Session F48: Quantum Gates in Superconducting Circuits

High-fidelity resonator-induced phase gate with single-mode squeezing

Despite recent breakthroughs in the demonstration of small-scale quantum error correction, reaching the fidelity required for fault tolerance with entangling gates still remains a challenge. We propose a protocol to increase the fidelity of a two-qubit resonator induced phase gate by using a off-resonant narrowband squeezing drive. For this gate, two superconducting transmon qubits are dispersively coupled to a microwave resonator. By off-resonantly driving the resonator, a controlled-Z gate can be implemented between the qubits [1]. However, photons leaving the resonator reveal the qubit which-path information leading to decoherence. We show that driving the resonator with a field squeezed at an optimal angle and strength erases the qubit which-path information and consequently increases the gate fidelity. We find that, under realistic conditions and modest squeezing power, it is possible to implement a high-fidelity two-qubit controlled-Z gate with short gate times. [1] A. W. Cross and J. M. Gambetta Phys Rev A 91, 032325 (2015).   

Characterization of the resonator induced phase gate

The Resonator induced phase (RIP) gate is a versatile microwave gate that can perform collective qubit operations.  We characterize the performance of the RIP gate using various drive powers and detunings in a 4-qubit superconducting system.  We find a good agreement between the experimental results and the theoretical predictions in the gate rate and minimum gate time.  The minimum gate time is limited by residual photons in the bus cavity caused by a non-adiabatic response to the drive.  We measure the multi-qubit interactions and analyze how the rates depend on the cavity-qubit coupling and the detuning to the drive and how these interactions can be used for quantum information processing.   

Demonstrating Multi-Qubit Operations in a Superconducting 3D circuit QED Architecture

We present our recent results on multi-qubit operations in a superconducting 3D circuit QED (cQED) system using a resonator-induced phase (RIP) gate. In our system, four qubits are coupled by a single bus resonator. The RIP gate is implemented by applying a microwave pulse to the bus that performs entangling operations.  We demonstrate controlled-phase gates using RIP on 2-qubit subsystems with gate fidelities between 95\%-97\% evaluated by randomized benchmarking. Via a multi-qubit echo scheme, we perform isolated two-qubit interactions in the full 4-qubit system to generate a GHZ state.   

Understanding and improving the cross resonance gate in superconducting qubits

We present improvements in both theoretical understanding and experimental implementation of the cross resonance (CR) gate that have led to shorter two qubit gatetimes and interleaved randomized benchmarking fidelities exceeding 99\%. The CR gate is an all-microwave two qubit gate offers that does not require tunability and is therefore well suited to quantum computing architectures based on 2D superconducting qubits. The performance of the gate has previously been hindered by long gatetimes and fidelities averaging 96-97\%. We have developed a calibration procedure that accurately measures the full CR Hamiltonian. The resulting measurements agree with theoretical analysis of the gate and also elucidate the error terms that have previously limited the gate fidelity. The increase in fidelity that we have achieved was accomplished by introducing a second microwave drive tone on the target qubit to cancel unwanted components of the CR Hamiltonian.   

High-fidelity single-shot three-qubit gates via machine learning.

Three-qubit quantum gates play a crucial role in quantum error correction and quantum information processing. Here I discuss how to generate policies for quantum control to design three-qubit gates namely, Toffoli, Controlled-Not-Not and Fredkin gates for an architecture of nearest-neighbor-coupled superconducting artificial atoms. The resulted fidelity for each gate is above the 99.9{\%} which is the threshold fidelity for fault-tolerant quantum computing. We test our policy in the presence of decoherence-induced noise as well as show its robustness under random external noise. The three-qubit gates are designed via our machine learning algorithm called Subspace-Selective Self-Adaptive Differential Evolution (SuSSADE).   

