In trapped-atom quantum computers, high-fidelity control of optical qubits is challenging due to the motion of atoms in the trap. If not corrected, the atom motion gets entangled with the qubit degrees of freedom through two fundamental mechanisms, (i) photon recoil and (ii) thermal motion, both leading to a reduction of the gate fidelity. We develop motion-insensitive pulses that suppress both sources of infidelity by modulating the phase of the driving laser field in time. To eliminate photon recoil, we use bang-bang pulses$-$derived using time-optimal control$-$which shorten the gate duration by about 20 times compared to conventional pulses. However, even when photon recoil is eliminated, we find that the gate error does not vanish, but is rather limited by a bound arising from thermal motion-induced entanglement. Remarkably, this bound is independent of the Rabi frequency, meaning that, unlike for photon recoil, operating in the resolved sideband regime does not mitigate this source of infidelity. To overcome this bound, we derive smooth-phase pulses, which allow for a further reduction of the gate error by more than an order of magnitude for typical thermal atoms. Motion-insensitive pulses can be refined to compensate for laser inhomogeneities, enhancing the gate performance in practical situations. Our results are validated through simulations of one-qubit gates operating on the optical clock transition of ${}^{88}$Sr atoms trapped in an optical tweezers array.
Engineering magnetically insensitive qubits in metastable electronic D-states of trapped ions
IonQ, Inc.（IonQ公司）；Joint Quantum Institute and Department of Physics, University of Maryland（马里兰大学联合量子研究所与物理系）；Infleqtion, Inc.（Infleqtion公司）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Keysight Technologies（是德科技）；Duke Quantum Center, Department of Electrical and Computer Engineering and Department of Physics, Duke University（杜克大学电气与计算机工程系、物理系及杜克量子中心）
For neutral atom qubits, the residual thermal motion of the cold atoms constitutes a major challenge that limits the accessible two-qubit gate fidelity. Recently, an interesting type of two-qubit controlled-PHASE quantum gate protocol has been introduced for neutral atom qubit platform, which relies upon off-resonant modulated driving and Rydberg blockade effect. Building upon this progress, we have further developed an upgrade in the form of dual-pulse off-resonant modulated driving. Besides the inherent advantages of avoiding shelving population in Rydberg levels, not necessarily requiring i…
The establishment of a scalable scheme for quantum computing with addressable and long-lived qubits would be a scientific watershed, harnessing the laws of quantum physics to solve classically intractable problems. The design of many proposed quantum computational platforms is driven by competing needs: isolating the quantum system from the environment to prevent decoherence, and easily and accurately controlling the system with external fields. For example, neutral-atom optical-lattice architectures provide environmental isolation through the use of states that are robust against fluctuating …
We introduce an always-on, exchange-only qubit made up of three localized semiconductor spins that offers a true "sweet spot" to fluctuations of the quantum dot energy levels. Both single- and two-qubit gate operations can be performed using only exchange pulses while maintaining this sweet spot. We show how to interconvert this qubit to other three-spin encoded qubits as a new resource for quantum computation and communication.
