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arXiv:quant-ph/0003034 · Physical Review A

Resonant cancellation of off-resonant effects in a multilevel qubit

Lin Tian, Seth Lloyd

Published Oct 16, 2000• 55 citations
arXivHTMLPDF

Abstract

Off-resonant effects are a significant source of error in quantum computation. This paper presents a group-theoretic proof that off-resonant transitions to the higher levels of a multilevel qubit can be completely prevented in principle. This result can be generalized to prevent unwanted transitions due to qubit-qubit interactions. A simple scheme exploiting dynamic pulse control techniques is presented that can cancel transitions to higher states to arbitrary accuracy.

DOI
10.1103/physreva.62.050301

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Off-resonant effects are a significant source of error in quantum computation. This paper presents a group-theoretic proof that off-resonant transitions to the higher levels of a multilevel qubit can be completely prevented in principle. This result can be generalized to prevent unwanted transitions due to qubit-qubit interactions. A simple scheme exploiting dynamic pulse control techniques is presented that can cancel transitions to higher states to arbitrary accuracy.
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High-fidelity control of superconducting qubits requires carefully shaped microwave pulses to avoid several different kinds of error at once. This article is a pedagogical bridging text aimed at upper-level undergraduate and early graduate students who have completed an introductory quantum mechanics course and a first course in quantum computing or quantum information, but who have not yet encountered the physical implementation of qubit gates. We integrate physical intuition for pulse design, analytical gate-level descriptions, and practical hardware considerations into a single, derivation-driven narrative, with explicit learning objectives. We begin with simple pulse envelopes and their spectral properties, showing how finite bandwidth produces leakage outside the computational subspace. This motivates the derivative removal by adiabatic gate (DRAG) technique, which we derive explicitly using the Magnus expansion, obtaining a clear, order-by-order account of which physical error channel appears at which order and why DRAG's cancellation is necessarily incomplete. We discuss the practical hardware realities of control pulse generation, focusing on arbitrary waveform generators (AWG), local oscillators (LO), and IQ mixing. Finally, we extend the discussion to two-qubit operation via the cross-resonance gate, and interpret how driving the control qubit at the target qubit's transition frequency necessarily produces several unwanted interaction terms alongside the desired one, and how successive generations of pulse-engineering strategies have been designed to suppress them.
Summary form only given. Experiments in many fields of quantum physics require well-defined quantum states and well-defined interactions. For example, the basic ingredient of the quantum computer is a well-defined qubit - a two-state quantum system. Real quantum systems, however, possess many states and special care is needed to isolate just two of them. In real and artificial atoms this is usually done with polarized laser light, carefully aligned with the quantization axis. However, unwanted transition channels may still be present, which reduce the fidelity of the operations. For example, when an ultracold atomic ensemble held in an optical dipole trap is addressed by right circularly polarized light, many atoms often “see” an admixture of σ+ and σ- light (i.e., elliptical polarization [1]) since not all of them are exactly in the focus of the laser fields. Unwanted transitions may be present also due to imperfect polarization or alignment, off-resonant couplings, perturbing excitations in molecules and solids, etc.We propose a simple and efficient technique for automatic compensation of such errors, even without knowing their magnitudes, which uses composite pulse sequences [2-5] to dynamically suppress unwanted transitions, while simultaneously controlling the qubit in a robust way. We illustrate the technique in threeand four-state quantum systems forming linkages reminiscent of the letters V, Ξ and Y, but it can readily be adapted to more complex systems. By suitably choosing the phases of the constituent pulses, the unwanted transitions can be suppressed with very high fidelity, while compensation of deviations in laser polarizations, intensities and detunings can be done simultaneously. The accuracy, the flexibility and the simplicity of the proposed technique make it a potentially important tool in applications requiring high control fidelity, such as quantum information processing and quantum optics.transitions
Uhrig's dynamical decoupling pulse sequence has emerged as a universal and highly promising approach to decoherence suppression. So far, both the theoretical and experimental studies have examined single-qubit decoherence only. This work extends Uhrig's universal dynamical decoupling from one-qubit to two-qubit systems and even to general multilevel quantum systems. In particular, we show that by designing appropriate control Hamiltonians for a two-qubit or a multilevel system, Uhrig's pulse sequence can also preserve a generalized quantum coherence measure to the order of 1+O(TN+1)1+O({T}^{N+1})1+O(TN+1) with only NNN pulses. Our results lead to a very useful scheme for efficiently locking two-qubit entangled states. Future important applications of Uhrig's pulse sequence in preserving the quantum coherence of multilevel quantum systems can also be anticipated.
The ability to perform fast and accurate rotations between the computational basis states of quantum bits is one of the most fundamental requirements for building a quantum computer. Because physical qubits generally contain more than two levels, faster gates often result in a higher leakage rate outside of the computational space. In this Letter, we enhance the state-of-the-art single qubit gate by introducing active leakage cancellation. This is accomplished via a second drive tone near the leakage transition such that we cancel the leakage caused by the main drive. Furthermore, we describe a measurement sequence that can be used to calibrate the parameters of this leakage cancellation drive. Finally, we apply the technique to superconducting transmon qubits and achieve leakage suppression by up to a factor of 20 when compared to pulses shaped with the standard derivative removal by adiabatic gate technique. This results in a coherence-limited gate infidelity of 7.5×10^{-5} with leakage below 10^{-5} level, for a 10 ns π/2 gate and 196 MHz qubit anharmonicity.