Fast microwave-driven three-qubit gates for cavity-coupled superconducting qubits

Abstract

Although single and two-qubit gates are sufficient for universal quantum computation, single-shot three-qubit gates greatly simplify quantum error correction schemes and algorithms. We design fast, high-fidelity three-qubit entangling gates based on microwave pulses for transmon qubits coupled through a superconducting resonator. We show that when interqubit frequency differences are comparable to single-qubit anharmonicities, errors occur primarily through a single unwanted transition. This feature enables the design of fast three-qubit gates based on simple analytical pulse shapes that are engineered to minimize such errors. We show that a three-qubit ccz gate can be performed in 260 ns with fidelities exceeding 99.38%, or 99.99% with numerical optimization.Quantum information processing is one of the most exciting and rapidly growing fields of modern science, in large part due to quantum algorithms, which promise exponential speedup in solving important problems. Quantum two-level systems (qubits) are the fundamental carriers of quantum information, and among the most promising of these are qubits based on superconducting circuits [1,2]. Such an architecture is attractive because of the mature circuit fabrication technology and the ability to couple qubits together via resonators to implement logic gates [3].For universal quantum computing, a certain set of high-fidelity logic gates suffices to implement any algorithm; this set is comprised of single-qubit gates along with one maximally entangling two-qubit gate. Threequbit gates, which play a prominent role in algorithms, can be decomposed in terms of a sequence of single-and two-qubit gates [4]. In the case of a maximally entangling three-qubit control-control-z (ccz) gate (described below), one must perform seven single-qubit gates and six entangling two-qubit gates, as shown in Fig. 1. The large number of gates needed makes it natural to explore whether a direct, single-shot three-qubit gate is preferable in terms of speed and fidelity.There are two ways to implement logic gates in superconducting qubit systems. One is via tuning of the energy levels, which brings states into and out of resonance. The other is via oscillating microwave fields that induce transitions between energy levels, which offers the advantage of less susceptibility to charge noise. Both approaches face the challenge of spectral crowding in these systems, especially in the context of superconducting transmon qubits where each qubit is a weakly anharmonic oscillator out of which the two lowest levels are selected to encode information [5]. In the case of many qubits coupled together, there is a large number of closely spaced transitions that need to be avoided during quantum gate operations. Generically, a way to avoid unwanted transitions is to consider the time-energy uncertainty principle, which tells us to make the operations slow. In realistic systems, however, this is not an option, as we need to perform operations at a time scale that is much faster than decay and decoherence. ...

Asymptotic improvements to quantum circuits via qutrits

“…Accordingly, we adopt a baseline superconducting noise model, labeled as SC, corresponding to a superconducting device which has 10x lower gate errors and 10x longer T 1 duration than the current IBM hardware. This range of parameters has already been achieved experimentally in superconducting devices for gate errors [55,56] and for T 1 duration [57,58] independently. Faster gates Noise Model 3p 1 15p 2 T 1 SC 10 −4 10 −3 1 ms SC+T1 10 −4 10 −3 10 ms SC+GATES 10 −5 10 −4 1 ms SC+T1+GATES 10 −5 10 −4 10 ms Table 2: Noise models simulated for superconducting devices.…”

The roles of drift and control field constraints upon quantum control speed limits

“…The authors conjecture that this is the case for gates within a small neighborhood of any given fast gates, i.e., gates which can be implemented by the controls alone. Furthermore, recently it has been shown that simple analytically obtained pulses can lead to high fidelity gates  » 0.01 [67,68]. Further numerical control optimization yields yet higher fidelities at the cost of requiring significantly higher frequency components within the numerically optimized pulse [68].…”

“…Furthermore, recently it has been shown that simple analytically obtained pulses can lead to high fidelity gates  » 0.01 [67,68]. Further numerical control optimization yields yet higher fidelities at the cost of requiring significantly higher frequency components within the numerically optimized pulse [68]. It would be favorable to obtain criteria characterizing the set of gates for which 'simple' pulses exist and further to understand the highest frequency required in a pulse to implement a gate perfectly.…”

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

“…In the dispersive regime, the simplest way to ensure that this transition is the only one excited by the pulse is to use a very narrowband pulse-an approach which necessarily leads to long gate times. To avoid making this sacrifice in gate speed, we instead employ the SWIPHT method 43,46 to remove the effects of inadvertently driving unwanted transitions without resorting to spectrally narrow, slow pulses. For typical experimental values of the qubit-cavity couplings g 1,2 , there is exactly one nearest "harmful" transition, namely the |001 ⇔ |011 transition, which competes with the target transition, |000 ⇔ |010 .…”