Superconducting Qubit Systems Research Articles

Gate-error analysis in simulations of quantum computers with transmon qubits

In the model of gate-based quantum computation, the qubits are controlled by a sequence of quantum gates. In superconducting qubit systems, these gates can be implemented by voltage pulses. The success of implementing a particular gate can be expressed by various metrics such as the average gate fidelity, the diamond distance, and the unitarity. We analyze these metrics of gate pulses for a system of two superconducting transmon qubits coupled by a resonator, a system inspired by the architecture of the IBM Quantum Experience. The metrics are obtained by numerical solution of the time-dependent Schr\"odinger equation of the transmon system. We find that the metrics reflect systematic errors that are most pronounced for echoed cross-resonance gates, but that none of the studied metrics can reliably predict the performance of a gate when used repeatedly in a quantum algorithm.

A graph-theoretical representation of multiphoton resonance processes in superconducting quantum circuits.

We propose a graph-theoretical formalism to study generic circuit quantum electrodynamics systems consisting of a two level qubit coupled with a single-mode resonator in arbitrary coupling strength regimes beyond rotating-wave approximation. We define colored-weighted graphs, and introduce different products between them to investigate the dynamics of superconducting qubits in transverse, longitudinal, and bidirectional coupling schemes. The intuitive and predictive picture provided by this method, and the simplicity of the mathematical construction, are demonstrated with some numerical studies of the multiphoton resonance processes and quantum interference phenomena for the superconducting qubit systems driven by intense ac fields.

Measurement-Induced State Transitions in a Superconducting Qubit: Beyond the Rotating Wave Approximation.

Many superconducting qubit systems use the dispersive interaction between the qubit and a coupled harmonic resonator to perform quantum state measurement. Previous works have found that such measurements can induce state transitions in the qubit if the number of photons in the resonator is too high. We investigate these transitions and find that they can push the qubit out of the two-level subspace, and that they show resonant behavior as a function of photon number. We develop a theory for these observations based on level crossings within the Jaynes-Cummings ladder, with transitions mediated by terms in the Hamiltonian that are typically ignored by the rotating wave approximation. We find that the most important of these terms comes from an unexpected broken symmetry in the qubit potential. We confirm the theory by measuring the photon occupation of the resonator when transitions occur while varying the detuning between the qubit and resonator.

Experimental system design for the integration of trapped-ion and superconducting qubit systems.

We present a design for the experimental integration of ion trapping and superconducting qubit systems as a step towards the realization of a quantum hybrid system. The scheme addresses two key difficulties in realizing such a system: a combined microfabricated ion trap and superconducting qubit architecture, and the experimental infrastructure to facilitate both technologies. Developing upon work by Kielpinski et al. (Phys Rev Lett 108(13):130504, 2012. doi:10.1103/PhysRevLett.108.130504), we describe the design, simulation and fabrication process for a microfabricated ion trap capable of coupling an ion to a superconducting microwave LC circuit with a coupling strength in the tens of kHz. We also describe existing difficulties in combining the experimental infrastructure of an ion trapping set-up into a dilution refrigerator with superconducting qubits and present solutions that can be immediately implemented using current technology.

Simulating the Kibble-Zurek mechanism of the Ising model with a superconducting qubit system.

The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching speed. Our results provide the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena.

Demonstration of robust quantum gate tomography via randomized benchmarking

Typical quantum gate tomography protocols struggle with a self-consistency problem: the gate operation cannot be reconstructed without knowledge of the initial state and final measurement, but such knowledge cannot be obtained without well-characterized gates. A recently proposed technique, known as randomized benchmarking tomography (RBT), sidesteps this self-consistency problem by designing experiments to be insensitive to preparation and measurement imperfections. We implement this proposal in a superconducting qubit system, using a number of experimental improvements including implementing each of the elements of the Clifford group in single ‘atomic’ pulses and custom control hardware to enable large overhead protocols. We show a robust reconstruction of several single-qubit quantum gates, including a unitary outside the Clifford group. We demonstrate that RBT yields physical gate reconstructions that are consistent with fidelities obtained by RB.

Machine Learning for Discriminating Quantum Measurement Trajectories and Improving Readout.