Superconducting qubits with in-situ tunable properties are important for constructing a quantum computer. Qubit tunability, however, often comes at the expense of increased noise sensitivity. Here, we propose a flux-tunable superconducting qubit that minimizes the dephasing due to magnetic flux noise by engineering controllable flux "sweet spots" at frequencies of interest. This is realized by using a SQUID with asymmetric Josephson junctions shunted by a superinductor formed from an array of junctions. Taking into account correlated global and local noises, it is possible to improve dephasing…
A central task towards building a practical quantum computer is to protect individual qubits from decoherence while retaining the ability to perform high-fidelity entangling gates involving arbitrary two qubits. Here we propose and demonstrate a dephasing-insensitive procedure for storing and processing quantum information in an all-to-all connected superconducting circuit involving multiple frequency-tunable qubits, each of which can be controllably coupled to any other through a central bus resonator. Although it is generally believed that the extra frequency tunability enhances the control …
We propose and study ways speeding up of the entangling operations in the trapped ions system with high fidelity. First, we find a scheme to increase the speed of a two-qubit gate without the limitation of trap frequency, which was considered as the fundamental limit. Second, we study the fast gate scheme for entangling more than two qubits simultaneously. We apply the method of applying multiple frequency components on laser beams for the gate operations. In particular, in order to avoid infinite terms from the coupling to carrier transition, we focus on the phase-insensitive gate scheme here…
Short dephasing times pose one of the main challenges in realizing a quantum computer. Different approaches have been devised to cure this problem for superconducting qubits, a prime example being the operation of such devices at optimal working points, so-called "sweet spots." This latter approach led to significant improvement of $T_2$ times in Cooper pair box qubits [D. Vion et al., Science 296, 886 (2002)]. Here, we introduce a new type of superconducting qubit called the "transmon." Unlike the charge qubit, the transmon is designed to operate in a regime of significantly increased ratio o…
Quantum manipulation based on geometric phases provides a promising way towards robust quantum gates. However, in the current implementation of nonadiabatic geometric phases, operational and/or random errors tend to destruct the conditions that induce geometric phases, thereby smearing their noise-resilient feature. In a recent experiment [Y. Xu et al., Phys. Rev. Lett. 124, 230503 (2020)], high-fidelity universal geometric quantum gates have been implemented in a superconducting circuit, which are robust to different types of errors under different configurations of the geometric evolution pa…
We propose an optical scheme for generating entanglement between co-trapped identical or dissimilar alkaline earth atomic ions ($^{40}\text{Ca}^+$, $^{88}\text{Sr}^+$, $^{138}\text{Ba}^+$, $^{226}\text{Ra}^+$) which exhibits fundamental error rates below $10^{-4}$ and can be implemented with a broad range of laser wavelengths spanning from ultraviolet to infrared. We also discuss straightforward extensions of this technique to include the two lightest Group-2 ions ($\text{Be}^+$, $\text{Mg}^+$) for multispecies entanglement. The key elements of this wavelength-insensitive geometric phase gate …
The ubiquitous presence of $1/f$ flux noise was a significant barrier to long-coherence in superconducting qubits until the development of qubits that could operate in static, flux noise insensitive configurations commonly referred to as `sweet-spots'. Several proposals for entangling gates in superconducting qubits tune the flux bias away from these spots, thus reintroducing the dephasing problem to varying degrees. Here we revisit one such proposal, where interactions are parametrically activated by rapidly modulating the flux bias of the qubits around these sweet-spots, and study the effect…
State preparation, qubit rotation, and high fidelity readout are demonstrated for two separate \baseven qubit types. First, an optical qubit on the narrow 6S$_{1/2}$ to 5D$_{5/2}$ transition at 1.76 $μ$m is implemented. Then, leveraging the techniques developed there for readout, a ground state hyperfine qubit using the magnetically insensitive transition at 8 GHz is accomplished.
We describe a simple protocol for the single-step generation of $N$-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full $N$-body interactions. Similar to the Mølmer-Sørensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this $N$-body gate operation allows the single-step implementation of a family of $N$-bit gate operations …
The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad frequency tunability, strong anharmonicity, high reproducibility, and relaxation times in excess of $40\,μ$s at its flux-insensitive point. Qubit relaxation times $T_1$ across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise, and 1/f flux noise, a noise source previously considered primarily in…
In quantum information science, the external control of qubits must be balanced with the extreme isolation of the qubits from the environment. Atomic qubit systems typically mitigate this balance through the use of gated laser fields that can create superpositions and entanglement between qubits. Here we propose the use of high-order optical Stark shifts from optical fields to manipulate the splitting of atomic qubits that are insensitive to other types of fields. We demonstrate a fourth-order AC Stark shift in a trapped atomic ion system that does not require extra laser power beyond that nee…
We use the quasienergy structure that emerges when a fluxonium superconducting circuit is driven periodically to encode quantum information with dynamically induced flux-insensitive sweet spots. The framework of Floquet theory provides an intuitive description of these high-coherence working points located away from the half-flux symmetry point of the undriven qubit. This approach offers flexibility in choosing the flux bias point and the energy of the logical qubit states as shown in [\textit{Huang et al., 2020}]. We characterize the response of the system to noise in the modulation amplitude…
We propose a new concept for a two-qubit gate operating on a pair of trapped ions based on laser coherent control techniques. The gate is insensitive to the temperature of the ions, works also outside the Lamb-Dicke regime, requires no individual addressing by lasers, and can be orders of magnitude faster than the trap period.
