The presence of decoherence in quantum computers necessitates the suppression of noise. Dynamically corrected gates via specially designed control pulses offer a path forward, but hardware-specific experimental constraints can cause complications. Existing methods to obtain smooth pulses are either restricted to two-level systems, require an optimization over noise realizations or limited to piecewise-continuous pulse sequences. In this work, we present the first general method for obtaining truly smooth pulses that minimizes sensitivity to noise, eliminating the need for sampling over noise realizations and making assumptions regarding the underlying statistics of the experimental noise. We parametrize the Hamiltonian using a neural network, which allows the use of a large number of optimization parameters to adequately explore the functional control space. We demonstrate the capability of our approach by finding smooth shapes which suppress the effects of noise within the logical subspace as well as leakage out of that subspace.
The three-electron configuration of gate-defined double quantum dots encodes a promising qubit for quantum information processing. I propose a two-qubit entangling gate using a pulse-gated manipulation procedure. The requirements for high-fidelity entangling operations are equivalent to the requirements for the pulse-gated single-qubit manipulations that have been successfully realized for Si QDs. This two-qubit gate completes the universal set of all-pulse-gated operations for the three-electron double-dot qubit and paves the way for a scalable setup to achieve quantum computation.
It is shown that a family of analytically solvable pulses can be used to obtain high fidelity quantum phase gates with surprising robustness against imperfections in the system or pulse parameters. Phase gates are important because they can implement the necessary operations for universal quantum computing. They are particularly suited for systems such as self-assembled quantum dots, trapped ions, and defects in solids, as these are typically manipulated by the transient excitation of a state outside the qubit subspace.
We employ pulse shaping to abate single-qubit gate errors arising from the weak anharmonicity of transmon superconducting qubits. By applying shaped pulses to both quadratures of rotation, a phase error induced by the presence of higher levels is corrected. Using a derivative of the control on the quadrature channel, we are able to remove the effect of the anharmonic levels for multiple qubits coupled to a microwave resonator. Randomized benchmarking is used to quantify the average error per gate, achieving a minimum of 0.007+/-0.005 using 4 ns-wide pulse.
Dynamically correcting for unwanted interactions between a quantum system and its environment is vital to achieving the high-fidelity quantum control necessary for a broad range of quantum information technologies. In recent work, we uncovered the complete solution space of all possible driving fields that suppress transverse quasistatic noise errors while performing single-qubit operations. This solution space lives within a simple geometrical framework that makes it possible to obtain globally optimal pulses subject to a set of experimental constraints by solving certain geometrical optimiza…
We show how to eliminate the first-order effects of the spin-orbit interaction in the performance of a two-qubit quantum gate. Our procedure involves tailoring the time dependence of the coupling between neighboring spins. We derive an effective Hamiltonian which permits a systematic analysis of this tailoring. Time-symmetric pulsing of the coupling automatically eliminates several undesirable terms in this Hamiltonian. Well chosen pulse shapes can produce an effectively isotropic exchange gate, which can be used in universal quantum computation with appropriate coding.
A quantum dot hybrid qubit formed from three electrons in a double quantum dot has the potential for great speed, due to presence of level crossings where the qubit becomes charge-like. Here, we show how to take full advantage of the level crossings in a pulsed gating scheme, which decomposes the spin qubit into a series of charge transitions. We develop one and two-qubit dc quantum gates that are simpler than the previously proposed ac gates. We obtain closed form solutions for the control sequences and show that these sub-nanosecond gates can achieve high fidelities.
We study numerically the dynamics of two-qubit gates with superconducting charge qubits. The exact ratio of $E_J$ to $E_L$ and the corresponding operation time are calculated in order to implement two-qubit gates. We investigate the effect of finite rise/fall times of pulses in realization of two-qubit gates. It is found that the error in implementing two-qubit gates grows quadratically in rise/fall times of pulses.