Current methods for classifying measurement trajectories in superconducting qubit systems produce fidelities systematically lower than those predicted by experimental parameters. Here, we place current classification methods within the framework of machine learning (ML) algorithms and improve on them by investigating more sophisticated ML approaches. We find that nonlinear algorithms and clustering methods produce significantly higher assignment fidelities that help close the gap to the fidelity possible under ideal noise conditions. Clustering methods group trajectories into natural subsets within the data, which allows for the diagnosis of systematic errors. We find large clusters in the data associated with T1 processes and show these are the main source of discrepancy between our experimental and ideal fidelities. These error diagnosis techniques help provide a path forward to improve qubit measurements.

Analytical approach to swift nonleaky entangling gates in superconducting qubits

We develop schemes for designing pulses that implement fast and precise entangling quantum gates in superconducting qubit systems despite the presence of nearby harmful transitions. Our approach is based on purposely involving the nearest harmful transition in the quantum evolution instead of trying to avoid it. Using analytical tools, we design simple microwave control fields that implement maximally entangling gates with fidelities exceeding 99% in times as low as 40 ns. We demonstrate our approach in a two-qubit circuit QED system by designing the two most important quantum entangling gates: a conditional-NOT gate and a conditional-Z gate. Our results constitute an important step toward overcoming the problem of spectral crowding, one of the primary challenges in controlling multi-qubit systems.

Control of the quantum interference in a superconducting qubit system

We propose a scheme to control quantum interference pattern in a system of a superconducting qubit coupled to its own data bus by applying a controllable time-dependent electromagnetic field. It is shown that the quantum interference induced by the initial phase difference is closely related to the quantum correlations between two superconducting qubits which are coupled to their own data bus and the geometric discord can also be increased by applying the controllable electromagnetic field.

A Proposal for Realizing a 3-Qubit Controlled-Phase Gate with Superconducting Qubit Systems Coupled to a Cavity

We present a way to realize a 3-qubit quantum controlled-phase gate with superconducting qubit systems coupled to a cavity. This proposal does not require adjustment of the qubit level spacings or identical qubit-cavity coupling constants. Moreover, since only a resonant interaction is applied, the gate can be performed fast, within ∼ 10 nanosecond. This proposal is quite general, which can be applied to various types of superconducting qubits, atoms trapped in a cavity, or quantum dots coupled to a resonator.

Enhancing quantum discord in superconducting qubit systems by a controllable electromagnetic field

We study the dynamics of quantum correlations of the systems consisting of two non-interacting superconducting qubits interacting with their own data bus and common data bus, where the qubits are driven by a controllable time-dependent electromagnetic field. We investigate how the time-dependent electromagnetic field affects the dynamics of the quantum discord and the three-partite entanglement of the systems. It is found that the quantum discord vanishes only asymptotically although entanglement disappears suddenly during the time evolution and the quantum discord between two qubits can be increased by adjusting the time-dependent electromagnetic field.

Efficient Measurement of Quantum Gate Error by Interleaved Randomized Benchmarking

We describe a scalable experimental protocol for estimating the average error of individual quantum computational gates. This protocol consists of interleaving random Clifford gates between the gate of interest and provides an estimate as well as theoretical bounds for the average error of the gate under test, so long as the average noise variation over all Clifford gates is small. This technique takes into account both state preparation and measurement errors and is scalable in the number of qubits. We apply this protocol to a superconducting qubit system and find a bounded average error of 0.003 [0,0.016] for the single-qubit gates X(π/2) and Y(π/2). These bounded values provide better estimates of the average error than those extracted via quantum process tomography.

Preserving quantum correlations in two superconducting qubits by applying time-dependent magnetic fields

We propose a scheme to preserve quantum correlations in a dissipative superconducting qubit system, which consists of two noninteracting dissipative superconducting flux qubits, each driven by a time-dependent magnetic field. We investigate the influence of the initial states and the time-dependent magnetic fields on the dynamics of quantum correlations between the two flux qubits. It is shown that the quantum correlations between the two qubits can be improved in the Markovian regime and well preserved in the non-Markovian regime by applying the time-dependent magnetic fields.

Entanglement control in a superconducting qubit system by an electromagnetic field

By making use of the dynamical algebraic method we investigate a quantum system consisting of superconducting qubits interacting with data buses, where the qubits are driven by time-dependent electromagnetic field and obtain an explicit expression of time evolution operator. Furthermore, we explore the entanglement dynamics and the influence of the time-dependent electromagnetic field and the initial state on the entanglement sudden death and birth for the system. It is shown that the entanglement between the qubit and bus as well as the entanglement sudden death and birth can be controlled by the time-dependent electromagnetic field.

