Computational Subspace Research Articles

The Floquet Fluxonium Molecule: Driving Down Dephasing in Coupled Superconducting Qubits

High-coherence qubits, which can store and manipulate quantum states for long times with low error rates, are necessary building blocks for quantum computers. Here we propose a driven superconducting erasure qubit, the Floquet fluxonium molecule, which minimizes bit-flip rates through disjoint support of its qubit states and suppresses phase flips by a novel second-order insensitivity to flux-noise dephasing. We estimate the bit-flip, phase-flip, and erasure rates through numerical simulations, with predicted coherence times of approximately 50 ms in the computational subspace and erasure lifetimes of about 500μs. We also present a protocol for performing high-fidelity single-qubit rotation gates via additional flux modulation, on timescales of roughly 500 ns, and propose a scheme for erasure detection and logical readout. Our results demonstrate the utility of drives for building new qubits that can outperform their static counterparts. Published by the American Physical Society 2024

Coupler-Assisted Leakage Reduction for Scalable Quantum Error Correction with Superconducting Qubits.

Superconducting qubits are a promising platform for building fault-tolerant quantum computers, with recent achievement showing the suppression of logical error with increasing code size. However, leakage into noncomputational states, a common issue in practical quantum systems including superconducting circuits, introduces correlated errors that undermine quantum error correction (QEC) scalability. Here, we propose and demonstrate a leakage reduction scheme utilizing tunable couplers, a widely adopted ingredient in large-scale superconducting quantum processors. Leveraging the strong frequency tunability of the couplers and stray interaction between the couplers and readout resonators, we eliminate state leakage on the couplers, thus suppressing space-correlated errors caused by population propagation among the couplers. Assisted by the couplers, we further reduce leakage to higher qubit levels with high efficiency (98.1%) and low error rate on the computational subspace (0.58%), suppressing time-correlated errors during QEC cycles. The performance of our scheme demonstrates its potential as an indispensable building block for scalable QEC with superconducting qubits.

Extended quantum process tomography of logical operations on an encoded bosonic qubit

We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We have enhanced our methodology over previous implementations of csQPT by leveraging Kraus operators and constrained gradient descent to learn the underlying process. We show the results of our method by characterizing a logical quantum gate implemented using displacement and selective number-dependent arbitrary phase operations on an encoded qubit. Our use of csQPT allows for the reconstruction of Kraus operators for the larger Hilbert space rather than being limited to the logical subspace. This approach enables us to more accurately identify and quantify the various error mechanisms that can lead to gate infidelity, including those occurring outside of the computational subspace. We showcase the potential of our approach by demonstrating the ability to quantify leakage outside of the computational subspace, a key factor for developing more robust and reliable quantum gates in high-dimensional systems. Published by the American Physical Society 2024

Hexagonal Boron Nitride Quantum Simulator: Prelude to Spin and Photonic Qubits.

The quest for qubit operation at room temperature is accelerating the field of quantum information science and technology. Solid state quantum defects with spin-optical properties are promising spin- and photonic qubit candidates for room temperature operations. In this regard, a single boron vacancy within hexagonal boron nitride (h-BN) lattice such as VB- defect has coherent quantum interfaces for spin and photonic qubits owing to the large band gap of h-BN (6 eV) that can shield a computational subspace from environmental noise. However, for a VB- defect in h-BN to be a potential quantum simulator, the design and characterization of the Hamiltonian involving mutual interactions of the defect and other degrees of freedom are needed to fully understand the effect of defects on the computational subspace. Here, we studied the key coupling tensors such as zero-field splitting, Zeeman effect, and hyperfine splitting in order to build the Hamiltonian of the VB- defect. These eigenstates are spin triplet states that form a computational subspace. To study the phonon-assisted single photon emission in the VB- defect, the Hamiltonian is characterized by electron-phonon interaction with Jahn-Teller distortions. A theoretical demonstration of how the VB- Hamiltonian is utilized to relate these quantum properties to spin- and photonic-quantum information processing. For selecting promising host 2D materials for spin and photonic qubits, we present a data-mining perspective based on the proposed Hamiltonian engineering of the VB- defect in which h-BN is one of four materials chosen to be room temperature qubit candidates.

