High-fidelity qutrit entangling gates for superconducting circuits

Unveiling the Non-Abelian Statistics of D(S_{3}) Anyons Using a Classical Photonic Simulator

Simulators can realize novel phenomena by separating them from the complexities of a full physical implementation. Here, we put forward a scheme that can simulate the exotic statistics of D(S_{3}) non-Abelian anyons with minimal resources. The qudit lattice representation of this planar code supports local encoding of D(S_{3}) anyons. As a proof-of-principle demonstration, we employ a classical photonic simulator to encode a single qutrit and manipulate it to perform the fusion and braiding properties of non-Abelian D(S_{3}) anyons. The photonic technology allows us to perform the required nonunitary operations with much higher fidelity than what can be achieved with current quantum computers. Our approach can be directly generalized to larger systems or to different anyonic models, thus enabling advances in the exploration of quantum error correction and fundamental physics alike.

Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields

Efficient scaling and flexible control are key aspects of useful quantum computing hardware. Spins in semiconductors combine quantum information processing with electrons, holes or nuclei, control with electric or magnetic fields, and scalable coupling via exchange or dipole interaction. However, accessing large Hilbert space dimensions has remained challenging, due to the short-distance nature of the interactions. Here, we present an atom-based semiconductor platform where a 16-dimensional Hilbert space is built by the combined electron-nuclear states of a single antimony donor in silicon. We demonstrate the ability to navigate this large Hilbert space using both electric and magnetic fields, with gate fidelity exceeding 99.8% on the nuclear spin, and unveil fine details of the system Hamiltonian and its susceptibility to control and noise fields. These results establish high-spin donors as a rich platform for practical quantum information and to explore quantum foundations.

Non-Pauli Errors Can Be Efficiently Sampled in Qudit Surface Codes

Surface codes are the most promising candidates for fault-tolerant quantum computation. Single qudit errors are typically modeled as Pauli operators, to which general errors are converted via randomizing methods. In this Letter, we quantify remaining correlations after syndrome measurement for a qudit 2D surface code subject to non-Pauli errors via loops on the lattice, using percolation theory. Below the error correction threshold, remaining correlations are sparse and locally constrained. Syndromes for qudit surface codes are therefore efficiently samplable for non-Pauli errors, independent of the exact forms of the error and decoder.

Quantum and Classical Spin-Network Algorithms for q-Deformed Kogut-Susskind Gauge Theories

Treating the infinite-dimensional Hilbert space of non-Abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we employ q-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. In contrast to other formulations, this approach simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. This enables the development of both quantum as well as quantum-inspired classical spin-network algorithms for q-deformed gauge theories. To be explicit, we focus on SU(2)_{k} gauge theories with k∈N that are controlled by the deformation parameter q=e^{2πi/(k+2)}, a root of unity, and converge to the standard SU(2) Kogut-Susskind model as k→∞. In particular, we demonstrate that this formulation is well suited for efficient tensor network representations by variational ground-state simulations in 2D, providing first evidence that the continuum limit can be reached with k=O(10). Finally, we develop a scalable quantum algorithm for Trotterized real-time evolution by analytically diagonalizing the SU(2)_{k} plaquette interactions. Our work gives a new perspective for the application of tensor network methods to high-energy physics and paves the way for quantum simulations of non-Abelian gauge theories far from equilibrium where no other methods are currently available.

Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover's Algorithm with Qudits

Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states-qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems-so-called ququints-that use ququints' space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O(N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover's algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.

Experimental Realization of Two Qutrits Gate with Tunable Coupling in Superconducting Circuits

Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose. While such a strategy has the advantage of being in line with the common binary logic, it in some sense wastes the ready-for-use resources in the large Hilbert space of these intrinsic multidimensional systems. Quantum computation beyond qubits (e.g., using qutrits or qudits) has thus been discussed and argued to be more efficient than its qubit counterpart in certain scenarios. However, one of the essential elements for qutrit-based quantum computation, two-qutrit quantum gate, remains a major challenge. In this Letter, we propose and demonstrate a highly efficient and scalable two-qutrit quantum gate in superconducting quantum circuits. Using a tunable coupler to control the cross-Kerr coupling between two qutrits, our scheme realizes a two-qutrit conditional phase gate with fidelity 89.3% by combining simple pulses applied to the coupler with single-qutrit operations. We further use such a two-qutrit gate to prepare an EPR state of two qutrits with a fidelity of 95.5%. Our scheme takes advantage of a tunable qutrit-qutrit coupling with a large on:off ratio. It therefore offers both high efficiency and low crosstalk between qutrits, thus being friendly for scaling up. Our Letter constitutes an important step toward scalable qutrit-based quantum computation.