A proposal for implementing ann-qubit controlled-rotation gate with three-level superconducting qubit systems in cavityQED

We present a method for implementing ann-qubit controlled-rotation gate with three-level superconducting qubit systems incavity quantum electrodynamics. The two logical states of a qubit are representedby the two lowest levels of each system while a higher energy level is used forthe gate implementation. The method operates essentially by preparing aW state conditioned on the states of the control qubits, creating a single photon in the cavitymode, and then performing an arbitrary rotation on the states of the target qubit with theassistance of the cavity photon. It is interesting to note that the basic operational stepsfor implementing the proposed gate do not increase with the number of qubitsn, and the gate operation time decreases as the number of qubits increases. This proposal isquite general, and can be applied to various types of superconducting devices in a cavity orcoupled to a resonator.

Non-Markovian entanglement dynamics in coupled superconducting qubit systems

We theoretically analyze the entanglement generation and dynamics by coupled Josephson junction qubits. Considering a current-biased Josephson junction (CBJJ), we generate maximally entangled states. In particular, the entanglement dynamics is considered as a function of the decoherence parameters, such as the temperature, the ratio r ≡ $\omega_c$ / $\omega_0$ between the reservoir cutoff frequency $\omega_c$ and the system oscillator frequency $\omega_0$ , and the energy levels split of the superconducting circuits in the non-Markovian master equation. We analyzed the entanglement sudden death (ESD) and entanglement sudden birth (ESB) by the non-Markovian master equation. Furthermore, we find that the larger the ratio r and the thermal energy k BT , the shorter the decoherence. In this superconducting qubit system we find that the entanglement can be controlled and the ESD time can be prolonged by adjusting the temperature and the superconducting phases $\Phi_k$ which split the energy levels.

Fault-tolerant architectures for superconducting qubits

In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum error-correction codes, which I will briefly review, have not significantly changed since their introduction 15 years ago. But an interesting picture has emerged of an efficient use of these codes that may put fault-tolerant operation within reach. It is now understood that two-dimensional surface codes, close relatives of the original toric code of Kitaev, can be adapted as shown by Raussendorf and Harrington to effectively perform logical gate operations in a very simple planar architecture, with error thresholds for fault-tolerant operation simulated to be 0.75%. This architecture uses topological ideas in its functioning, but it is not ‘topological quantum computation’—there are no non-abelian anyons in sight. I offer some speculations on the crucial pieces of superconducting hardware that could be demonstrated in the next couple of years that would be clear stepping stones towards this surface-code architecture.

Superconducting qubit systems come of age

The precision control demonstrated in two recent experiments makes those systems serious contenders in the long race for a quantum computer.

Dissipative dynamics of superconducting hybrid qubit systems

We perform a theoretical study of composed superconducting qubit systems for the case of a coupled qubit configuration based on a hybrid qubit circuit made of both charge and phase qubits, which are coupled via a σx ⊗ σz interaction. We compute the system's eigen-energies in terms of the qubit transition frequencies and the strength of the inter-qubit coupling, and describe the sensitivity of the energy crossing/anti-crossing features to such coupling. We compute the hybrid system's dissipative dynamics for the cases of i) collective and ii) independent decoherence, whereby the system interacts with one common and two different baths of harmonic oscillators, respectively. The calculations have been performed within the Bloch-Redfield formalism and we report the solutions for the populations and the coherences of the system's reduced density matrix. The dephasing and relaxation rates are explicitly calculated as a function of the heat bath temperature.

Verification of stable operation of rapid single flux quantum devices with frequency-dependent dissipation

It has been suggested that rapid single flux quantum (RSFQ) devices could be used as the classical interface of superconducting qubit systems. One problem is that the interface acts as a dissipative environment for a qubit. Recently, ways to modify the RSFQ damping to reduce the dissipation have been introduced. One of the solutions is to damp the Josephson junctions by a frequency-dependent linear circuit instead of the plain resistor. The approach has previously been experimentally tested with a simple SFQ comparator. In this paper we perform experiments with a full RSFQ circuit, and thus conclude that in terms of stable operation the approach is applicable to scalable RSFQ circuits. Realization and optimization issues are also discussed.