Superconducting Qubit Circuits Research Articles

Compact superconducting transmon qubit circuits made of ultrathin NbN

We design and fabricate a compact superconducting qubit circuit made of nano-thick NbN film on a high-resistivity silicon substrate, carrying seven transmon qubits. By comparing with the conventional superconducting qubit circuits made of superconducting films with hundred-nanometer thickness, our superconducting qubit circuit has much smaller size in the readout circuit, whose resonator length is only about 1/20 of that in a conventional superconducting circuit. Transmons are measured and characterized in the frequency and time domains with different flux bias. The transition frequency f01 can be adjusted in the range of several GHz. The qubit circuits made of such nano-thick material with high kinetic inductance are promising in the integration of quantum circuits.

Optimization of shadow evaporation and oxidation for reproducible quantum Josephson junction circuits

The most commonly used physical realization of superconducting qubits for quantum circuits is a transmon. There are a number of superconducting quantum circuits applications, where Josephson junction critical current reproducibility over a chip is crucial. Here, we report on a robust chip scale Al/AlOx/Al junctions fabrication method due to comprehensive study of shadow evaporation and oxidation steps. We experimentally demonstrate the evidence of optimal Josephson junction electrodes thickness, deposition rate and deposition angle, which ensure minimal electrode surface and line edge roughness. The influence of oxidation method, pressure and time on critical current reproducibility is determined. With the proposed method we demonstrate Al/AlOx/Al junction fabrication with the critical current variation (sigma /langle {I_{c} } rangle ) less than 3.9% (from 150 × 200 to 150 × 600 nm2 area) and 7.7% (for 100 × 100 nm2 area) over 20 × 20 mm2 chip. Finally, we fabricate separately three 5 × 10 mm2 chips with 18 transmon qubits (near 4.3 GHz frequency) showing less than 1.9% frequency variation between qubits on different chips. The proposed approach and optimization criteria can be utilized for a robust wafer-scale superconducting qubit circuits fabrication.

Quantum state transport in a square-lattice superconducting qubit circuit under gauge potential

In this paper, we study the transport properties of quantum states in the square-lattice quantum bit model by using inductive couplers to generate the artificial gauge potential (effective magnetic flux). It is found by theoretical calculation that the eigenstates of single particle and single hole have the same eigen energy spectrum, and the average particle and hole currents, sinusoidally modulated by the effective magnetic flux, are opposite to each other with respect to the same eigen energy. For an initial single-particle or single-hole state where only one lattice site is occuplied, if the time-inversion symmetry is preserved (the effective magnetic flux is an integral multiple of 4π), the components of the time-dependent wave functions of the single particle and the single hole are equal, otherwise they are not equal. The analysis demonstrates that the above calculation results are due to the fact that the particle-hole operation for the system Hamiltonian is equivalent to the time inversion. In addition, it is found that when the effective magnetic flux is π, a single particle or a single hole is only transported between the initial bit and two adjacent bits, and when the effective magnetic flux is 0, a single particle or a single hole is transported to the diagonal bit through two adjacent bits, and then transported in reverse. Regardless of the value of effective magnetic flux, both the single-particle and single-hole states share the same average (particle or hole) current and lattice site occupation probability.

Integration of Topological Insulator Josephson Junctions in Superconducting Qubit Circuits.

The integration of semiconductor Josephson junctions (JJs) in superconducting quantum circuits provides a versatile platform for hybrid qubits and offers a powerful way to probe exotic quasiparticle excitations. Recent proposals for using circuit quantum electrodynamics (cQED) to detect topological superconductivity motivate the integration of novel topological materials in such circuits. Here, we report on the realization of superconducting transmon qubits implemented with (Bi0.06Sb0.94)2Te3 topological insulator (TI) JJs using ultrahigh vacuum fabrication techniques. Microwave losses on our substrates, which host monolithically integrated hardmasks used for the selective area growth of TI nanostructures, imply microsecond limits to relaxation times and, thus, their compatibility with strong-coupling cQED. We use the cavity-qubit interaction to show that the Josephson energy of TI-based transmons scales with their JJ dimensions and demonstrate qubit control as well as temporal quantum coherence. Our results pave the way for advanced investigations of topological materials in both novel Josephson and topological qubits.

