here, we present control protocols that implement two-qubit entangling gates while substantially suppressing errors due to both types of noise. These…
Recent work on Ising-coupled double-quantum-dot spin qubits in GaAs with voltage-controlled exchange interaction has shown improved two-qubit gate fidelities from the application of oscillating exchange along with a strong magnetic field gradient between adjacent dots. By examining how noise propagates in the time-evolution operator of the system, we find an optimal set of parameters that provide passive stroboscopic circumvention of errors in two-qubit gates to first order. We predict over 99% two-qubit gate fidelities in the presence of quasistatic and 1/$\textit{f}$ noise, which is an order…
In addition to magnetic field and electric charge noise adversely affecting spin qubit operations, performing single-qubit gates on one of multiple coupled singlet-triplet qubits presents a new challenge---crosstalk, which is inevitable (and must be minimized) in any multiqubit quantum computing architecture. We develop a set of dynamically-corrected pulse sequences that are designed to cancel the effects of both types of noise (i.e., field and charge) as well as crosstalk to leading order, and provide parameters for these corrected sequences for all 24 of the single-qubit Clifford gates. We t…
We present the design and characterization of a three-Josephson-junction superconducting loop circuit with three large shunt capacitors. Used as a qubit, the circuit shows long energy-relaxation times, of the order of 40 ${ \unicode[Times]{x3BC}}$s and a spin-echo dephasing time of 9.4 ${ \unicode[Times]{x3BC}}$s. The circuit has high anharmonicity, of 2$π$$\times$3.69 GHz. We extract the multilevel relaxation and dephasing rates of the circuit used as a qutrit and discuss the possible sources for the decoherence. The high anharmonicity allows for fast qubit control with nanosecond-range gate …
Quantum annealing (QA) provides us with a way to solve combinatorial optimization problems. In the previous demonstration of the QA, a superconducting flux qubit (FQ) was used. However, the flux qubits in these demonstrations have a short coherence time such as tens of nano seconds. For the purpose to utilize quantum properties, it is necessary to use another qubit with a better coherence time. Here, we propose to use a capacitive-shunted flux qubit (CSFQ) for the implementation of the QA. The CSFQ has a few order of magnitude better coherence time than the FQ used in the QA. We theoretically …
Fast operations, an easily tunable Hamiltonian, and a straightforward two-qubit interaction make charge qubits a useful tool for benchmarking device performance and exploring two-qubit dynamics. Here, we tune a linear chain of four Si/SiGe quantum dots to host two double dot charge qubits. Using the capacitance between the double dots to mediate a strong two-qubit interaction, we simultaneously drive coherent transitions to generate correlations between the qubits. We then sequentially pulse the qubits to drive one qubit conditionally on the state of the other. We find that a conditional $π$-r…
Charge noise is the main hurdle preventing high-fidelity operation, in particular that of two-qubit gates, of semiconductor-quantum-dot-based spin qubits. While certain sweet spots where charge noise is substantially suppressed have been demonstrated in several types of spin qubits, the existence of one for coupled singlet-triplet qubits is unclear. We theoretically demonstrate, using full configuration-interaction calculations, that a range of nearly sweet spots appear in the coupled singlet-triplet qubit system when a strong enough magnetic field is applied externally. We further demonstrate…
Recent achievements in the field of gate defined semiconductor quantum dots reinforce the concept of a spin-based quantum computer consisting of nodes of locally connected qubits which communicate with each other via superconducting circuit resonator photons. In this work we theoretically demonstrate a versatile set of quantum gates between adjacent spin qubits defined in semiconductor quantum dots situated within the same node of such a spin-based quantum computer. The electric dipole acquired by the spin of an electron that moves across a double quantum dot potential in a magnetic field grad…
The search of a sweet spot, locus in qubit parameters where quantum control is first-order insensitive to noises, is key to achieve high-fidelity quantum gates. Efforts to search for such a sweet spot in conventional double-quantum-dot singlet-triplet qubits where each dot hosts one electron ("two-electron singlet-triplet qubit"), especially for two-qubit operations, have been unsuccessful. Here we consider singlet-triplet qubits allowing each dot to host more than one electron, with a total of four electrons in the double quantum dots ("four-electron singlet-triplet qubit"). We theoretically …
We propose a scheme for generating SU(2) adiabatic geometric phases in a circuit consisting of three capacitively coupled flux-biased Josephson phase qubits.