Leakage Benchmarking for Universal Gate Sets.

Errors are common issues in quantum computing platforms, among which leakage is one of the most-challenging to address. This is because leakage, i.e., the loss of information stored in the computational subspace to undesired subspaces in a larger Hilbert space, is more difficult to detect and correct than errors that preserve the computational subspace. As a result, leakage presents a significant obstacle to the development of fault-tolerant quantum computation. In this paper, we propose an efficient and accurate benchmarking framework called leakage randomized benchmarking (LRB), for measuring leakage rates on multi-qubit quantum systems. Our approach is more insensitive to state preparation and measurement (SPAM) noise than existing leakage benchmarking protocols, requires fewer assumptions about the gate set itself, and can be used to benchmark multi-qubit leakages, which has not been achieved previously. We also extended the LRB protocol to an interleaved variant called interleaved LRB (iLRB), which can benchmark the average leakage rate of generic n-site quantum gates with reasonable noise assumptions. We demonstrate the iLRB protocol on benchmarking generic two-qubit gates realized using flux tuning and analyzed the behavior of iLRB under corresponding leakage models. Our numerical experiments showed good agreement with the theoretical estimations, indicating the feasibility of both the LRB and iLRB protocols.

Pulse-controlled qubit in semiconductor double quantum dots

We present a numerically-optimized multipulse framework for the quantum control of a single-electron double quantum dot qubit. Our framework defines a set of pulse sequences, necessary for the manipulation of the ideal qubit basis, that avoids errors associated with excitations outside the computational subspace. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation. This basis generates spatially localized logical qubit states, making readout straightforward. We consider experimentally realistic semiconductor qubits with finite pulse rise and fall times and determine the fastest pulse sequence yielding the highest fidelity. We show that our protocol leads to improved control of a qubit. We present simulations of a double quantum dot in a semiconductor device to visualize and verify our protocol. These results can be generalized to other physical systems since they depend only on pulse rise and fall times and the energy gap between the two lowest eigenstates.

Speeding up qubit control with bipolar single-flux-quantum pulse sequences

The development of quantum computers based on superconductors requires the improvement of the qubit state control approach aimed at the increase of the hardware energy efficiency. A promising solution to this problem is the use of superconducting digital circuits operating with single-flux-quantum (SFQ) pulses, moving the qubit control system into the cold chamber. However, the qubit gate time under SFQ control is still longer than under conventional microwave driving. Here we introduce the bipolar SFQ pulse control based on ternary pulse sequences. We also develop a robust optimization algorithm for finding a sequence structure that minimizes the leakage of the transmon qubit state from the computational subspace. We show that the appropriate sequence can be found for arbitrary system parameters from the practical range. The proposed bipolar SFQ control reduces a single qubit gate time by halve compared to nowadays unipolar SFQ technique, while maintaining the gate fidelity over 99.99%.

Direct manipulation of a superconducting spin qubit strongly coupled to a transmon qubit

Spin qubits in semiconductors are currently one of the most promising architectures for quantum computing. However, they face challenges in realizing multi-qubit interactions over extended distances. Superconducting spin qubits provide a promising alternative by encoding a qubit in the spin degree of freedom of an Andreev level. Such an Andreev spin qubit could leverage the advantages of circuit quantum electrodynamic, enabled by an intrinsic spin-supercurrent coupling. The first realization of an Andreev spin qubit encoded the qubit in the excited states of a semiconducting weak-link, leading to frequent decay out of the computational subspace. Additionally, rapid qubit manipulation was hindered by the need for indirect Raman transitions. Here, we exploit a different qubit subspace, using the spin-split doublet ground state of an electrostatically-defined quantum dot Josephson junction with large charging energy. Additionally, we use a magnetic field to enable direct spin manipulation over a frequency range of 10 GHz. Using an all-electric microwave drive we achieve Rabi frequencies exceeding 200 MHz. We furthermore embed the Andreev spin qubit in a superconducting transmon qubit, demonstrating strong coherent qubit-qubit coupling. These results are a crucial step towards a hybrid architecture that combines the beneficial aspects of both superconducting and semiconductor qubits.