We propose doubly-ionized lanthanum (La$^{2+}$) as a possible qubit candidate for quantum networks. Transitions between the lowest levels in the atom are in the infrared, enabling a direct matter-light interface amenable to long-distance quantum communication. These transitions could also be used to directly laser-cool trapped La$^{2+}$ ions. The rich hyperfine structure of the ion may allow for a qubit stored in magnetic-field insensitive states, as well as protocols for atom-photon entanglement.
A scheme for coupling superconducting charge qubits via a one-dimensional superconducting transmission line resonator is proposed. The qubits are working at their optimal points, where they are immune to the charge noise and possess long decoherence time. Analysis on the dynamical time evolution of the interaction is presented, which is shown to be insensitive to the initial state of the resonator field. This scheme enables fast gate operation and is readily scalable to multiqubit scenario.
In this work, we derive analytic formulae that determine the effect of error mechanisms on one- and two-qubit gates in trapped ions and electrons. First, we analyze, and derive expressions for, the effect of driving field inhomogeneities on one-qubit gate fidelities. Second, we derive expressions for two-qubit gate errors, including static motional frequency shifts, trap anharmonicities, field inhomogeneities, heating, and motional dephasing. We show that, for small errors, each of our expressions for infidelity converges to its respective numerical simulation; this shows our formulae are suff…
We propose how to realize a three-step controlled-phase gate of one superconducting qubit simultaneously controlling n qubits selected from N qubits in a cavity (1<n<N). The operation time of this gate is independent of the number n of qubits involved in the gate operation. This phase gate controlling at once n qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on n qubits.
Pulsed lasers offer significant advantages over CW lasers in the coherent control of qubits. Here we review the theoretical and experimental aspects of controlling the internal and external states of individual trapped atoms with pulse trains. Two distinct regimes of laser intensity are identified. When the pulses are sufficiently weak that the Rabi frequency $Ω$ is much smaller than the trap frequency $\otrap$, sideband transitions can be addressed and atom-atom entanglement can be accomplished in much the same way as with CW lasers. By contrast, if the pulses are very strong ($Ω\gg \otrap$),…
Universal set of quantum gates are realized from the conduction-band electron spin qubits of quantum dots embedded in a microcavity via two-channel Raman interaction. All of the gate operations are independent of the cavity mode states, \emph{i.e.}, insensitive to the thermal cavity field. Individual addressing and effective switch of the cavity mediated interaction are directly possible here. Meanwhile, gate operations also can be carried out in parallel. The simple realization of needed interaction for selective qubits makes current scenario more suitable for scalable quantum computation.
The dominant error sources for state-of-the-art laser-free trapped-ion entangling gates are decoherence of the qubit state and the ion motion. The effect of these decoherence mechanisms can be suppressed with additional control fields, or with techniques that have the disadvantage of reducing gate speed. Here, we propose using a near-motional-frequency magnetic field gradient to implement a laser-free gate that is simultaneously resilient to both types of decoherence, does not require additional control fields, and has a relatively small cost in gate speed.