We theoretically analyze the errors in one- and two-qubit gates in SiMOS and Si/SiGe spin qubit experiments, and present a pulse sequence which can suppress the errors in exchange coupling due to charge noise using ideal local rotations. In practice, the overall fidelity of the pulse sequence will be limited only by the quality of the single-qubit gates available: the C-phase infidelity comes out to be $\approx 2.5 \times$ the infidelity of the single-qubit operations. Based on experimental data, we model the errors and show that C-phase gate infidelities can be suppressed by two orders in mag…
We present a comprehensive theoretical treatment of SUPCODE, a method for generating dynamically corrected quantum gate operations, which are immune to random noise in the environment, by using carefully designed sequences of soft pulses. SUPCODE enables dynamical error suppression even when the control field is constrained to be positive and uniaxial, making it particularly suited to counteracting the effects of noise in systems subject to these constraints such as singlet-triplet qubits. We describe and explain in detail how to generate SUPCODE pulse sequences for arbitrary single-qubit gate…
Evolution-Level Quantum Optimal Control of Single-Qubit Gates with Physics-Informed Neural Networks
School of Physics and Information Technology, Shaanxi Normal University（陕西师范大学物理与信息工程学院）；School of Science, Xi’an University of Posts and Telecommunications（西安邮电大学理学院）
We design efficient controlled-rotation gates with arbitrary angle acting on three-spin encoded qubits for exchange-only quantum computation. Two pulse sequence constructions are given. The first is motivated by an analytic derivation of the efficient Fong-Wandzura sequence for an exact CNOT gate. This derivation, briefly reviewed here, is based on elevating short sequences of SWAP pulses to an entangling two-qubit gate. To go beyond CNOT, we apply a similar elevation to a modified short sequence consisting of SWAPs and one pulse of arbitrary duration. This results in two-qubit sequences that …
We show that all geometric quantum gates (GQG's in short), which are quantum gates only with geometric phases, are robust against control field strength errors. As examples of this observation, we show (1) how robust composite rf-pulses in NMR are geometrically constructed and (2) a composite rf-pulse based on Trotter-Suzuki Formulas is a GQG.
We present a fast phase gate scheme that is experimentally achievable and has an operation time more than two orders of magnitude faster than current experimental schemes for low numbers of pulses. The gate time improves with the number of pulses following an inverse power law. Unlike implemented schemes which excite precise motional sidebands, thus limiting the gate timescale, our scheme excites multiple motional states using discrete ultra-fast pulses. We use beam-splitters to divide pulses into smaller components to overcome limitations due to the finite laser pulse repetition rate. This pr…
The resonator-induced phase gate is a multi-qubit controlled-phase gate for fixed-frequency superconducting qubits. Through off-resonant driving of a bus resonator, statically coupled qubits acquire a state-dependent phase. However, photon loss leads to dephasing during the gate, and any residual entanglement between the resonator and qubits after the gate leads to decoherence. Here we consider how to shape the drive pulse to minimize these unwanted effects. First, we review how the gate's entangling and dephasing rates depend on the system parameters and validate closed-form solutions against…
Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work, we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters and initially assuming a noise-free environment, we present simple control pulses that generate CNOT, CPHASE, and CZ gates with average fidelities greater than 99.99\% and gate times as short as 45 ns. Moreover, using the local invariants of the system's evolution operator, we sho…
The three-qubit conditional swap gate(Fredkin gate) is a universal gate that can be used to create any logic circuit and has many direct usages. In this paper, we experimentally realized Fredkin gate with only three transition pulses in solution of alanine. It appears that no experimental realization of Fredkin gate with fewer pulses has yet been reported up to now. In addition, the simple structure of our scheme makes it easy to be implemented in experiments.
We study the performance of SUPCODE---a family of dynamically correcting pulses designed to cancel simultaneously both Overhauser and charge noise for singlet-triplet spin qubits---adapted to silicon devices with electrostatic control. We consider both natural Si and isotope-enriched Si systems, and in each case we investigate the behavior of individual gates under static noise and perform randomized benchmarking to obtain the average gate error under realistic 1/f noise. We find that in most cases SUPCODE pulses offer roughly an order of magnitude reduction in gate error, and especially in th…
We present composite pulse sequences that perform fault-tolerant two-qubit gate operations on exchange-only quantum dot spin qubits in various experimentally relevant geometries. We show how to perform dynamically corrected two-qubit gates in exchange-only systems with the leading hyperfine error term cancelled. These pulse sequences are constructed to conform to the realistic experimental constraint of strictly non-negative couplings. We establish that our proposed pulse sequences lead to several orders of magnitude improvement in the gate fidelity compared with their uncorrected counterparts…
We analyze analytically and numerically quantum logic gates in a one-dimensional spin chain with Heisenberg interaction. Analytic solutions for basic one-qubit gates and swap gate are obtained for a quantum computer based on logical qubits. We calculated the errors caused by imperfect pulses which implement the quantum logic gates. It is numerically demonstrated that the probability error is proportional to $ε^4$, while the phase error is proportional to $ε$, where $ε$ is the characteristic deviation from the perfect pulse duration.