Genetic Algorithm for Searching Bipolar Single-Flux-Quantum Pulse Sequences for Qubit Control

Nowadays most of superconducting quantum processors use charge qubits of a transmon type. They require implementation of energy efficient qubit state control scheme. A promising approach is the use of superconducting digital circuits operating with single-flux-quantum (SFQ) pulses. The duration of SFQ pulse control sequence is typically larger than that of conventional microwave drive pulses but its length can be optimized for the system with known parameters. Here we introduce a genetic algorithm for unipolar or bipolar SFQ control sequence search that minimize qubit state leakage from the computational subspace. The algorithm is also able to find a solution in the form of a repeating subsequence in order to save memory on the control chip. Its parallel implementation can find the appropriate sequence for arbitrary system parameters from a practical range in a reasonable time. The algorithm is illustrated by the example of the rotation gate around the Y-axis by an angle $$\pi/2$$ with fidelity over 99.99 $$\%$$ . In this paper, we present the results for a single-qubit system, but in the future we will apply the developed approach to study a system of two qubits.

Effects of leakage on the realization of a discrete time crystal in a chain of singlet-triplet qubits

A chain of singlet-triplet qubits can be an excellent realization of the Ising model, which is in turn a good platform for realizing a discrete time crystal (DTC). However, leakage of the qubits out of their computational subspace may be a problem for such a realization. The authors show that, while leakage is indeed a serious problem for the realization of a DTC, it is not insurmountable - one can mitigate leakage by applying a magnetic field that alternates from one qubit to the next.

Nonadiabatic geometric quantum computation of W-state codes using invariant-based reverse engineering

In this paper, we propose a protocol to realize nonadiabatic geometric quantum computation (NGQC)of W-state codes in a spin system using invariant-based reverse engineering. The Heisenberg XY interaction of spin qubits provides a two-dimensional computational subspace spanned by a pair of W states. By applying a time-dependent magnetic on the spin qubits, we realize the effective Pauli operations for the computational subspace. Assisted by the invariant-based reverse engineering, the waveform of the control field is designed and the evolution paths for the NGQC is found. The performance of the protocol under the influence of experimental imperfections is estimated by the numerical simulations with available parameters. The results demonstrate that the protocol is robust against systematic error, random noise and decoherence. Therefore, the protocol may be promising to implement fast and robust manipulation of W states in spin systems.

Control and mitigation of microwave crosstalk effect with superconducting qubits

Improving gate performance is vital for scalable quantum computing. Universal quantum computing also requires gate fidelity to reach a high level. For a superconducting quantum processor, which operates in the microwave band, the single-qubit gates are usually realized with microwave driving. The crosstalk between microwave pulses is a non-negligible error source. In this article, we propose an error mitigation scheme to address this crosstalk issue for single-qubit gates. There are three steps in our method. First, by controlling the detuning between qubits, the microwave induced classical crosstalk error can be constrained within the computational subspace. Second, by applying the general decomposition procedure, the arbitrary single-qubit gate can be decomposed as a sequence of X and virtual Z gates. Finally, by optimizing the parameters in virtual Z gates, the error constrained in the computational space can be corrected. Using our method, no additional compensation signals are needed, arbitrary single-qubit gate time will not be prolonged, and the circuit depth containing simultaneous single-qubit gates will also not increase. The simulation results show that, in a specific regime of qubit–qubit detuning, the infidelities of simultaneous single-qubit gates can be as low as that without microwave crosstalk.

