Universal control of a bosonic mode via drive-activated native cubic interactions

Abstract

Linear bosonic modes offer a hardware-efficient alternative for quantum information processing but require access to some nonlinearity for universal control. The lack of nonlinearity in photonics has led to encoded measurement-based quantum computing, which relies on linear operations but requires access to resourceful (’nonlinear’) quantum states, such as cubic phase states. In contrast, superconducting microwave circuits offer engineerable nonlinearities but suffer from static Kerr nonlinearity. Here, we demonstrate universal control of a bosonic mode composed of a superconducting nonlinear asymmetric inductive element (SNAIL) resonator, enabled by native nonlinearities in the SNAIL element. We suppress static nonlinearities by operating the SNAIL in the vicinity of its Kerr-free point and dynamically activate nonlinearities up to third order by fast flux pulses. We experimentally realize a universal set of generalized squeezing operations, as well as the cubic phase gate, and exploit them to deterministically prepare a cubic phase state in 60 ns. Our results initiate the experimental field of polynomial quantum computing, in the continuous-variables notion originally introduced by Lloyd and Braunstein.

Simulating Chemistry on Bosonic Quantum Devices

“…This can open the door for quantum algorithms that can use the multiple levels of one oscillator rather than using multiple qubits. 60,61,132,133 Thus, we can encode and study chemical problems within a compact bosonic framework, aiding to the development of enhanced, highquantum-volume bosonic devices with scalable error-tolerance.…”

“…For example, there has been recent progress in developing universal bosonic circuits based on the cQED platform, that can in principle represent any unitary of arbitrary dimension, including gates based on multiple qubits. This can open the door for quantum algorithms that can use the multiple levels of one oscillator rather than using multiple qubits. ,,, Thus, we can encode and study chemical problems within a compact bosonic framework, aiding to the development of enhanced, high-quantum-volume bosonic devices with scalable error-tolerance.…”

“…For example, the Pauli-Z matrix can be represented as Z = [ true 1 0 0 − 1 ] → 1 − 2 â † â using the SBM mapping. Similarly, any 2 × 2 Hamiltonian such as the Pauli operators can be mapped onto the Hamiltonian of a currently available bosonic quantum device known as driven superconducting nonlinear asymmetric inductive element (SNAIL) ,, Ĥ SNAIL = ℏ ω â † â + g 3 false( â + â † false) 3 Given that all 1-qubit gates correspond to unitary dynamics generated by a 2 × 2 Hamiltonian, they can therefore be generated by such SNAIL devices. Furthermore, 4 × 4 Hamiltonian matrices, which correspond to 2-qubit gates, can also be implemented by combining the SNAIL with a combination of Josephson junctions that gives rise to fourth-order terms in the device Hamiltonian …”

Holographic Gaussian Boson Sampling with Matrix Product States on 3D cQED Processors

“…Much faster gates on 100 ns scale or shorter can be implemented with parametric charge or flux drives , using novel Josephson ancilla circuitry that supports three-wave mixing processes. These ancillae, including, for example, SNAIL (Superconducting Nonlinear Asymmetric Inductive eLement), ,− RF SQUID, and ATS have been under intensive development recently. Their integration with high-coherence 3D systems has led to record beam-splitter fidelity in the range of 99.9–99.99%. , …”