We propose various composite $π$-pulse sequences for implementing robust z-axis rotation gates widely used in quantum information processing (QIP) scenarios, and discuss their error tolerance of the pulse strength error (PSE) and off-resonance error (ORE), i.e., two typical systematic errors in NMR systems. Compared to existing composite gates, our designed composite pulses exhibit higher gate fidelity and shorter sequence time cost. Furthermore, such short pulse sequences are generalized by simple analytic formulas which can suppress these errors to any desired order simultaneously with linea…
Quantum computation requires high-fidelity single-qubit and two-qubit gates on a scalable platform. Silicon spin qubits are a promising platform toward realization of this goal. In this paper we show how to perform single-qubit and CZ gates in a linear chain of three spin qubits with always-on exchange coupling, which is relevant for certain dot- and donor-based silicon devices. We also show how to make the CZ gate robust against both charge noise and pulse length error using a two-tone pulse shaping method. The robust pulse maintains a fidelity of 99.99% at 3.5% fluctuations in exchange or pu…
We present a new method for determining pulse imperfections and improving the single-gate fidelity in a superconducting qubit. By applying consecutive positive and negative $π$ pulses, we amplify the qubit evolution due to microwave pulse distortion, which causes the qubit state to rotate around an axis perpendicular to the intended rotation axis. Measuring these rotations as a function of pulse period allows us to reconstruct the shape of the microwave pulse arriving at the sample. Using the extracted response to predistort the input signal, we are able to improve the pulse shapes and to reac…
We show that some composite pulses widely employed in NMR experiments are regarded as non-adiabatic geometric quantum gates with Aharanov-Anandan phases. Thus, we reveal the presence of a fundamental issue on quantum mechanics behind the traditional technique of the composite pulses. To examine the robustness of such composite pulses against fluctuations, we present a practical noise model in a two-level system. Then, we find that the composite pulses possesses purely geometrical nature even under a specific type of fluctuations.
The experimental optimization of a two-qubit controlled-Z (CZ) gate is realized following two different data-driven gradient ascent pulse engineering (GRAPE) protocols in the aim of optimizing the gate operator and the output quantum state, respectively. For both GRAPE protocols, the key computation of gradients utilizes mixed information of the input Z-control pulse and the experimental measurement. With an imperfect initial pulse in a flattop waveform, our experimental implementation shows that the CZ gate is quickly improved and the gate fidelities subject to the two optimized pulses are ar…
We propose a method to design pulses in a resonant three-level system to enhance the robustness of non-adiabatic geometric gate operations. By optimizing the shape of the pulse envelope, we show that the gate operations are more robust against frequency detuning than they are with Gaussian and square pulses. Our method provides a way to design pulses that can be employed in a system where robustness against frequency variations or inhomogeneous broadening is required,and may be extended to ensure robustness against other physical imperfections such as intensity fluctuations and random noises.
We present a general procedure to implement a NOT gate by composite pulses robust against both offset uncertainties and control field variations. We define different degrees of robustness in this two-parameter space, namely along one, two or all directions. We show that the phases of the composite pulse satisfy a nonlinear system, and can be computed analytically or numerically.
We theoretically consider a cross-resonance (CR) gate implemented by pulse sequences proposed by Calderon-Vargas & Kestner, Phys. Rev. Lett. 118, 150502 (2017). These sequences mitigate systematic error to first order, but their effectiveness is limited by one-qubit gate imperfections. Using additional microwave control pulses, it is possible to tune the effective CR Hamiltonian into a regime where these sequences operate optimally. This improves the overall feasibility of these sequences by reducing the one-qubit operations required for error correction. We illustrate this by simulating rando…
We propose a new protocol to implement ultra-fast two-qubit phase gates with trapped ions using spin-dependent kicks induced by resonant transitions. By only optimizing the allocation of the arrival times in a pulse train sequence the gate is implemented in times faster than the trapping oscillation period $T<2π/ω$. Such gates allow us to increase the number of gate operations that can be completed within the coherence time of the ion-qubits favoring the development of scalable quantum computers.
