Raman qubits, represented by two ground or metastable quantum states coupled via an intermediate state, hold some advantages over directly coupled qubits, most notably much longer radiative lifetimes, shorter gate duration, and lower radiation intensity due to using electric-dipole allowed optical transitions. They are also relatively simple to implement and control, making them an attractive option for building quantum gates for quantum computers. In this work, we present a simple and fast tomographic method to measure the errors of Raman qubit gates possessing the Morris-Shore dynamic symmetry. The latter occurs when the qubit states are on two-photon resonance and the driving fields have the same time dependence. The method is based on repeating the same gate multiple times, which amplifies the small coherent errors to sufficiently large values, which can be measured with high accuracy and precision. Then the (small) gate errors can be determined from the amplified errors by using the analytical connections between them.
Raman qubits, represented by two ground or metastable quantum states coupled via an intermediate state, hold some advantages over directly coupled qubits, most notably much longer radiative lifetimes, shorter gate duration, and lower radiation intensity due to using electric-dipole allowed optical transitions. They are also relatively simple to implement and control, making them an attractive option for building quantum gates for quantum computers. In this work, we present a simple and fast tomographic method to measure the errors of Raman qubit gates possessing the Morris-Shore dynamic symmetry. The latter occurs when the qubit states are on two-photon resonance and the driving fields have the same time dependence. The method is based on repeating the same gate multiple times, which amplifies the small coherent errors to sufficiently large values, which can be measured with high accuracy and precision. Then the (small) gate errors can be determined from the amplified errors by using the analytical connections between them.
We present a general systematic approach to design robust and high-fidelity quantum logic gates with Raman qubits using the technique of composite pulses.We use two mathematical tools-the Morris-Shore and Majorana decompositions-to reduce the three-state Raman system to an equivalent two-state system.They allow us to exploit the numerous composite pulses designed for two-state systems by extending them to Raman qubits.We construct the NOT, Hadamard, and rotation gates by means of the Morris-Shore transformation with the same uniform approach: sequences of pulses with the same phases for each gate but different ratios of Raman couplings.The phase gate is constructed by using the Majorana decomposition.All composite Raman gates feature very high fidelity, well beyond the quantum computation benchmark values, and significant robustness to experimental errors.All composite phases and pulse areas are given by analytical formulas, which makes the method scalable to any desired accuracy and robustness to errors.
Abstract In quantum computation the target fidelity of the qubit gates is very high, with the admissible error being in the range from 10−3 to 10−4 and even less, depending on the protocol. The direct experimental determination of such a tiny error is very challenging by standard quantum-process tomography. Instead, the method of randomized benchmarking, which uses a random sequence of Clifford gates, has become a standard tool for determination of the average gate error as the decay constant in the exponentially decaying fidelity. In this paper, the task for determining a tiny error is addressed by sequentially repeating the same gate multiple times, which leads to the coherent amplification of the error, until it reaches large enough values to be measured reliably. If the transition probability is p = 1 − ϵ with ϵ ≪ 1 in the single process, then classical intuition dictates that the probability after N passes should be P N ≈ 1 − N ϵ . However, this classical expectation is misleading because it neglects interference effects. This paper presents a rigorous theoretical analysis based on the SU(2) symmetry of the qubit propagator, resulting in explicit analytic relations that link the N-pass propagator to the single-pass one in terms of Chebyshev polynomials. In particular, the relations suggest that in some special cases the N-pass transition probability degrades as P N = 1 − N 2 ϵ , i.e. dramatically faster than the classical probability estimate. In the general case, however, the relation between the single-pass and N-pass propagators is much more involved. Recipes are proposed for unambiguous determination of the gate errors in the general case for both Clifford and non-Clifford gates.