Superconducting qubits in a flip-chip architecture

Flip-chip architectures have recently enabled significant scaling-up of multi-qubit circuits and have been used to assemble hybrid quantum systems that combine different substrates, for example, for quantum acoustics experiments. The standard flip-chip method uses superconducting galvanic connections between two substrates, typically implemented using sophisticated indium wafer-bonding systems, which give highly reliable and temperature-cyclable assemblies, but are expensive, somewhat inflexible in design, and require robust substrates that can sustain the large compressive forces required to cold-weld the indium bonds. A much simpler method is to assemble dies using very low-force contacts and air-dried adhesives, although this does not provide a galvanic contact between the dies. Here, we demonstrate that the latter technique can be used to reliably couple superconducting qubit circuits, in which the qubits are on separate dies, without the need for a galvanic connection. We demonstrate full vector qubit control of each qubit on each of the two dies, with high-fidelity single-shot readout, and further demonstrate entanglement-generating excitation swaps as well as benchmark a controlled-Z entangling gate between the two qubits on the two dies. This exemplifies a simple and inexpensive assembly method for two-plus-one-dimensional quantum circuit integration that supports the use of delicate or unusually shaped substrates.

A fast and large bandwidth superconducting variable coupler

Variable microwave-frequency couplers are highly useful components in classical communication systems and likely will play an important role in quantum communication applications. Conventional semiconductor-based microwave couplers have been used with superconducting quantum circuits, enabling, for example, the in situ measurements of multiple devices via a common readout chain. However, the semiconducting elements are lossy and furthermore dissipate energy when switched, making them unsuitable for cryogenic applications requiring rapid, repeated switching. Superconducting Josephson junction-based couplers can be designed for dissipation-free operation with fast switching and are easily integrated with superconducting quantum circuits. These enable on-chip, quantum-coherent routing of microwave photons, providing an appealing alternative to semiconductor switches. Here, we present and characterize a chip-based broadband microwave variable coupler, tunable over 4–8 GHz with over 1.5 GHz instantaneous bandwidth, based on the superconducting quantum interference device with two parallel Josephson junctions. The coupler is dissipation-free and features large on-off ratios in excess of 40 dB, and the coupling can be changed in about 10 ns. The simple design presented here can be readily integrated with superconducting qubit circuits and can be easily generalized to realize a four- or more port device.

Vortex-Meissner phase transition induced by a two-tone-drive-engineered artificial gauge potential in the fermionic ladder constructed by superconducting qubit circuits

We propose to periodically modulate the onsite energy via two-tone drives, which can be furthermore used to engineer artificial gauge potential. As an example, we show that the fermionic ladder model penetrated with effective magnetic flux can be constructed by superconducting flux qubits using such two-tone-drive-engineered artificial gauge potential. In this superconducting system, the single-particle ground state can range from vortex phase to Meissner phase due to the competition between the interleg coupling strength and the effective magnetic flux. We also present the method to experimentally measure the chiral currents by the single-particle Rabi oscillations between adjacent qubits. In contrast to previous methods of generating artifical gauge potential, our proposal does not need the aid of auxiliary couplers and in principle remains valid only if the qubit circuit maintains enough anharmonicity. The fermionic ladder model with effective magnetic flux can also be interpreted as one-dimensional spin-orbit-coupled model, which thus lay a foundation towards the realization of quantum spin Hall effect.

Solid-state qubits integrated with superconducting through-silicon vias

As superconducting qubit circuits become more complex, addressing a large array of qubits becomes a challenging engineering problem. Dense arrays of qubits benefit from, and may require, access via the third dimension to alleviate interconnect crowding. Through-silicon vias (TSVs) represent a promising approach to three-dimensional (3D) integration in superconducting qubit arrays—provided they are compact enough to support densely-packed qubit systems without compromising qubit performance or low-loss signal and control routing. In this work, we demonstrate the integration of superconducting, high-aspect ratio TSVs—10 μm wide by 20 μm long by 200 μm deep—with superconducting qubits. We utilize TSVs for baseband control and high-fidelity microwave readout of qubits using a two-chip, bump-bonded architecture. We also validate the fabrication of qubits directly upon the surface of a TSV-integrated chip. These key 3D-integration milestones pave the way for the control and readout of high-density superconducting qubit arrays using superconducting TSVs.