We present a method to perform fault-tolerant single-qubit gate operations using Landau-Zener tunneling. In a single Landau-Zener pulse, the qubit transition frequency is varied in time so that it passes through the frequency of the radiation field. We show that a simple three-pulse sequence allows eliminating errors in the gate up to the third order in errors in the qubit energies or the radiation frequency.
We show how to create quantum gates of arbitrary speed between trapped ions, using a laser walking wave, with complete insensitivity to drift of the optical phase, and requiring cooling only to the Lamb-Dicke regime. We present pulse sequences that satisfy the requirements and are easy to produce in the laboratory.
An approach is proposed to implement the universal quantum gates between the ions confined individually in the separated traps. Instead of the typical adiabatic operations, performed for manipulating the ion-ion coupling, here the switchable couplings between ions are implemented non-adiabatically by using the fast laser pulses. Consequently, the desirable quantum gates between the ions could be implemented by using only a series of laser pulses. The proposal may be conveniently generalized to the quantum computation with the scalable ion-traps.
Experimental realization of quantum information processing in the field of nuclear magnetic resonance (NMR) has been well established. Implementation of conditional phase shift gate has been a significant step, which has lead to realization of important algorithms such as Grover's search algorithm and quantum Fourier transform. This gate has so far been implemented in NMR by using coupling evolution method. We demonstrate here the implementation of the conditional phase shift gate using transition selective pulses. As an application of the gate, we demonstrate Grover's search algorithm and qua…
We present a method to construct high-fidelity quantum phase gates, which are insensitive to errors in various experimental parameters. The phase gates consist of a pair of two sequential broadband composite pulses, with a phase difference $π+α/2$ between them, where $α$ is the desired gate phase. By using composite pulses which compensate systematic errors in the pulse area, the frequency detuning, or both the area and the detuning, we thereby construct composite phase gates which compensate errors in the same parameters. Particularly interesting are phase gates which use the recently discove…
Broadband implementations of time-optimal geodesic pulse elements are introduced for the efficient creation of effective trilinear coupling terms for spin systems consisting of three weakly coupled spins 1/2. Based on these pulse elements, the time-optimal implementation of indirect SWAP operations is demonstrated experimentally. The duration of indirect SWAP gates based on broadband geodesic sequence is reduced by 42.3% compared to conventional approaches.
One can implement fast two-qubit entangling gates by exploiting the Rydberg blockade. Although various theoretical schemes have been proposed, experimenters have not yet been able to demonstrate two-atom gates of high fidelity due to experimental constraints. We propose a novel scheme, which only uses a single Rydberg pulse illuminating both atoms, for the construction of neutral-atom controlled-phase gates. In contrast to the existing schemes, our approach is simpler to implement and requires neither individual addressing of atoms nor adiabatic procedures. With parameters estimated based on a…
Fast entangling gates have been proposed for trapped ions that are orders of magnitude faster than current implementations. We present here a detailed analysis of the challenges involved in performing a successful fast gate. We show that the RWA is a stable approximation with respect to pulse numbers: the timescale on which we can neglect terms rotating at the atomic frequency is negligibly affected by the number of pulses in the fast gate. In contrast, we show that the laser pulse instability does give rise to a pulse-number dependent effect; the fast gate infidelity is compounded with the nu…
We propose a pulsed dynamical decoupling protocol as the generator of tunable, fast, and robust quantum phase gates between two microwave-driven trapped ion hyperfine qubits. The protocol consists of sequences of $π$-pulses acting on ions that are oriented along an externally applied magnetic field gradient. In contrast to existing approaches, in our design the two vibrational modes of the ion chain cooperate under the influence of the external microwave driving to achieve significantly increased gate speeds. Our scheme is robust against the dominant noise sources, which are errors on the magn…
A classical logic gate connecting input and output light pulses is demonstrated. The gate operation is based on three steps: First, two incoming light pulses are stored in a Bose-Einstein condensate, second, atomic four-wave mixing generates a new matter wave, and third, the light pulses are retrieved. In the presence of the new matter wave, the retrieval generates a new optical wave. The latter will only be generated if both input light pulses are applied, thus realizing an AND gate. Finally, we show that the gate operation is phase coherent, an essential prerequisite for a quantum logic gate…