Metastable qubits in atomic systems can enable large-scale quantum computing by simplifying hardware requirements and adding efficient erasure conversion to the preexisting toolbox of high-fidelity laser-based control. For trapped atomic ions, the fundamental error floor of this control is given by spontaneous Raman and Rayleigh scattering from short-lived excited states. We measure spontaneous Raman scattering rates out of a metastable D5/2 qubit manifold of a single trapped 40Ca+ ion illuminated by 976 nm light that is $\ensuremath{-}44$ THz detuned from the dipole-allowed transition to the P3/2 manifold. This supports the calculation of error rates from both types of scattering during one- and two-qubit gates on this platform, thus demonstrating that infidelities less than ${10}^{\ensuremath{-}4}$ are possible.
One of the main enablers in quantum computing is having qubit control that is precise and fast. However, qubits typically have multilevel structures making them prone to unwanted transitions from fast gates. This leakage out of the computational subspace is especially detrimental to algorithms as it has been observed to cause long-lived errors, such as in quantum error correction. This forces a choice between either achieving fast gates or having low leakage. Previous works focus on suppressing leakage by mitigating the first to second excited state transition, overlooking multi-photon transitions, and achieving faster gates with further reductions in leakage has remained elusive. Here, we demonstrate single qubit gates with a total leakage error consistently below 2.0×10−5, and obtain fidelities above 99.98% for pulse durations down to 6.8 ns for both X and X/2 gates. This is achieved by removing direct transitions beyond nearest-neighbor levels using a double recursive implementation of the Derivative Removal by Adiabatic Gate (DRAG) method, which we name the R2D method. Moreover, we find that at such short gate durations and strong driving strengths the main error source is from these higher order transitions. This is all shown in the widely-used superconducting transmon qubit, which has a weakly anharmonic level structure and suffers from higher order transitions significantly. We also introduce an approach for amplifying leakage error that can precisely quantify leakage rates below 10−6. The presented approach can be readily applied to other qubit types as well.
Abstract Semiconductor spin qubits demonstrated single-qubit gates with fidelities up to 99.9 % benchmarked in the single-qubit subspace. However, tomographic characterizations reveal non-negligible crosstalk errors in a larger space. Additionally, it was long thought that the two-qubit gate performance is limited by charge noise, which couples to the qubits via the exchange interaction. Here, we show that coherent error sources such as a limited bandwidth of the control signals, diabaticity errors, microwave crosstalk, and non-linear transfer functions can equally limit the fidelity. We report a simple theoretical framework for pulse optimization that relates erroneous dynamics to spectral concentration problems and allows for the reuse of existing signal shaping methods on a larger set of gate operations. We apply this framework to common gate operations for spin qubits and show that simple pulse shaping techniques can significantly improve the performance of these gate operations in the presence of such coherent error sources. The methods presented in the paper were used to demonstrate two-qubit gate fidelities with F > 99.5 % in Xue et al (2022 Nature 601 343). We also find that single and two-qubit gates can be optimized using the same pulse shape. We use analytic derivations and numerical simulations to arrive at predicted gate fidelities greater than 99.9% with duration less than, 4 / ( Δ E z ) where Δ E z is the difference in qubit frequencies.
One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems from a combination of control errors and random single qubit errors from interaction with the environment. While great strides have been made in mitigating control errors, intrinsic qubit error remains a serious problem that limits gate fidelity in modern qubit architectures. Simultaneously, recent developments of small error-corrected logical qubit devices promise significant increases in logical state lifetime, but translating those improvements into increases in gate fidelity is a complex challenge. In this Letter, we construct protocols for gates on and between small logical qubit devices which inherit the parent device's tolerance to single qubit errors which occur at any time before or during the gate. We consider two such devices, a passive implementation of the three-qubit bit flip code, and the author's own [E. Kapit, Phys. Rev. Lett. 116, 150501 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.150501] very small logical qubit (VSLQ) design, and propose error-tolerant gate sets for both. The effective logical gate error rate in these models displays superlinear error reduction with linear increases in single qubit lifetime, proving that passive error correction is capable of increasing gate fidelity. Using a standard phenomenological noise model for superconducting qubits, we demonstrate a realistic, universal one- and two-qubit gate set for the VSLQ, with error rates an order of magnitude lower than those for same-duration operations on single qubits or pairs of qubits. These developments further suggest that incorporating small logical qubits into a measurement based code could substantially improve code performance.