Synthetic high angular momentum spin dynamics in a microwave oscillator

Abstract

Spins and oscillators are foundational to much of physics and applied sciences. For quantum information, a spin 1/2 exemplifies the most basic unit, a qubit. High angular momentum spins (HAMSs) and harmonic oscillators provide multi-level manifolds (e.g., qudits) which have the potential for hardware-efficient protected encodings of quantum information and simulation of many-body quantum systems. In this work, we demonstrate a new quantum control protocol that conceptually merges these disparate hardware platforms. Namely, we show how to modify a harmonic oscillator on-demand to implement a continuous range of generators associated to resonant driving of a harmonic qudit, which we can interpret as accomplishing linear and nonlinear control over a harmonic HAMS degree of freedom. The spin-like dynamics are verified by demonstration of linear spin coherent (SU(2)) rotations, nonlinear spin control, and comparison to other manifolds like simply-truncated oscillators. Our scheme allows the first universal control of such a harmonic qudit encoding: we use linear operations to accomplish four logical gates, and further show that nonlinear harmonicity-preserving operations complete the logical gate set. Our results show how motion on a closed Hilbert space can be useful for quantum information processing and opens the door to superconducting circuit simulations of higher angular momentum quantum magnetism.

References in corpus (45)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Circuit Quantum Electrodynamics
• Quantum Spin Liquids
• Quantum Spin Liquid States
• Quantum Spin Liquids
• Dynamically protected cat-qubits: a new paradigm for universal quantum computation
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Qudits and high-dimensional quantum computing
• The Kerr-Cat Qubit: Stabilization, Readout, and Gates
• Real-time quantum error correction beyond break-even
• New class of quantum error-correcting codes for a bosonic mode
• Encoding a qubit in a trapped-ion mechanical oscillator
• A quantum memory with near-millisecond coherence in circuit QED
• Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator
• Demonstration of quantum error correction and universal gate set on a binomial bosonic logical qubit
• Maximum Likelihood, Minimum Effort
• Cavity State Manipulation Using Photon-Number Selective Phase Gates
• Beating the break-even point with a discrete-variable-encoded logical qubit
• Fast Universal Control of an Oscillator with Weak Dispersive Coupling to a Qubit
• Universal Control of an Oscillator with Dispersive Coupling to a Qubit
• Confined quantum Zeno dynamics of a watched atomic arrow
• Protecting a Bosonic Qubit with Autonomous Quantum Error Correction
• Coherent oscillations inside a quantum manifold stabilized by dissipation
• Suppression of photon shot noise dephasing in a tunable coupling superconducting qubit
• Quantum control of bosonic modes with superconducting circuits
• Error-transparent operations on a logical qubit protected by quantum error correction
• Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model
• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Error-corrected gates on an encoded qubit
• Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences
• Quantum dynamics of an electromagnetic mode that cannot contain N photons
• Engineering bilinear mode coupling in circuit QED: Theory and experiment
• Encoding a qubit in a spin
• Multimode photon blockade
• High-fidelity software-defined quantum logic on a superconducting qudit
• Navigating the 16-dimensional Hilbert space of a high-spin donor qudit with electric and magnetic fields
• Schrödinger cat states of a nuclear spin qudit in silicon
• Programmable quantum simulations of bosonic systems with trapped ions
• Empowering high-dimensional quantum computing by traversing the dual bosonic ladder
• Fault-tolerant quantum computation using large spin cat-codes
• Conditional not displacement: fast multi-oscillator control with a single qubit
• Cubic phase gates are not suitable for non-Clifford operations on GKP states
• Drive-induced nonlinearities of cavity modes coupled to a transmon ancilla
• Robust Macroscopic Schrödinger's Cat on a Nucleus
• Two-qubit operations for finite-energy Gottesman-Kitaev-Preskill encodings

Cited by in corpus (6)

• Quantum Error Correction of Qudits Beyond Break-even
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Multi-frequency control and measurement of a spin-7/2 system encoded in a transmon qudit
• Quantum error correction beyond $SU(2)$: spin, bosonic, and permutation-invariant codes from convex geometry
• A Mathematical Structure for Amplitude-Mixing Error-Transparent Gates for Binomial Codes
• Kramers-protected hardware-efficient error correction with Andreev spin qubits