Crosstalk Insensitive Trapped-Ion Entanglement through Coupling Matrix Engineering
Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算联合中心）；Department of Physics, University of Maryland（马里兰大学物理系）；Department of Electrical and Computer Engineering, University of Washington（华盛顿大学电气与计算机工程系）
Precision metrology and quantum measurement often demand matter be prepared in well defined quantum states for both internal and external degrees of freedom. Laser-cooled neutral atoms localized in a deeply confining optical potential satisfy this requirement. With an appropriate choice of wavelength and polarization for the optical trap, two electronic states of an atom can experience the same trapping potential, permitting coherent control of electronic transitions independent of the atomic center-of-mass motion. We review a number of recent experiments that use this approach to investigate …
Internal states of polar molecules can be controlled by microwave-frequency electric dipole transitions. If the applied microwave electric field has a spatial gradient, these transitions also affect the motion of these dipolar particles. This capability can be used to engineer phonon-mediated quantum gates between e.g. trapped polar molecular ion qubits without laser illumination and without the need for cooling near the motional ground state. The result is a high-speed quantum processing toolbox for dipoles in thermal motion that combines the precision microwave control of solid-state qubits …
Hybrid qubit-oscillator module from motional states of two interacting atoms
JILA, NIST and Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系、NIST和JILA）；Center for Theory of Quantum Matter, University of Colorado, Boulder（科罗拉多大学博尔德分校量子物质理论中心）；Institut Quantique and Département de Physique, Université de Sherbrooke（舍布鲁克大学量子研究所和物理系）；Joint Center for Quantum Information and Computer Science, University of Maryland and NIST, College Park（马里兰大学和NIST联合量子信息与计算机科学中心）；Joint Quantum Institute, University of Maryland and NIST, College Park（马里兰大学和NIST联合量子研究所）
We report high-fidelity laser-beam-induced quantum logic gates on magnetic-field-insensitive qubits comprised of hyperfine states in $^{9}$Be$^+$ ions with a memory coherence time of more than 1 s. We demonstrate single-qubit gates with error per gate of $3.8(1)\times 10^{-5}$. By creating a Bell state with a deterministic two-qubit gate, we deduce a gate error of $8(4)\times10^{-4}$. We characterize the errors in our implementation and discuss methods to further reduce imperfections towards values that are compatible with fault-tolerant processing at realistic overhead.
To date, the highest fidelity quantum logic gates between two qubits have been achieved with variations on the geometric-phase gate in trapped ions, with the two leading variants being the Molmer-Sorensen gate and the light-shift (LS) gate. Both of these approaches have their respective advantages and challenges. For example, the latter is technically simpler and is natively insensitive to optical phases, but it has not been made to work directly on a clock-state qubit. We present a new technique for implementing the LS gate that combines the best features of these two approaches: By using a s…
Fast robust two-qubit gate operation with low susceptibility to crosstalk are the key to scalable quantum information processing. Parametrically driven gate is inherently insensitive to crosstalk while superadiabatic control can speed up the gate without losing accuracy. We propose and experimentally implement superadiabatic two-qubit gates using parametric modulation on superconducting quantum circuits. Our results demonstrate the preservation of adiabaticity at a gate speed close to the quantum limit, in addition to robustness against control instability. We demonstrate a CZ gate with error …
We study quantum coherence in a semiconductor charge qubit formed from a GaAs double quantum dot containing a single electron. Voltage pulses are applied to depletion gates to drive qubit rotations and non-invasive state readout is achieved using a quantum point contact charge detector. We measure a maximum coherence time of ~7 ns at the charge degeneracy point, where the qubit level splitting is first-order-insensitive to gate voltage fluctuations. We compare measurements of the coherence time as a function of detuning with predictions from a 1/f noise model.
The CNOT gate is a two-qubit gate which is essential for universal quantum computation. A well-established approach to implement it within Majorana-based qubits relies on subsequent measurement of (joint) Majorana parities. We propose an alternative scheme which operates a protected CNOT gate via the holonomic control of a handful of system parameters, without requiring any measurement. We show how the adiabatic tuning of pair-wise couplings between Majoranas can robustly lead to the full entanglement of two qubits, insensitive with respect to small variations in the control of the parameters.
