Pulsed Reset Protocol for Fixed-Frequency Superconducting

Pulsed reset protocol for fixed-frequency superconducting qubits D. J. Egger, M. Werninghaus, M. Ganzhorn, G. Salis, A. Fuhrer, P. Müller, S. Filipp IBM Research GmbH, Zurich Research Laboratory, Säumerstrasse 4, 8803 Rüschlikon, Switzerland (Dated: April 2, 2019) Improving coherence times of quantum bits is a fundamental challenge in the field of quantum computing. With long-lived qubits it becomes, however, inefficient to wait until the qubits have relaxed to their ground state after completion of an experiment. Moreover, for error-correction schemes it is important to rapidly re-initialize syndrome qubits. We present a simple pulsed qubit reset protocol based on a two-pulse sequence. A first pulse transfers the excited state population to a higher excited qubit state and a second pulse into a lossy environment provided by a low-Q transmission line resonator, which is also used for qubit readout. We show that the remaining excited state population can be suppressed to 1:7 ± 0:1% and that this figure may be reduced by further improving the pulse calibration. INTRODUCTION rapidly tuned into resonance [16], a scheme that is also used for generating traveling single-photon Fock-states Building a fully operational and useful quantum com- [17, 18]. When the qubit frequency cannot be tuned in- puter requires many good, high-coherence qubits along situ [19] and the coupling between qubits and other cir- with high-fidelity gates. An equally important require- cuits is fixed, coherent microwave pulses provide the only ment is the ability to (re-)initialize qubits in their ground way to manipulate the system. In such an architecture state [1]. In the context of error correction codes [2], fast qubit initialization has to be implemented either with the reset of syndrome qubits must be accomplished on a quantum-circuit refrigerator [20] or with microwaves. timescales much shorter than the coherence time, at best It has been demonstrated that the system can be steered comparable to the duration of single-qubit pulses. An- by multi-tone microwave drives into a steady-state that other field of application is speeding up the execution of leaves the qubit in the ground state [21]. Recently, in a variational quantum algorithms [3–8] in which the quan- paper also including a review of other reset methods, a tum system has to be re-initialized quickly to start the fast unconditional reset protocol was demonstrated in an next gate sequence with modified parameters. An effi- architecture using two low quality factor resonators, one cient reset mechanism can also be used for cooling qubits for qubit readout and one for qubit reset [22]. [9]. Here, we demonstrate that an effective Jaynes- The easiest way to reset a qubit involves waiting sev- Cummings type interaction from a single external drive can successfully reset the qubit within a few hundred eral times the decay (T1) time so that the energy stored nanoseconds using only the readout resonator. This in the qubit relaxes into the environment. As the T1 times of superconducting qubits increase to values above avoids introducing a second resonator used for reset and 100 µs [10] this passive reset becomes inefficient and re- thus saves space on the chip. Similarly to [22], our reset quires millisecond waiting times. Several methods have protocol is based on an induced Rabi oscillation between been developed to actively reset superconducting qubits. the second-excited state of a superconducting transmon- One approach is to (re-)initialize the qubits by measuring type qubit and a harmonic oscillator [23]. This tech- their individual states and inverting them via a π-pulse nique has been employed to generate shaped microwave conditioned on the measurement outcome [11, 12]. Such photons [24] to establish entanglement between remote an active reset protocol suffers from the relatively long qubits [25–27]. It has also been used to measure a vacuum-induced geometric phase [28], a quantized ver- arXiv:1802.08980v2 [quant-ph] 1 Apr 2019 latency times, typically in the few hundred nanoseconds range, of the readout-chain and state descrimination. It sion of Berry’s well-known geometric phase. An attrac- is also limited by the fidelity of the qubit measurement. tive feature of this tunable coupling mechanism is its ap- An un-conditional reset protocol with no need for active plicability to fixed-frequency qubit architectures, as for feedback, as proposed here, requires less time and does instance used in the IBM Q Experience [29]. It can even not rely on fast hardware components. Such a mecha- serve to entangle qubits by generating a holonomic trans- nism requires a low-temperature dissipative