Session L46: Focus: Quantum Gates in Superconducting Qubits Continued

Faster gate operations through strong parametric coupling of superconducting circuits

In order to realize a gate-based quantum computer, one essential factor is improving the number of high fidelity gate operations possible. A rough estimate of this number is given by the (coherence time)/(gate operation time) or the (gate speed)/(coherence decay rate). Ideally, one would like the smallest coherence decay rate and the highest gate speed. However, the difficulty is that these two quantities tend to be at odds with one another: that is to say, maintaining the coherence of qubits requires strong isolation, whereas fast gate operations requires generating strong coupling between qubits. In this talk, I will discuss the use of parametric coupling techniques as a useful tool for maintaining qubit coherence while operating gate’s at high speed. We rely on the use of a flux-biased direct current superconducting quantum interference device (dc-SQUID) that can provide non-resonant tunable interactions between qubit-qubit, qubit-resonator, or resonator-resonator systems. We will highlight past and present experimental work with these systems and discuss our efforts to maximize the number of gate operations   

Charting the design landscape of circuit QED for optimal gates

We map out the experimentally reachable design landscape of circuit QED in terms of achievable fidelity of universal gate sets for arbitrary perfectly entangling two-qubit gate. Using state-of-the-art control techniques, we exhaustively explore the landscape for creation and removal of entanglement, needed respectively for two- and single-qubit gates. Our approach is valid for both fixed- and tunable-frequency qubits, where in the tunable case a separation between points of a few 100MHz is allowed for different gates. We also compare to the case where the qubits are driven directly with dedicated lines. We find a system-wide global optimal regime in the parameter space where multiple transition paths destructively interfere so that net static coupling is suppressed but microwave-activated coupling can still attain high values. This regime allows for a significant speedup compared to using static coupling to entangle qubits, and over working in the usual strongly dispersive regime.   

Quantum optimal control with automatic differentiation using graphics processors

We implement quantum optimal control based on automatic differentiation and harness the acceleration afforded by graphics processing units (GPUs). Automatic differentiation allows us to specify advanced optimization criteria and incorporate them into the optimization process with ease. We will describe efficient techniques to optimally control weakly anharmonic systems that are commonly encountered in circuit QED, including coupled superconducting transmon qubits and multi-cavity circuit QED systems. These systems allow for a rich variety of control schemes that quantum optimal control is well suited to explore.   

Experimental Pauli-frame randomization on a superconducting qubit

Coherent errors can interfere, and in this manner, conspire to be much more damaging than stochastic errors of similar infidelity. One technique to deal with such errors is {\it Pauli-frame randomization}\footnote{E. Knill, Nature {\bf 434}, 7029 (2005).} \footnote{J. Wallman and J. Emerson arXiv:1512.01098 [quant-ph] (2015).}, which works by randomizing computational gates so that the effective errors becomes incoherent, and therefore, less damaging. In this talk we describe the practical implementation of Pauli-frame randomization on a transmon qubit (including its automation), as well as how to rigorously test Pauli-frame randomization through the use of gate set tomography. This effort is supported in part by the U.S. Army Research Office under contract W911NF-14-C-0048. The content of the information does not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred.   

Robustness of error-suppressing entangling gates in cavity-coupled transmon qubits

Superconducting transmon qubits are one of the most promising platforms for quantum information processing due to their long coherence times and to their scalability into larger qubit networks. However, their weakly anharmonic spectrum leads to spectral crowding in multiqubit systems, making it challenging to implement fast, high-fidelity gates while avoiding leakage errors. To address this challenge, we have developed a protocol known as SWIPHT, which yields smooth, simple microwave pulses designed to suppress leakage without sacrificing gate speed through spectral selectivity. Here, we demonstrate that SWIPHT systematically produces two-qubit gate fidelities for cavity-coupled transmons in the range 99.0{\%}-99.9{\%} with gate times in the 15-200ns regime. These high fidelities persist over a wide range of qubit frequencies and other system parameters that encompasses many current experimental setups. Our results are obtained from full numerical simulations that include current experimental levels of relaxation and dephasing.   

Experimental realization of two-qubit non-Abelian geometric gates for fixed frequency superconducting qubits

Fixed-frequency superconducting qubits are controlled with microwave pulses both to generate single-qubit rotations and to activate entangling interactions. A two-qubit entangling gate, needed to form a universal set of logic gates, can be created in many ways. Here we show an experimental implementation of a two-qubit non-Abelian geometric gate. These gates have the potential to be less sensitive to certain types of noise since the state vectors are swept along closed paths in Hilbert space. With two transmon qubits connected via a resonator we implement an entangling two-qubit gate by creating a lambda system using the transitions between the second excited state of each qubit and the first excited state of the resonator. The non-Abelian geometric gate is activated by simultaneously driving these two transitions. Arbitrary rotations in a two-qubit subspace can be created by changing the amplitudes and phases of the two drives. This two-qubit gate combined with non-Abelian geometric single qubit rotations completes the necessary toolbox for a quantum computer based on non-Abelian geometric gates.   