We propose a circuit quantum electrodynamics (QED) realization of a protocol to generate a Greenberger-Horne-Zeilinger (GHZ) state for $N$ superconducting transmon qubits homogeneously coupled to a superconducting transmission line resonator in the dispersive limit. We derive an effective Hamiltonian with pairwise qubit exchange interactions of the XY type, $\tilde{g}(XX+YY)$, that can be globally controlled. Starting from a separable initial state, these interactions allow to generate a multi-qubit GHZ state within a time $t_{\text{GHZ}}\sim \tilde{g}^{-1}$. We discuss how to probe the non-lo…
The recent experimental advances in capacitively coupled singlet-triplet qubits, particularly the demonstration of entanglement, opens the question of what type of entangling gates the system's Hamiltonian can produce directly via a single square pulse. We address this question by considering the system's Hamiltonian from first principles and using the representation of its nonlocal properties in terms of local invariants. In the analysis we include the three different ways in which the system can be biased and their effect on the generation of entangling gates. We find that, in one of the pos…
Singlet-triplet qubits in lateral quantum dots in semiconductor heterostructures exhibit high-fidelity single-qubit gates via exchange interactions and magnetic field gradients. High-fidelity two-qubit entangling gates are challenging to generate since weak interqubit interactions result in slow gates that accumulate error in the presence of noise. However, the interqubit electrostatic interaction also produces a shift in the local double well detunings, effectively changing the dependence of exchange on the gate voltages. We consider an operating point where the effective exchange is first or…
The ability to tune qubits to flat points in their energy dispersions ("sweet spots") is an important tool for mitigating the effects of charge noise and dephasing in solid-state devices. However, the number of derivatives that must be simultaneously set to zero grows exponentially with the number of coupled qubits, making the task untenable for as few as two qubits. This is a particular problem for adiabatic gates, due to their slower speeds. Here, we propose an adiabatic two-qubit gate for quantum dot hybrid qubits, based on the tunable, electrostatic coupling between distinct charge configu…
We investigate capacitively coupled two-qubit quantum gates based on quantum dots. For exchange-only coded qubits electron spin $S$ and its projection $S_z$ are exact quantum numbers. Capacitive coupling between qubits, as distinct from interqubit exchange, preserves these quantum numbers. We prove, both analytically and numerically, that conservation of the spins of individual qubits has dramatic effect on performance of two-qubit gates. By varying the level splittings of individual qubits, $J_a$ and $J_b$, and the interqubit coupling time $t$, we can find an infinite number of triples $(J_a,…
We report the characterization of a two-qubit processor implemented with two capacitively coupled tunable superconducting qubits of the transmon type, each qubit having its own non-destructive single-shot readout. The fixed capacitive coupling yields the \sqrt{iSWAP} two-qubit gate for a suitable interaction time. We reconstruct by state tomography the coherent dynamics of the two-bit register as a function of the interaction time, observe a violation of the Bell inequality by 22 standard deviations after correcting readout errors, and measure by quantum process tomography a gate fidelity of 9…
We report coherent operation of a singlet-triplet qubit controlled by the arrangement of two electrons in an adjacent double quantum dot. The system we investigate consists of two pairs of capacitively coupled double quantum dots fabricated by electrostatic gates on the surface of a GaAs heterostructure. We extract the strength of the capacitive coupling between qubit and double quantum dot and show that the present geometry allows fast conditional gate operation, opening pathways to multi-qubit control and implementation of quantum algorithms with spin qubits.
