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arXiv:2203.07331 · Physical Review Research

Effective nonlocal parity-dependent couplings in qubit chains

Maximilian Nägele, Christian Schweizer, Federico Roy, Stefan Filipp

Published Aug 30, 2022• 6 citations
arXivHTMLPDF

Abstract

For the efficient implementation of quantum algorithms, practical ways to generate many-body entanglement are a basic requirement. Specifically, coupling multiple qubit pairs at once can be advantageous and may provide multiqubit operations useful in the construction of hardware-tailored algorithms. Here we extend the theory of fractional state transfer and harness the simultaneous coupling of qubits on a chain to engineer a set of nonlocal parity-dependent quantum operations suitable for a wide range of applications. The resulting effective long-range couplings directly implement a parametrizable Trotter-step for Jordan-Wigner fermions, and they can be used for simulations of quantum dynamics, efficient state generation in variational quantum eigensolvers, parity measurements for error-correction schemes, and the generation of efficient multiqubit gates. Moreover, we present numerical simulations of the gate operation in a superconducting quantum circuit architecture, which show a high gate fidelity for realistic experimental parameters.

DOI
10.1103/physrevresearch.4.033166

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For the efficient implementation of quantum algorithms, practical ways to generate many-body entanglement are a basic requirement. Specifically, coupling multiple qubit pairs at once can be advantageous and may provide multiqubit operations useful in the construction of hardware-tailored algorithms. Here we extend the theory of fractional state transfer and harness the simultaneous coupling of qubits on a chain to engineer a set of nonlocal parity-dependent quantum operations suitable for a wide range of applications. The resulting effective long-range couplings directly implement a parametrizable Trotter-step for Jordan-Wigner fermions, and they can be used for simulations of quantum dynamics, efficient state generation in variational quantum eigensolvers, parity measurements for error-correction schemes, and the generation of efficient multiqubit gates. Moreover, we present numerical simulations of the gate operation in a superconducting quantum circuit architecture, which show a high gate fidelity for realistic experimental parameters.
As quantum information technologies advance, challenges in scaling and connectivity persist, particularly the need for long-range qubit connectivity and efficient entanglement generation. Perfect State Transfer enables time-optimal state transfer between distant qubits using only nearest-neighbor couplings, enhancing device connectivity. Moreover, the transfer protocol results in effective parity-dependent non-local interactions, extending its utility to entanglement generation. Here, we experimentally demonstrate Perfect State Transfer and multi-qubit entanglement generation on a chain of six superconducting transmon qubits with tunable couplers, controlled via parametric drives. By simultaneously activating and engineering all couplings, we implement the transfer for up to six qubits, verifying single-excitation dynamics for different initial states. Extending the protocol to multiple excitations, we confirm its parity-dependent nature, where excitation number controls the phase of the transferred state. Finally, leveraging this property, we prepare a Greenberger-Horne-Zeilinger state using a single transfer operation, showcasing potential of Perfect State Transfer for efficient entanglement generation.
Multi-qubit parity measurements are at the core of many quantum error correction schemes. Extracting multi-qubit parity information typically involves using a sequence of multiple two-qubit gates. In this paper, we propose a superconducting circuit device with native support for multi-qubit parity-controlled gates (PCG). These are gates that perform rotations on a parity ancilla based on the multi-qubit parity operator of adjacent qubits, and can be directly used to perform multi-qubit parity measurements. The circuit consists of a set of concatenated Josephson ring modulators and effectively realizes a set of transmon-like qubits with strong longitudinal nearest-neighbor couplings. PCGs are implemented by applying microwave drives to the parity ancilla at specific frequencies. We investigate the scheme's performance with numerical simulation using realistic parameter choices and decoherence rates, and find that the device can perform four-qubit PCGs in 30 ns with process fidelity surpassing 99%. Furthermore, we study the effects of parameter disorder and spurious coupling between next-nearest neighboring qubits. Our results indicate that this approach to realizing PCGs constitute an interesting candidate for near-term quantum error correction experiments.
The set of quantum logic gates that can be easily implemented is fundamental to the performance of quantum computers, as it governs the accuracy of basic quantum operations and dictates the complexity of implementing quantum algorithms. Traditional approaches to extending gate sets often require operating devices outside the ideal parameter regimes used to realize qubits, leading to increased control complexity while offering only a limited set of gates. Here we experimentally demonstrate a unified and versatile gate scheme capable of generating arbitrary two-qubit gates using only an exchange interaction and qubit driving on a superconducting quantum processor. We achieve high fidelities averaging 99.38% across a wide range of commonly used two-qubit unitaries, enabling precise multipartite entangled state preparation. Furthermore, we successfully produce a B gate, which efficiently synthesizes the entire family of two-qubit gates. Our results establish that fully exploiting the capabilities of the exchange interaction can yield a comprehensive and highly accurate gate set. With maximum expressivity, optimal gate time, demonstrated high fidelity and easy adaption to other quantum platforms, our unified control scheme offers the prospect of improved performance in quantum hardware and algorithm development. The efficiency of a quantum computer depends on which basic operations it can implement. Now a scheme that can implement any two-qubit logic gate has been demonstrated on a superconducting architecture.
We propose a method for the efficient quantum simulation of fermionic systems with superconducting circuits. It consists in the suitable use of Jordan-Wigner mapping, Trotter decomposition, and multiqubit gates, be with the use of a quantum bus or direct capacitive couplings. We apply our method to the paradigmatic cases of 1D and 2D Fermi-Hubbard models, involving couplings with nearest and next-nearest neighbours. Furthermore, we propose an optimal architecture for this model and discuss the benchmarking of the simulations in realistic circuit quantum electrodynamics setups.
Implementing high-fidelity multiqubit gates is critical for reducing circuit depth in near-term quantum processors and fault-tolerant architectures. However, realizing multiqubit interactions and entanglement remains a critical challenge that limits the implementation of multiqubit gates. Here we propose an all-microwave scheme to realize single-step multiqubit gates incorporating n control and m target qubits, tailored for frequency-tunable superconducting transmon networks. By leveraging cross-resonance (CR) drives, this approach induces effective two-body ZX interactions that are significantly stronger than those achieved in conventional resonant regimes, circumventing the need for tunable couplers. The system's effective Hamiltonian is analytically derived using both quad frame rotation and rigorous block diagonalization. These combined theoretical methods facilitate the identification of optimal parameter regimes that simultaneously enhance desired target couplings and suppress parasitic higher-order terms, such as ZXX interactions. Through numerical simulations and gradient-based pulse-shape optimization, we demonstrate three-qubit gates achieving fidelities exceeding 99.9% within a 60 ns gate duration. Furthermore, we evaluate the fundamental scalability of this framework by extending the optimization to a five-qubit CXXXX architecture, confirming the physical viability of the multi-target driving scheme. Because these multiqubit operations naturally emulate stabilizer measurements, this architecture provides a hardware-efficient strategy for reducing the circuit depth of stabilizer-type operations by replacing sequential two-qubit gate decompositions with single-step multiqubit gates.
We propose an experimentally feasible architecture with controllable long-range couplings built up from local exchange interactions. The scheme consists of a spin bus, with strong, always-on interactions, coupled dynamically to external qubits of the Loss and DiVincenzo type. Long-range correlations are enabled by a spectral gap occurring in a finite-size chain. The bus can also form a hub for multiqubit entangling operations. We show how multiqubit gates may be used to efficiently generate W states (an important entanglement resource). The spin bus therefore provides a route for scalable solid-state quantum computation, using currently available experimental resources.