Quantum approximate optimization on a gate-model superconducting processor

The Quantum Approximate Optimization Algorithm (QAOA) [Farhi et al. arXiv:1411.4028] is a promising application for near-term quantum computing devices and has potential to demonstrate quantum supremacy [Farhi & Harrow arXiv:1602.07674]. We compile and run the QAOA algorithm on a programmable superconducting qubit processor, assessing its performance on instances of the MAX-CUT and k-coloring problems. Experimental performance is analyzed to measure the robustness of QAOA to device noise, and we comment on its outlook as a near-term demonstration of quantum supremacy.   

Efficient gate set tomography on a multi-qubit superconducting processor

Quantum information processors with five or more qubits are becoming common.  Complete, predictive characterization of such devices — e.g. via any form of tomography, including gate set tomography — appears impossible because the parameter space is intractably large.  Randomized benchmarking scales well, but cannot predict device behavior or diagnose failure modes.  We introduce a new type of gate set tomography that uses an efficient ansatz to model physically plausible errors, but scales polynomially with the number of qubits.  We will describe the theory behind this multi-qubit tomography and present experimental results from using it to characterize a multi-qubit processor made by Rigetti Quantum Computing.   

Implementation of gate set tomography on transmon qubit to characterize and optimize single qubit gates

Characterizing the fidelities of quantum gates and improving them are essential requirements to build a scalable quantum computation platform. Two typical methods for such purpose, i.e., randomized benchmarking and quantum process tomography, contain drawbacks that cannot be compensated without the aid of the other, which demands the development of a new stand-alone protocol. Gate set tomography (GST) is one of such protocols developed to obtain detailed information of qubit gates that are free from the state preparation and measurement (SPAM) errors. We have implemented GST on several packages of single transmon qubit embedded in a 3 dimensional cavity. As a result, GST analysis not only estimated the process matrices of target gates but also suggested the direction for further calibration to achieve more accurate gate operations.   

Gate-set tomography on two coupled transmons

Gate set tomography (GST) is a high-accuracy method of reconstructing the evolution of a quantum register [Blume-Kohout et al., arXiv:1310.4492 and Blume-Kohout et al., arXiv:1605.07674]. We describe the implementation of GST on two coupled transmon qubits. The ideal gate set includes single-qubit gates and an entangling gate locally equivalent to a CNOT. The analysis shows good agreement with predictions from theoretical models of our system -- including the effects of coherent errors, which serve to illustrate important differences between average infidelity and diamond norm error rates. Finally, we describe how to mitigate these errors for improved performance.   

Tunable quantum gate between a superconducting atom and a propagating microwave photon

We propose a two-qubit quantum logic gate between a superconducting atom and a propagating microwave photon. The atomic qubit is encoded on its lowest two levels and the photonic qubit is encoded on its carrier frequencies. The gate operation completes deterministically upon reflection of a photon, and various two-qubit gates (SWAP, $\sqrt{\rm SWAP}$, and Identity) are realized through {\it in situ} control of the drive field. The proposed gate is applicable to construction of a network of superconducting atoms, which enables gate operations between non-neighboring atoms.   

Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator

A logical qubit is a subspace of a system’s total Hilbert space, carefully chosen so as to minimize the effect of the environment on the encoded information. A side effect of protecting the qubit from the environment is that it is likely to be difficult to control. Controlling the state of a logical qubit generally requires precise and arbitrary control over the entire system. We encode quantum information in the two-level subspace of four-component cat states, and demonstrate a universal set of operations which manipulate this cat qubit with high fidelity. We create these operations with numerically optimized pulse waveforms, which exploits accurate knowledge of the Hamiltonian to manipulate the dispersively coupled oscillator-transmon system. Our results show the power of applying numerical techniques to control linear oscillators and pave the way for utilizing their large Hilbert space as a resource in quantum information processing.   

Robust quantum gates for stochastic time-varying noise

How to effectively construct robust quantum gates for time-varying noise is a very important but still outstanding problem. Here we develop a systematic method to find pulses for quantum gate operations robust against both low- and high-frequency (comparable to the qubit transition frequency) stochastic time-varying noise. Our approach, taking into account the noise properties of quantum computing systems, can output single smooth pulses in the presence of multi-sources of noise. Furthermore, our method is quite general and not sensitive to system models and noise models, and will make essential steps toward constructing high-fidelity and robust quantum gates for fault-tolerant quantum computation. Finally, we discuss and compare the gate operation performance by our method with that by the filter-transfer-function method.