Electrical resonators are widely used in quantum information processing, by engineering an electromagnetic interaction with qubits based on real or virtual exchange of microwave photons. This interaction relies on strong coupling between the qubits' transition dipole moments and the vacuum fluctuations of the resonator in the same manner as cavity QED, and has consequently come to be called "circuit QED" (cQED). Great strides in the control of quantum information have already been made experimentally using this idea. However, the central role played by photon exchange induced by quantum fluctu…
The identification of spacial noise correlation is of critical importance in developing error-corrected quantum devices, but it has barely been studied so far. In this work, we utilize an effective new method called qubit motion, to efficiently determine the noise correlations between any pair of qubits in a 7-qubit superconducting quantum system. The noise correlations between the same pairs of qubits are also investigated when the qubits are at distinct operating frequencies. What's more, in this multi-qubit system with the presence of noise correlations, we demonstrate the enhancing effect …
I show a scheme which allows a perfect transfer of an unknown single-qubit atomic state from one atom to another by letting two atoms interact simultaneously with a cavity QED. During the interaction between atom and cavity, the cavity is only virtually excited and accordingly the scheme is insensitive to the cavity field states and cavity decay. Based on this scheme, a network for transfer of an arbitrary single-qubit atomic state between atoms is engineered. Then the scheme is generalized to perfectly transfer an arbitrary 2-qubit atomic state and accordingly a network for transfer of an arb…
It is well established that the collective motion of ion crystals can be used as a quantum bus for multi-qubit entanglement. However, as the number of ions increases, it becomes difficult to directly entangle ions far apart and resolve all motional modes of the ion crystal. We introduce a scalable and flexible scheme for efficient entanglement between any pair of ions within a large ion chain, using an evenly distributed 50-ion crystal as an example. By performing amplitude and frequency modulation, we find high-fidelity pulse sequences that primarily drive a transverse motional mode with a wa…
We present a method to generate qubits of the vibrational motion of an ion. The method is developed in the non-rotating wave approximation regime, therefore we consider regimes where the dynamics has not been studied. Because the solutions are valid for a more extended range of parameters we call them generalized qubits.
We propose how to realize a three-step controlled-phase gate of one qubit simultaneously controlling $n$ qubits in a cavity or coupled to a resonator. The $n$ two-qubit controlled-phase gates, forming this multiqubit phase gate, can be performed simultaneously. The operation time of this phase gate is independent of the number $n$ of qubits. This phase gate controlling at once $n$ qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on $n$ qubits. We present two alternative approaches to implement this gate. One a…
We explore the implementation of pseudo-random single-qubit rotations and multi-qubit pseudo-random circuits constructed only from Clifford gates and the T-gate, a phase rotation of pi/4. Such a gate set would be appropriate for computations performed in a fault tolerant setting. For single-qubit rotations the distribution of parameters found for unitaries constructed from Clifford plus T quickly approaches that of random rotations and require significantly fewer gates than the construction of arbitrary single-qubit rotations. For Clifford plus T pseudo-random circuits we find an exponential c…
We explore the interplay between acceleration radiation and the dynamical Casimir effect (DCE) in the field of superconducting quantum technologies, analyzing the generation of entanglement between two qubits by means of the DCE in several states of qubit motion. We show that the correlated absorption and emission of photons is crucial for entanglement, which in some cases can be linked to the notion of simultaneity in special relativity.