Frequency up/down conversion by multiphoton pumping in superconducting qubit circuits

We propose a versatile scheme for multiphoton frequency up/down conversion in flux superconducting qubit circuits, driven by a pair of microwaves tuned near and far off the qubit resonance. Flux qubits can be engineered with strong anharmonicity such that the two lowest eigenstates are energetically well separated from the higher ones. We demonstrate the high order non-linear transitions between the two lowest levels in the three-photon regime, by coupling the qubit to bichromatic microwave fields with the same Rabi frequencies. Both up and down conversions are presented and accurately interpreted with many-mode Floquet formalism. An intuitive graph theoretic approach elucidates the physics of multiphoton pumping and population trapping. The analytical solutions also illustrate how controllability is achievable for desired single- or multiphoton pumping processes in a wide range of frequencies. The proposed design and theoretical approach are applicable in maintaining the inter-connectivity of future superconducting quantum machines.

Spectrum of the Dicke model in a superconducting qubit-oscillator system

We calculate the transmission spectrum of a superconducting circuit realization of the Dicke model and identify spectroscopic features that can serve as signatures of the superradiant phase. In particular, we calculate the resonance frequencies of the system as functions of the bias term, which is usually absent in studies on the Dicke model but is commonly present in superconducting qubit circuits. To avoid over-complicating the proposed circuit, we assume a fixed coupling strength. This situation precludes the possibility of observing signatures of the phase transition by varying the coupling strength across the critical point. We show that the spectrum obtained by varying the bias point under fixed coupling strength can contain signatures of the normal and superradiant phases: in the normal phase one expects to observe two spectral lines, while in the superradiant phase four spectral lines are expected to exist close to the qubits' symmetry point. Provided that parameter fluctuations and decoherence rates are sufficiently small, the four spectral lines should be observable and can serve as a signature of the superradiant phase.

Multiplexing Superconducting Qubit Circuit for Single Microwave Photon Generation

We report on a device that integrates eight superconducting transmon qubits in lambda /4 superconducting coplanar waveguide resonators fed from a common feedline. Using this multiplexing architecture, each resonator and qubit can be addressed individually, thus reducing the required hardware resources and allowing their individual characterisation by spectroscopic methods. The measured device parameters agree with the designed values, and the resonators and qubits exhibit excellent coherence properties and strong coupling, with the qubit relaxation rate dominated by the Purcell effect when brought in resonance with the resonator. Our analysis shows that the circuit is suitable for generation of single microwave photons on demand with an efficiency exceeding 80%.

Vacuum Gap Microstrip Microwave Resonators for 2.5-D Integration in Quantum Computing

Vacuum gap λ/2 microwave resonators are demonstrated as a route toward higher integration in superconducting qubit circuits. The resonators are fabricated from pieces on two silicon chips bonded together with an In-Sb bond. Measurements of the devices yield resonant frequencies in good agreement with simulations. Creating low loss circuits in this geometry is also discussed.

Epitaxial Al2O3 capacitors for low microwave loss superconducting quantum circuits

We have characterized the microwave loss of high-Q parallel plate capacitors fabricated from thin-film Al/Al2O3/Re heterostructures on (0001) Al2O3 substrates. The superconductor-insulator-superconductor trilayers were grown in situ in a hybrid deposition system: the epitaxial Re base and polycrystalline Al counterelectrode layers were grown by sputtering, while the epitaxial Al2O3 layer was grown by pulsed laser deposition. Structural analysis indicates a highly crystalline epitaxial Al2O3 layer and sharp interfaces. The measured intrinsic (low-power, low-temperature) quality factor of the resonators is as high as 3 × 104. These results indicate that low-loss grown Al2O3 is an attractive candidate dielectric for high-fidelity superconducting qubit circuits.

Fabrication of large dimension aluminum air-bridges for superconducting quantum circuits

Proper grounding between different ground planes in coplanar superconducting qubit circuits is important to avoid spurious resonances which increase decoherence. Here, the authors present a possible solution to suppress such undesired modes using superconducting aluminum air-bridges which have been fabricated on top of aluminum coplanar waveguide transmission lines. 3D electromagnetic simulations were done to guide the design of the air-bridges such that the input reflection (S11) of the bridges was kept at a minimum level. A fabrication method based on optical lithography techniques was developed and it resulted in air-bridges with a height of approximately 10 μm and lengths of up to 500 μm. The method can be generalized to arbitrary length air-bridge with heights even exceeding 15 μm.