We show that the use of shaped pulses improves the fidelity of a Rydberg blockade two-qubit entangling gate by several orders of magnitude compared to previous protocols based on square pulses or optimal control pulses. Using analytical Derivative Removal by Adiabatic Gate (DRAG) pulses that reduce excitation of primary leakage states and an analytical method of finding the optimal Rydberg blockade we generate Bell states with a fidelity of $F>0.9999$ in a 300 K environment for a gate time of only $50\;{\rm ns}$, which is an order of magnitude faster than previous protocols. These results esta…
We propose a selective dynamical decoupling scheme on a chain of permanently coupled qubits with XX type interactions, which is capable of dynamically suppressing any coupling in the chain by applying sequences of local pulses to the individual qubits. We demonstrate that high-fidelity single- and two-qubit gates can be achieved by this procedure and that sequences of gates can be implemented by this pulse control alone. We discuss the applicability and physical limitations of our model specifically for strongly coupled superconducting flux qubits. Since dynamically modifying the couplings bet…
The effective use of current Noisy Intermediate-Scale Quantum (NISQ) devices is often limited by the noise which is caused by interaction with the environment and affects the fidelity of quantum gates. In transmon qubit systems, the quantum gate fidelity can be improved by applying control pulses that can minimize the effects of the environmental noise. In this work, we employ physics-guided quantum optimal control strategies to design optimal pulses driving quantum gates on superconducting qubit systems. We test our results by conducting experiments on the IBM Q hardware using their OpenPulse…
We present the results of a numerical investigation which show the excitation of acoustoelectric modes of vibration in GaAs-based heterostructures due to sharp nano-second electric-field pulses applied across surface gates. In particular, we show that the pulses applied in quantum information processing applications are capable of exciting acoustoelectric modes of vibration including surface acoustic modes which propagate for distances greater than conventional device dimensions. We show that the pulse-induced acoustoelectric vibrations are capable of inducing significant undesired perturbatio…
Reducing the circuit depth of quantum circuits is a crucial bottleneck to enabling quantum technology. This depth is inversely proportional to the number of available quantum gates that have been synthesised. Moreover, quantum gate synthesis and control problems exhibit a vast range of external parameter dependencies, both physical and application-specific. In this article we address the possibility of learning families of optimal control pulses which depend adaptively on various parameters, in order to obtain a global optimal mapping from the space of potential parameter values to the control…
Quantum computing using two-dimensional NMR has recently been described using scalar coupling evolution technique [J. Chem. Phys.,109,10603 (1998)]. In the present paper, we describe two-dimensional NMR quantum computing with the help of selective pulses. A number of logic gates are implemented using two and three qubits with one extra observer spin. Some many-in-one gates (or Portmanteau gates) are implemented. Toffoli gate (or AND/NAND gate) and OR/NOR gates are implemented on three qubits. Deutsch-Jozsa quantum algorithm for one and two qubits, using one extra work qubit, has also been impl…
It has been known since the early days of quantum mechanics that hyperbolic secant pulses possess the unique property that they can perform cyclic evolution on two-level quantum systems independently of the pulse detuning. More recently, it was realized that they induce detuning- controlled phases without changing state populations. Here, we experimentally demonstrate the properties of hyperbolic secant pulses on superconducting transmon qubits and contrast them with the more commonly used Gaussian and square waves. We further show that these properties can be exploited to implement phase gate…
The fidelity of laser-driven quantum logic operations on trapped ion qubits tend to be lower than microwave-driven logic operations due to the difficulty of stabilizing the driving fields at the ion location. Through stabilization of the driving optical fields and use of composite pulse sequences, we demonstrate high fidelity single-qubit gates for the hyperfine qubit of a $^{171}\text{Yb}^+$ ion trapped in a microfabricated surface electrode ion trap. Gate error is characterized using a randomized benchmarking protocol, and an average error per randomized Clifford group gate of $3.6(3)\times1…