All-microwave cavity-mediated three-qubit gate between superconducting qubits

While single-qubit and entangling two-qubit operations are universal for quantum computing, in practice the availability of a single-shot multi-qubit entangling gate can be faster and of higher fidelity. For the case of three qubits coupled to a common cavity mode, we show that a high fidelity, fast CCZ gate can be implemented. Our proposal is based on partial spectrum engineering and pulse shaping. Because our approach does not rely on frequency selectivity, instead driving more than one transitions simultaneously, our three-qubit gate can be achieved on a timescale comparable to that of a two-qubit gate. Our protocol generalizes our recently introduced SWIPHT two-qubit gates.   

Tunable coupling between fixed-frequency superconducting transmon qubits, Part I: Concept, design, and prospects

The controlled realization of qubit-qubit interactions is essential for both the physical implementation of quantum error-correction codes and for reliable quantum simulations. Ideally, the fidelity and speed of corresponding two-qubit gate operations is comparable to those of single qubit operations. In particular, in a scalable superconducting qubit architecture coherence must not be compromised by the presence of additional coupling elements mediating the interaction between qubits. Here we present a coupling method between fixed-frequency transmon qubits based on the frequency modulation of an auxiliary circuit coupling to the individual transmons. Since the coupler remains in its ground state at all times, its coherence does not significantly influence the fidelity of consequent entangling operations. Moreover, with the possibility to create interactions along different directions, our method is suited to engineer Hamiltonians with adjustable coupling terms. This property can be utilized for quantum simulations of spins or fermions in transmon arrays, in which pairwise couplings between adjacent qubits can be activated on demand.   

Tunable coupling between fixed-frequency superconducting transmon qubits, Part II: Implementing a two-qubit XX-90 gate

In this talk we will present a two-qubit gate implemented in a tunable coupling architecture which consists of a flux-tunable qubit (``coupler'') coupling two fixed-frequency transmons (``qubits''). In this architecture, a resonant SWAP (XX+YY) interaction is generated between the qubits when the coupler is modulated at the qubit frequency difference, typically a few hundred MHz. This interaction has a number of advantages, in particular, it only requires AC flux control and can resonantly address individual qubit pairs. Here we present a protocol which realizes the XX-90 gate based on this interaction. This gate has the specific characteristic that it takes any of the four basis states ($|00\rangle,|10\rangle,|01\rangle,|11\rangle$) to Bell states. We demonstrate gate fidelities greater than 96\% characterized by state tomography and randomized benchmarking. Looking forward, this gate is a prime candidate for implementing the surface code because it can couple highly coherent qubits which are spaced far apart in frequency thereby minimizing crosstalk and collisions. \\ This work is supported by ARO under contract W911NF-14-1-0124.   

Gatemon Benchmarking and Two-Qubit Operation

Recent experiments have demonstrated superconducting transmon qubits with semiconductor nanowire Josephson junctions \footnote{G. de Lange et al., Physical Review Letters \textbf{115}, 127002 (2015).} \footnote{T. W. Larsen, K. D. Petersson et al., Physical Review Letters \textbf{115}, 127001 (2015).}. These hybrid gatemon qubits utilize field effect tunability singular to semiconductors to allow complete qubit control using gate voltages, potentially a technological advantage over conventional flux-controlled transmons. Here, we present experiments with a two-qubit gatemon circuit. We characterize qubit coherence and stability and use randomized benchmarking to demonstrate single-qubit gate errors of $\sim$0.5~\% for all gates, including voltage-controlled $Z$~rotations. We show coherent capacitive coupling between two gatemons and coherent SWAP operations. Finally, we perform a two-qubit controlled-phase gate with an estimated fidelity of $\sim$91~\%, demonstrating the potential of gatemon qubits for building scalable quantum processors.   

Dephasing-induced Leakage in Superconducting Qubits

Superconducting quantum devices such as the transmon or xmon are described as weakly anharmonic oscillators with multiple energy levels, the lowest two of which constitute a qubit. Quantum logic operations using these devices typically involve states outside of the qubit subspace; residual population in such states is known as leakage. While control methods are known to eliminate leakage from ideal devices, I will show that dephasing limits the effectiveness of these methods and discuss the implications of this dephasing-induced leakage for quantum information processing.   