Frequency division multiplexing readout and simultaneous manipulation of an array of flux qubits

An important desired ingredient of superconducting quantum circuits is a readout scheme whose complexity does not increase with the number of qubits involved in the measurement. Here, we present a readout scheme employing a single microwave line, which enables simultaneous readout of multiple qubits. Consequently, scaling up superconducting qubit circuits is no longer limited by the readout apparatus. Parallel readout of 6 flux qubits using a frequency division multiplexing technique is demonstrated, as well as simultaneous manipulation and time resolved measurement of 3 qubits. We discuss how this technique can be scaled up to read out hundreds of qubits on a chip.

Developing Superconducting Flux Qubit by Using Epitaxial NbN/AlN/NbN Junction

Abstract In an effort to eliminate the intrinsic noise sources that contained within the superconducting qubit circuits, we successfully fabricate superconducting flux qubit circuits (rf SQUID) with full epitaxially grown NbN/AlN/NbN tunnel junctions. The temperature dependent of magnetic flux shift has been investigated by using a NbN/AlN/NbN dc SQUID magnetometer in the temperature range from 20 mK to 2.5 K. Our results show that the shift of the magnetic flux is in the level of ∼1 mF 0 during the experiment.

Measurement of Epitaxial NbN/AlN/NbN Tunnel Junctions With a Low Critical Current Density at Low Temperature

Superconducting qubit circuits require high quality low critical current density Josephson tunnel junctions. We have developed high quality epitaxial NbN/AlN/NbN tunnel junctions with critical current density, Jc, ranging from as low as a few A/cm2 to a few tens of kA/cm2. In this work, we measured current-voltage characteristics for junctions with a Jc ~ 32 A/cm2 in the temperature range from 17 mK to above 6.7 K. All the junctions are in good quality and have a high gap voltage (>; 5.5 mV). We found that the junctions' sub-gap resistances were temperature dependent above 2.5 K and saturated at temperatures below 2.5 K. A junction sub-gap leakage current Ir of about 23 pA was measured. The voltage noise power spectral density for 3 junctions with different sizes has been measured at the base temperature of 17 mK with the junctions biased above the gap voltage. The spectral densities clearly show 1/f behavior at low frequency and are proportional to the junction's linear dimension.

1/f noise in NbN/AlN/NbN Josephson junction with a low critical current density

Fabricating high quality Josephson junction is essential in superconducting qubit circuits. In this letter, high quality tunnel junctions with a low critical current density of ∼32A/cm2 were fabricated. The 1/f noise parameter η was obtained from junctions’ low frequency voltage noise power spectral density Sv(f)=1fηA(IbRD)2. Our findings showed that the noise spectrum is junction linear dimension dependent, indicating the junction’s side leakage current induced by defects in the amorphous oxide insulator dominates the origin of the 1/f noise in our epitaxial NbN/AlN/NbN tunnel junctions.

Using superconducting qubit circuits to engineer exotic lattice systems

We propose an architecture based on superconducting qubits and resonators for the implementation of a variety of exotic lattice systems, such as spin and Hubbard models in higher or fractal dimensions and higher-genus topologies. Spin systems are realized naturally using qubits, while superconducting resonators can be used for the realization of Bose-Hubbard models. Fundamental requirements for these designs, such as controllable interactions between arbitrary qubit pairs, have recently been implemented in the laboratory, rendering our proposals feasible with current technology.

Scalable superconducting qubit circuits using dressed states

We study a coupling/decoupling method between a superconducting qubit and a data bus that uses a controllable time-dependent electromagnetic field (TDEF). As in recent experiments, the data bus can be either an LC circuit or a cavity field. When the qubit and the data bus are initially fabricated, their detuning should be made far larger than their coupling constant, so these can be treated as two independent subsystems. However, if a TDEF is applied to the qubit, then a "dressed qubit" (i.e., qubit plus the electromagnetic field) can be formed. By choosing appropriate parameters for the TDEF, the dressed qubit can be coupled to the data bus and, thus, the qubit and the data bus can exchange information with the assistance of the TDEF. This mechanism allows the scalability of the circuit to many qubits. With the help of the TDEF, any two qubits can be selectively coupled to (and decoupled from) a common data bus. Therefore, quantum information can be transferred from one qubit to another.