We present measurements of the capacitive coupling energy and the inter-dot capacitances in a linear quadruple quantum dot array in undoped Si/SiGe. With the device tuned to a regime of strong ($>$1 GHz) intra-double dot tunnel coupling, as is typical for double dot qubits, we measure a capacitive coupling energy of $20.9 \pm 0.3$ GHz. In this regime, we demonstrate a fitting procedure to extract all the parameters in the 4D Hamiltonian for two capacitively coupled charge qubits from a 2D slice through the quadruple dot charge stability diagram. We also investigate the tunability of the capaci…
A controlled-NOT logic gate based on conditional spectroscopy has been demonstrated recently for a pair of superconducting flux qubits [Plantenberg et al., Nature 447, 836 (2007)]. Here we study the fidelity of this type of gate applied to a phase qubit coupled to a resonator (or a pair of capacitively coupled phase qubits). Our results show that an intrinsic fidelity of more than 99% is achievable in 45ns.
In this paper we propose a scheme to implement a quantum teleportation based on the current experimental design [Nature (London) 431, 162 (2004); ibid 445, 515 (2007)] in which superconducting charge qubits are capacitively coupled to a single high-Q superconducting coplanar resonator. As advantage of this architecture, it permits the use of multiqubit gates between non-nearest qubits and the realization of parallel gates. We consider the case of two qubits inside the resonator, where the teleportation is accomplished.
Based on a quantum analysis of two capacitively coupled current-biased Josephson junctions, we propose two fundamental two-qubit quantum logic gates. Each of these gates, when supplemented by single-qubit operations, is sufficient for universal quantum computation. Numerical solutions of the time-dependent Schroedinger equation demonstrate that these operations can be performed with good fidelity.
We propose a method for precision statistical control of quantum processes based on superconductor phase qubits. Using the universal quantum tomography method, we provide a detailed analysis of accuracy of tomography for a 2-qubit gate SQiSW, which arises due to capacitive coupling between qubits. The developed approach could be successfully applied for quality and efficiency problems of superconductor quantum information technologies.
For a simple model of mutually interacting qubits it is shown how the errors induced by mutual interactions can be eliminated using concatenated coding. The model is solved exactly for arbitrary interaction strength, for two well-known codes, one and two levels deep: this allows one to see under which circumstances error amplitudes add coherently or incoherently. For deeper concatenation, approximate results are derived which make it possible to calculate an approximate ``threshold'' value for the product of interaction strength and free evolution time, below which the failure probability for …
Realising high fidelity entangled states in controlled quantum many-body systems is challenging due to experimental uncertainty in a large number of physical quantities. We develop a robust optimal control method for achieving this goal in finite-size multi-qubit systems despite significant uncertainty in multiple parameters. We demonstrate its effectiveness in the generation of the Greenberger-Horne-Zeilinger state on a star graph of capacitively coupled transmons, and discuss its crucial role for achieving the Heisenberg limit of precision in quantum sensing.
We demonstrate that charge-qubit cluster state generation by capacitive coupling is anisotropic. Specifically, horizontal vs vertical nearest-neighbor inter-qubit coupling differs in a rectangular lattice. We show how to ameliorate this anisotropy by applying potential biases to the array of double dots.