Suppressing Leakage in High Fidelity Single Qubit Gates for Superconducting Qubits

Recent results show that superconducting qubits are approaching the threshold for fault tolerant quantum error correction. However, leakage into non-qubit states remains a significant hurdle because leakage errors are highly detrimental for error correction schemes such as the surface code. I will demonstrate that with a simple addition to DRAG pulse shaping, leakage can be suppressed to the $10^{-5}$ level while simultaneously maintaining $10^{-3}$ gate fidelity. I will also show that the remaining leakage errors are due to heating of the qubit, suggesting further avenues for improvement.   

Circuit design implementing longitudinal coupling: a scalable scheme for superconducting qubits

We present a circuit construction for a new fixed-frequency superconducting qubit and show how it can be scaled up to a grid with strictly local interactions. The circuit QED realization we propose implements $\sigma_z$-type coupling between a superconducting qubit and any number of $LC$ resonators. The resulting \textit{longitudinal coupling} is inherently different from the usual $\sigma_x$-type \textit{transverse coupling}, which is the one that has been most commonly used for superconducting qubits. In a grid of fixed-frequency qubits and resonators with a particular pattern of always-on interactions, coupling is strictly confined to nearest and next-nearest neighbor resonators\footnote{P.-M. Billangeon et al., \textbf{Phy. Rev. B} 91:094517, 2015}; we note that just four distinct resonator frequencies, and only a single unique qubit frequency, suffice for the scalability of this scheme. There is never any direct coupling between the qubits. A controlled phase gate between two neighboring qubits can be realized with microwave drives on the qubits, without affecting the other qubits. This fact is a supreme advantage for the scalability of this scheme.   

Controllable frequency comb generation in a tunable superconducting coplanar waveguide resonator

Frequency combs have attracted considerable interest because they are extremely useful in a wide range of applications, such as optical metrology and high precision spectroscopy. Here we report the design and characterization of a controllable frequency comb generated in a tunable superconducting coplanar waveguide resonator in the microwave regime. Both the center frequency and teeth density of the comb are precisely controllable. The teeth spacing can be adjusted from Hz to MHz. The experimental results can be well explained via theoretical analysis.   

Design and Measurement of a Tunable Thin-Film LC Resonator for Coupling to Superconducting Circuits

We have designed and measured a tunable lumped element LC resonator for coupling to transmon qubits. We use an rf SQUID loop as a variable inductive element that shunts the inductor of the resonator and produces a shift in the resonator frequency that depends on the flux applied to the loop. In order to achieve a balanced response, we shunt the inductor with two single junction SQUID loops. Each junction has a critical current of approximately 300pA, which is small enough to prevent multiple trapped flux states. We tune the effective inductance of the loops by using a split, gradiometric modulation coil that is well isolated from the cavity at the resonance frequency. Our resonator is made of thermally evaporated aluminum on a sapphire substrate and has a resonance frequency of 5.3 GHz. It is mounted inside a 3D microwave cavity that has a TE101 frequency of 6.3 GHz.   

Quantization of lumped elements electrical circuits revisited

In 1995, the “Les Houches” seminar of Michel Devoret introduced a method to quantize lumped elements electrical circuits [1]. This method has since been formalized using the matricial formalism, in particular by G. Burkard [2,3]. Starting from these seminal contributions, we present a new algorithm to quantify electrical circuits. This algorithm unites the features of Devoret's and Burkad's approaches. We minimize the set of assumptions made so that the method can treat directly most electrical circuits. This includes circuits with resistances, mutual inductances, voltage and current sources. We conclude with a discussion about the choice of the basis in which the Hamiltonian operator should be written, an issue which is often overlooked. [1] M. H. Devoret, Les Houches, Session LXIII, 1995 [2] G. Burkard et al., Phys. Rev. B, 69, 064503, 2004 [3] F. Solgun, Ph.D. Dissertation, RWTH­ Aacehn, 2015