Pulse sequences for suppressing leakage in single-qubit gate operations

Abstract

Many realizations of solid-state qubits involve couplings to leakage states lying outside the computational subspace, posing a threat to high-fidelity quantum gate operations. Mitigating leakage errors is especially challenging when the coupling strength is unknown, e.g., when it is caused by noise. Here we show that simple pulse sequences can be used to strongly suppress leakage errors for a qubit embedded in a three-level system. As an example, we apply our scheme to the recently proposed charge quadrupole (CQ) qubit for quantum dots. These results provide a solution to a key challenge for fault-tolerant quantum computing with solid-state elements.PACS numbers: 03.67. Ac, 73.21.La, 85.35.Be Recent advances in semiconducting quantum dots make them promising candidates for universal quantum computing [1][2][3][4][5][6]. However, performing gate operations with high enough fidelity to support fault-tolerant error correction remains a key challenge [7]. Two ways that a qubit can fail to have high fidelity are (i) the qubit could decay or dephase, and (ii) quantum information could leak out of the qubit's logical subspace into other quantum states in the physical system [8][9][10][11][12]. While several recent proposals in quantum dots have focused on suppressing dephasing from environmental noise [13,14], relatively little effort has gone into suppressing leakage [12].Several approaches for reducing leakage errors have been developed for superconducting qubits, including analytic pulse shaping [1,9] and optimal quantum control [16,17]. It is also known that leakage errors are, in principle, suppressible for a system-bath model with a composite sequence of a large number of pulses [8]. However, suppressing leakage errors below the fault-tolerant threshold under experimental conditions for quantum dot qubits is challenging, because of the need to apply smoothly varying short control pulses [18] within a time much less than the coherence times of the system, and also because the qubits experience fluctuations that vary in time and strength [19]. For semiconducting systems, these constraints preclude using analytically derived pulse shapes, since these require knowing the noise strength as an input parameter [9], or quantum control strategies that rely on optimizing an unrealistically large number of control parameters [16,17].In this work, we develop a simple and experimentally feasible protocol based on composite pulses that suppresses leakage errors in a three-level quantum system where the leakage state is coupled to one of the logical states with an unknown but static coupling strength (referred to as the quasistatic noise approximation [19]). Whereas the leakage error scales quadratically with noise amplitude in conventional pulsed-gate schemes for this model, our protocol significantly improves the gate fidelities by eliminating computational errors in the logical subspace up to fourth order in the noise amplitude and leakage errors up to sixth order.In a basis comprised of two logical states and one leakage...

Phonon-induced decoherence of a charge quadrupole qubit

“…One of the main questions to be answered in this work is whether phonon-mediated noise presents a challenge for charge quadrupole qubits, and how phonon-induced decoherence compares to decoherence from charge noise, which was studied in [31,32]. Similar to [32], we assume the charge noise to be quasistatic, with fluctuations of the dipolar detuning parameter that follow a Gaussian distribution with a standard deviation of 1 μeV [58], as typical for experiments. A composite Z X Z 3 p p p -( ) ( ) ( ) pulse sequence was implemented, to eliminate the effects of leakage to leading order, and the average gate fidelity was calculated as described in [32].…”

“…Similar to [32], we assume the charge noise to be quasistatic, with fluctuations of the dipolar detuning parameter that follow a Gaussian distribution with a standard deviation of 1 μeV [58], as typical for experiments. A composite Z X Z 3 p p p -( ) ( ) ( ) pulse sequence was implemented, to eliminate the effects of leakage to leading order, and the average gate fidelity was calculated as described in [32]. The pulse sequence used in these simulations is shown in figure 6, with additional details given in appendix G. For the phonon noise, we use the same pulse sequence.…”

“…The pulse sequence used in these simulations is shown in figure 6, with additional details given in appendix G. For the phonon noise, we use the same pulse sequence. However, we modified the Ramsey sequence in figure 5 by setting t=0 during the Z rotation, as proposed in [32]. This has the benefit of suppressing the phononinduced tunneling during Ramsey oscillations, so that decoherence occurs only during Larmor precession.…”

“…One of the main sources of qubit decoherence in each of these systems is charge noise, which can arise from high-temperature electrical noise in the voltage controls or the motion of defects and free charges in the heterostructure. The recently proposed charge quadrupole qubit, formed of one electron in a triple QD, is robust against uniform electric field fluctuations due to the high symmetry of its basis states [31,32]. The qubit states are symmetric with respect to the central QD, thus forming a decoherence-free subspace, which is well-known for spin qubits [33][34][35], but novel for charge qubits.…”

“…An important parameter for qubit control is the tunnel coupling, which strongly affects the qubit energy. Since phonon-induced decoherence increases as the tunnel coupling increases, and the decoherence arising from charge noise [31,32] decreases as the tunnel coupling increases, both sources of decoherence must be considered to identify the optimal working regime for the qubit. We demonstrate that there is a working regime where qubit infidelity from both these processes is less than 0.01%.…”