Universal Fidelity Reduction of Quantum Operations from Weak Dissipation.

Quantum information processing is in real systems often limited by dissipation, stemming from remaining uncontrolled interaction with microscopic degrees of freedom. Given recent experimental progress, we consider weak dissipation, resulting in a small error probability per operation. Here, we find a simple formula for the fidelity reduction of any desired quantum operation, where the ideal evolution is confined to the computational subspace. Interestingly, this reduction is independent of the specific operation; it depends only on the operation time and the dissipation. Using our formula, we investigate the situation where dissipation in different parts of the system has correlations, which is detrimental for the successful application of quantum error correction. Surprisingly, we find that a large class of correlations gives the same fidelity reduction as uncorrelated dissipation of similar strength.

Multiqudit interactions in molecular spins

We study photon-mediated interactions between molecular spin qudits in the dispersive regime of operation. We derive from a microscopic model the effective interaction between molecular spins, including their crystal field anisotropy (i.e., the presence of non-linear spin terms) and their multi-level structure. Finally, we calculate the long time dynamics for a pair of interacting molecular spins using the method of multiple scales analysis. This allows to find the set of 2-qudit gates that can be realized for a specific choice of molecular spins and to determine the time required for their implementation. Our results are relevant for the implementation of logical gates in general systems of qudits with unequally spaced levels or to determine an adequate computational subspace to encode and process the information.

Error-resistant nonadiabatic binomial-code geometric quantum computation using reverse engineering

We propose a scheme to realize error-resistant nonadiabatic binomial-code geometric quantum computation using reverse engineering. A strong Kerr nonlinearity restricts the evolution in a computational subspace of the binomial code and a two-photon squeezing drive provides the connections between the logical states. The effective Hamiltonian possesses SU(2) dynamic structure and is analyzed through reverse engineering based on a dynamic invariant. By combining reverse engineering with the optimal control method, we find the evolution paths for nonadiabatic geometric quantum computation and derive the control field robust against the systematic error. Numerical simulations show that the scheme holds excellent resistance to the systematic error and is still well implemented in the presence of resonator leakage with the current superconducting nonlinear resonator technology. Therefore, the scheme may provide a promising approach for accurate nonadiabatic binomial-code geometric quantum computation.

Two-Qubit Geometric Gates Based on Ground-State Blockade of Rydberg Atoms

We achieve the robust nonadiabatic holonomic two-qubit controlled gate in one step based on the ground-state blockade mechanism between two Rydberg atoms. By using the Rydberg-blockade effect and the Raman transition mechanism, we can produce the blockade effect of double occupation of the corresponding ground state, i.e., ground-state blockade, to encode the computational subspace into the ground state, thus effectively avoiding the spontaneous emission of the excited Rydberg state. On the other hand, the feature of geometric quantum computation independent of the evolutionary details makes the scheme robust to control errors. In this way, the controlled quantum gate constructed by our scheme not only greatly reduces the gate infidelity caused by spontaneous emission but is also robust to control errors.

Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms

Neutral-atom arrays have recently emerged as a promising platform for quantum information processing. One important remaining roadblock for the large-scale application of these systems is the ability to perform error-corrected quantum operations. To entangle the qubits in these systems, atoms are typically excited to Rydberg states, which could decay or give rise to various correlated errors that cannot be addressed directly through traditional methods of fault-tolerant quantum computation. In this work, we provide the first complete characterization of these sources of error in a neutral-atom quantum computer and propose hardware-efficient, fault-tolerant quantum computation schemes that mitigate them. Notably, we develop a novel and distinctly efficient method to address the most important errors associated with the decay of atomic qubits to states outside of the computational subspace. These advances allow us to significantly reduce the resource cost for fault-tolerant quantum computation compared to existing, general-purpose schemes. Our protocols can be implemented in the near term using state-of-the-art neutral-atom platforms with qubits encoded in both alkali and alkaline-earth atoms.9 MoreReceived 6 June 2021Revised 3 February 2022Accepted 12 April 2022DOI:https://doi.org/10.1103/PhysRevX.12.021049Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasOptical pumpingQuantum algorithmsQuantum computationQuantum gatesQuantum information processingQuantum protocolsSpontaneous emissionQuantum InformationAtomic, Molecular & Optical