environment formation in a three-dimensional subspace spanned by that is coupled to the qubit in a controlled way. A su- the resonator and two qubits [30]. perconducting qubit may, for instance, be coupled to a low-temperature resistive bath by controlling a coupling resonator [13]. In a circuit QED setting [14, 15] the dis- DESCRIPTION OF THE SYSTEM sipative environment may be provided by a transmission line resonator with low quality factor that may also be The system is made up of a fixed-frequency super- a readout resonator. Frequency-tunable qubits can be conducting qubit coupled with strength g to a co-planar 2 (a) (c) ۧ waveguide resonator used both for read-out and reset of Transfer pulse |푓 푒→푓 the qubit. The Hamiltonian describing the system [24], ~ Qubit pulses & X휋 X푒→푓 in a frame rotating at the frequency !d of the drive with |1ۧ 휋 To AWG a slowly-varying complex envelope Ω(t), is Fast excitation loss |푒ۧ +30 dB sample to environment y ^y^ α^y^y^^ |0ۧ |푔ۧ ~ |푓0ۧ → |푔1ۧ drive ^ H = δra^ a^ + δqb b + b b b b Readout Qubit 2 resonator y y 1 y ∗ (b) 푒→푓 +g ^b a^ + ^b a^ + Ω(t)^b + Ω (t)^b : (1) Qubit drive 푋휋 Quantum computation` 푓0ۧ → |푔1ۧ| 2 Reset pulses y Here ¯h = 1, ^b (^b ) is the qubit lowering (raising) operator Resonator drive 퐼푑 Readout whilst a^ (a^y) is the resonator lowering (raising) operator. The effective transition energies between the qubit and Figure 1. (a) Level diagram of the transmon-resonator sys- resonator are δq = !ge !d and δq = !r !d, respectively. tem along with the relevant pulses to reset the qubit. (b) − − The qubit has a transition frequency !ge=2π = 4:904 GHz Pulsed reset protocol. Before a quantum algorithm com- between its ground state g and its first excited state e . mences, the reset pulse sequence is carried out: first the re- j i j i maining qubit population in state jei is shelved to state jfi The anharmonicity is α=2π = 330 MHz resulting in a e!f transition frequency of ! =2π =− 4:574 GHz between the with the pulse Xπ , second the population in jfi is trans- ef ferred to the readout resonator with the jf0i $ jg1i drive first and the second excited state f . The readout res- j i where it rapidly decays to the environment. (c) Room tem- onator transition frequency is !r=2π = 6:838 GHz. The perature electronics. A 30 dB amplifier enhances the rate at qubit resonator coupling g=2π = 67 MHz is computed which the jf0i $ jg1i transition is driven. from the dispersive shift χ/2π = 335 48 kHz measured by probing the resonance of the readout± resonator for different qubit states [31]. The measured T1-times of the The effective coupling strength between f0 and g1 is qubit and resonator are 48 µs and 235 ns, respectively. j i j i The protocol described in this paper makes use of gαΩ(t) the qubit-resonator transitions between the f0 and g~(t) = (3) p g1 states where 0 is the ground state andj i1 is 2δ(δ + α) thej i excited state ofj thei resonator, see Fig.1(a).j Thei with the qubit-resonator detuning δ = ! ! . The single-qubit transitions and the qubit-resonator transi- r ge rate of the f0 g1 microwave activated− transition tion are controlled by applying the real microwave drive decreases withj qubit-resonatori $ j i detuning but can be com- Ω (t) cos(! t '(t)) with a corresponding complex am- 0 d pensated by stronger driving with reported effective cou- plitude Ω(t)− = Ω (t)ei'(t) where Ω (t) and '(t) are 0 0 pling rates up to approximately 10 MHz [23]. slowly varying. Pulse generation details are shown in Fig.1(c). Applying a drive at the qubit frequency !d = !ge (!ef ) PULSED RESET PROTOCOL g!e e!f with ' = 0 creates a rotation Xβ (Xβ ) around the x-axis of the g ; e ( e ; f ) Bloch-sphere with an- We utilize the f0 g1 controllable quantum link gle R Ω(t)dt fj= βi j[32ig].fj Ai differentj ig rotation axis in the as a fast, simple andj i unconditional $ j i method to reset su- equatorial plane can be selected by changing the phase perconducting qubits using only the readout resonator ' of the drive. Similarly, applying a drive at the differ- and an extra microwave drive. Our reset protocol does ence frequency between the f state of the transmon and not require flux-tunable qubits, thus preserving the long the excited resonator state j1i, i.e. ! = ! + ! ! , d ge ef r coherence times of fixed-frequency transmon qubits. The activates induced Jaynes-Cummings-typej i vacuum-Rabi− reset works as follows: before performing quantum com- oscillations between these states. Adiabatic elimination putations with the qubit logical states g and e a Xe!f of the qubit e state, which is far detuned from the drive π pulse transfers any remaining populationj i in statej i e to frequency givesj i the effective Hamiltonian [23, 24] state f .

Load more