In superconducting circuits with interbit untunable (e.g., capacitive) couplings, ideal local quantum operations cannot be exactly performed on individual Josephson qubits. Here we propose an effective dynamical decoupling approach to overcome the "fixed-interaction" difficulty for effectively implementing elemental logical gates for quantum computation. The proposed single-qubit operations and local measurements should allow testing Bell's inequality with a pair of capacitively-coupled Josephson qubits. This provides a powerful approach, besides spectral-analysis [Nature \textbf{421}, 823 (20…
Mutual information and swap operation in the two-qubit Heisenberg model with the Dzyaloshinskii-Moriya (DM) anisotropic antisymmetric interaction are investigated. It is found that the mutual information I of such a quantum channel is sensitive to the initial conditions and declines with the increase of the temperature. The DM interaction can lead to a higher mutual information, especially for the ferromagnetic case. The entanglement quality of input states cannot enhance the mutual information of the quantum channel. When the DM interaction is large, the mutual information will be the maximum…
Fixed-frequency qubits can suffer from always-on interactions that inhibit independent control. Here, we address this issue by experimentally demonstrating a superconducting architecture using qubits that comprise of two capacitively-shunted Josephson junctions connected in series. Historically known as tunable coupling qubits (TCQs), such two-junction qubits support two modes with distinct frequencies and spatial symmetries. By selectively coupling only one type of mode and using the other as our computational basis, we greatly suppress crosstalk between the data modes while permitting all-mi…
Analysis of the recently proposed thought experiment with the path entangled photon pairs is extended here to spin entangled electron pairs. The detailed comparison of the two cases showed the range of distinctions and similarities in their monitoring. The general results contradict the Concurrency Rule stating that intimately linked characteristics of a simple system must change concurrently under changing conditions. Instead, the analysis showed that the systems coherence, while changing continuously with entanglement strength on the global scale, remains zero on the local level. This effect…
Entropic inequalities related to the quantum mutual information for bipartite system and tomographic mutual information is studied for Werner state of two qubits. Quantum correlations corresponding to entanglement properties of the qubits in Werner state are discussed.
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…
Josephson junctions have been shown to be a promising solid-state system for implementation of quantum computation. The significant two-qubit gates are generally realized by the capacitive coupling between the nearest neighbour qubits. We propose an effective Hamiltonian to describe charge qubits coupled through the cavity. We find that nontrivial two-qubit gates may be achieved by this coupling. The ability to interconvert localized charge qubits and flying qubits in the proposed scheme implies that quantum network can be constructed using this large scalable solid-state system.
For the complete estimation of arbitrary unknown quantum states by measurements, the use of mutually unbiased bases has been well-established in theory and experiment for the past 20 years. However, most constructions of these bases make heavy use of abstract algebra and the mathematical theory of finite rings and fields, and no simple and generally accessible construction is available. This is particularly true in the case of a system composed of several qubits, which is arguably the most important case in quantum information science and quantum computation. In this paper, we close this gap b…
In the present study, we have proposed a scheme for two-way quantum communication in which the two legitimate participants mutually exchange their quantum information to each other by using a four-qubit cluster state as the quantum channel. Recently, by utilizing a four-qubit cluster state as the quantum channel, Kazemikhah et al. [Int. J. Theor. Phys., 60 (2021) 378] tried to design a scheme for the mutual exchange of quantum information between two legitimate participants. However, in the present study, it has been shown that in their scheme the transmission of quantum information cannot be …
Universal quantum computing relies on high-fidelity entangling operations. Here we demonstrate that four coupled qubits can operate as a quantum gate, where two qubits control the operation on two target qubits (a four-qubit gate). This configuration can implement four different controlled two-qubit gates: two different entangling swap and phase operations, a phase operation distinguishing states of different parity, and the identity operation (idle quantum gate), where the choice of gate is set by the state of the control qubits. The device exploits quantum interference to control the operati…
We have analyzed and proposed coupling mechanisms between Three Josephson Junction Flux Qubits (3JJQ). For this, we have developed a numerical method to extract the effective Hamiltonian of a system of coupled qubits via the Schrieffer-Wolff transformation (SWT). We then give a comprehensive introduction to the 3JJQ, and study it analytically by approximating its potential with a Harmonic well. With a clear understanding of the 3JJQs, we use the SWT to gain intuition about their effective dipolar interaction with the electromagnetic field, and use that intuition to propose and study analytical…