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) exchange interaction with uniform and non-uniform coupling constants. We show that for an odd number of sites a spin cluster qubit can be defined in terms of the ground state doublet. This qubit is remarkably insensitive to the placement and coupling anisotropy of spins within the cluster. One- and two-qubit quantum gates can be generated by magnetic fields and inter-cluster exchange, and leakage during quantum gate operation is small. Spin cluster qubits inherit the long decohe…
We demonstrate the experimental realization of a two-qubit Mølmer-Sørensen gate on a magnetic field-insensitive hyperfine transition in $^9$Be$^+$ ions using microwave-near fields emitted by a single microwave conductor embedded in a surface-electrode ion trap. The design of the conductor was optimized to produce a high oscillating magnetic field gradient at the ion position. The measured gate fidelity is determined to be $98.2\pm1.2\,\%$ and is limited by technical imperfections, as is confirmed by a comprehensive numerical error analysis. The conductor design can potentially simplify the imp…
We demonstrate a coherence time of 2.1(1)~s for electron spin superposition states of a single trapped $^{40}$Ca$^+$ ion. The coherence time, measured with a spin-echo experiment, corresponds to residual rms magnetic field fluctuations $\leq$~2.7$\times$10$^{-12}$~T. The suppression of decoherence induced by fluctuating magnetic fields is achieved by combining a two-layer $μ$-metal shield, which reduces external magnetic noise by 20 to 30~dB for frequencies of 50~Hz to 100~kHz, with Sm$_2$Co$_{17}$ permanent magnets for generating a quantizing magnetic field of 0.37~mT. Our results extend the …
We theoretically study a quantum destructive interference (QDI) induced photon blockade in a two-qubit driven cavity QED system with dipole-dipole interaction (DDI). In the absence of dipole-dipole interaction, we show that a QDI-induced photon blockade can be achieved only when the qubit resonance frequency is different from the cavity mode frequency. When DDI is introduced the condition for this photon blockade is strongly dependent upon the pump field frequency, and yet is insensitive to the qubit-cavity coupling strength. Using this tunability feature we show that the conventional energy-l…
Composite pulses are an efficient tool for robust quantum control. In this work, we derive the form of the composite pulse sequence to implement robust single-qubit gates in a three-level system, where two low-energy levels act as a qubit. The composite pulses can efficiently cancel the systematic errors up to a certain order. We find that the three-pulse sequence cannot completely eliminate the first order of systematic errors, but still availably makes the fidelity resistant to variations in a specific direction. When employing more pulses in the sequence ($N>3$), the fidelity can be insensi…
The search of a sweet spot, locus in qubit parameters where quantum control is first-order insensitive to noises, is key to achieve high-fidelity quantum gates. Efforts to search for such a sweet spot in conventional double-quantum-dot singlet-triplet qubits where each dot hosts one electron ("two-electron singlet-triplet qubit"), especially for two-qubit operations, have been unsuccessful. Here we consider singlet-triplet qubits allowing each dot to host more than one electron, with a total of four electrons in the double quantum dots ("four-electron singlet-triplet qubit"). We theoretically …
Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coh…
The author analyzes quantum computation with the hybrid qubit (HQ) that is encoded using the three-electron configuration of a double quantum dot. All gate operations are controlled with electric signals, while the qubit remains at an optimal operation point that is insensitive to noise. An effective single-qubit description is derived, and two-qubit interactions are suggested using Coulomb and exchange interactions. Universal quantum control is described and numerically simulated using realistic parameters for HQs in Si and GaAs. High-fidelity quantum computing at the threshold of quantum err…
We propose an effective scheme for realizing a Jaynes-Cummings (J-C) model with the collective nitrogen-vacancy center ensembles (NVE) bosonic modes in a hybrid system. Specifically, the controllable transmon qubit can alternatively interact with one of the two NVEs, which results in the production of $N$ particle entangled states. Arbitrary $N$ particle entangled states, NOON states, N-dimensional entangled states and entangled coherent states are demonstrated. Realistic imperfections and decoherence effects are analyzed via numerical simulation. Since no cavity photons or excited levels of t…
Current superconducting quantum processors require strategies for coping with material defects and imperfect parameter targeting in order to scale up while maintaining high performance. To that end, in-situ control of qubit frequencies with magnetic flux can be used to avoid spurious resonances. However, increased dephasing due to 1/f flux noise limits performance at all of these operating points except for noise-protected sweet spots, which are sparse under DC flux bias and monochromatic flux modulation. Here we experimentally demonstrate that two-tone flux modulation can be used to create a …
