Universal qudit gate synthesis for transmons

Abstract

Gate-based quantum computers typically encode and process information in two-dimensional units called qubits. Using $d$-dimensional qudits instead may offer intrinsic advantages, including more efficient circuit synthesis, problem-tailored encodings and embedded error correction. In this work, we design a superconducting qudit-based quantum processor wherein the logical space of transmon qubits is extended to higher-excited levels. We propose a universal gate set featuring a two-qudit cross-resonance entangling gate, for which we predict fidelities beyond $99\%$ in the $d=4$ case of ququarts with realistic experimental parameters. Furthermore, we present a decomposition routine that compiles general qudit unitaries into these elementary gates, requiring fewer entangling gates than qubit alternatives. As proof-of-concept applications, we numerically demonstrate the synthesis of $\mathrm{SU}(16)$ gates for noisy quantum hardware and an embedded error correction sequence that encodes a qubit memory in a transmon ququart to protect against pure dephasing noise. We conclude that universal qudit control -- a valuable extension to the operational toolbox of superconducting quantum information processing -- is within reach of current transmon-based architectures and has applications to near-term and long-term hardware.

10+6 pages, 9+3 figures, revised version published in PRX Quantum

References in corpus (16)

• Charge insensitive qubit design derived from the Cooper pair box
• Simple pulses for elimination of leakage in weakly nonlinear qubits
• Synthesis of Quantum Logic Circuits
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• The Future of Quantum Computing with Superconducting Qubits
• Coherence and Decay of Higher Energy Levels of a Superconducting Transmon Qubit
• Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms
• High-Fidelity Qutrit Entangling Gates for Superconducting Circuits
• Operation and intrinsic error budget of a two-qubit cross-resonance gate
• Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities
• Experimental single-setting quantum state tomography
• Quantum logic and entanglement by neutral Rydberg atoms: methods and fidelity
• Minimal qudit code for a qubit in the phase-damping channel
• Performing SU($d$) operations and rudimentary algorithms in a superconducting transmon qudit for $d=3$ and $d=4$
• Decomposing the generalized Toffoli gate with qutrits
• Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space

Cited by in corpus (36)

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• An efficient quantum algorithm for preparation of uniform quantum superposition states
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• Demonstration of a parity-time symmetry breaking phase transition using superconducting and trapped-ion qutrits
• Visualizing Entanglement in multi-Qubit Systems
• Universal quantum computing with qubits embedded in trapped-ion qudits
• Quantum Simulations of SO(5) Many-Fermion Systems using Qudits
• An architecture for two-qubit encoding in neutral ytterbium-171 atoms
• Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
• Improving Transmon Qudit Measurement on IBM Quantum Hardware
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• Platonic dynamical decoupling sequences for interacting spin systems
• The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems
• QuForge: A Library for Qudits Simulation
• Inequality constraints in variational quantum circuits with qudits
• Dissipative phase transition: from qubits to qudits
• Persistent Tensors and Multiqudit Entanglement Transformation
• Ab Initio Polaritonic Chemistry on Diverse Quantum Computing Platforms: Qubit, Qudit, and Hybrid Qubit-Qumode Architectures
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• Symmetry-enhanced Counterdiabatic Quantum Algorithm for Qudits
• Simple ways of preparing qudit Dicke states
• Local fermion-to-qudit mappings: a practical recipe for four-level systems
• Three-qubit encoding in ytterbium-171 atoms for simulating 1+1D QCD
• A Mathematical Structure for Amplitude-Mixing Error-Transparent Gates for Binomial Codes
• Quantum circuits for simulating neutrino propagation in matter
• Fault-Tolerant Encoding of Logical Qudits in Spin Systems
• Creating two-qudit maximally entangled quantum link through bulk
• Synthesis of Single Qutrit Circuits from Clifford+R
• Remote entanglement generation via enhanced quantum state transfer
• Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control
• Entanglement swapping for partially entangled qudits and the role of quantum complementarity
• Imperfect Entangling Power of Quantum Gates