DOA tracking for seamless connectivity in beamformed IoT-based drones

In recent times, there has been a surge of interest around the usage of adaptive antenna arrays of Internet of Things (IoT) based Drones in the communication systems. Adaptive antenna arrays have the ability to form customized radiation patterns based on the changes in the environment by employing methods for estimating Direction of Arrival (DOA) and adaptive beamforming. Nevertheless, upon deploying adaptive antenna arrays in complex IoT platforms, the radiation patterns that result from the use of such adaptive algorithms may be adjusted to the preceding location of the node and not attuned to the current location. These issues that arise due to mobility can be resolved by continuously tracking the DOA of the intended target. As DOA is time varying in an IoT Drone environment, existing algorithms for estimating the DOA like MUltiple SIgnal Classification (MUSIC) and Estimation of Signal Parameter via Rotational Invariance Techniques (ESPRIT) cannot be used to track the signal subspace recursively, as they are based on batch eigenvalue decomposition which is highly time consuming with a time complexity of O(n3). Furthermore, DOA estimation algorithms do not result in robust subspace estimates when the Signal to Noise Ratio (SNR) is low.The main novelty of the proposed work is a low computational complexity subspace tracking algorithm for tracking DOA in order to provide seamless connectivity. Simulation results show that the proposed DOA tracking takes lesser time for tracking the current location of the drone target as opposed to conventional DOA estimation methods. Furthermore,it is observed that the tracking process remains unaffected by SNR.

Hardware-Efficient Leakage-Reduction Scheme for Quantum Error Correction with Superconducting Transmon Qubits

Leakage outside of the qubit computational subspace poses a threatening challenge to quantum error correction (QEC). We propose a scheme using two leakage-reduction units (LRUs) that mitigate these issues for a transmon-based surface code, without requiring an overhead in terms of hardware or QEC-cycle time as in previous proposals. For data qubits we consider a microwave drive to transfer leakage to the readout resonator, where it quickly decays, ensuring that this negligibly affects the coherence within the computational subspace for realistic system parameters. For ancilla qubits we apply a $|1\rangle\leftrightarrow|2\rangle$ $\pi$ pulse conditioned on the measurement outcome. Using density-matrix simulations of the distance-3 surface code we show that the average leakage lifetime is reduced to almost 1 QEC cycle, even when the LRUs are implemented with limited fidelity. Furthermore, we show that this leads to a significant reduction of the logical error rate. This LRU scheme opens the prospect for near-term scalable QEC demonstrations.

Proposal for Entangling Gates on Fluxonium Qubits via a Two-Photon Transition

We propose a family of microwave-activated entangling gates on two capacitively coupled fluxonium qubits. A microwave pulse applied to either qubit at a frequency near the half-frequency of the |00⟩-|11⟩ transition induces two-photon Rabi oscillations with a negligible leakage outside the computational subspace, owing to the strong anharmonicity of fluxoniums. By adjusting the drive frequency, amplitude, and duration, we obtain the gate family that is locally equivalent to the fermionic-simulation gates such as SWAP-like and controlled-phase gates. The gate error can be tuned below 10−4 for a pulse duration under 100 ns without excessive circuit parameter matching. Given that the fluxonium coherence time can exceed 1 ms, our gate scheme is promising for large-scale quantum processors.Received 17 December 2020Revised 4 May 2021Accepted 13 May 2021DOI:https://doi.org/10.1103/PRXQuantum.2.020345Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum computationQuantum gatesQuantum information with solid state qubitsPhysical SystemsSuperconducting qubitsQuantum InformationCondensed Matter & Materials Physics