Session Z41: Quantum Control: Feedback and Dissipation Engineering

Universal Control with Weak Kerr Cavities

Cavities with a weak Kerr nonlinearity can be used to prepare single photon states in the presence of a loss much larger than their nonlinearity. Two necessary ingredients are large displacements and two-photon driving [1]. Here, we prove that these systems can be used for universal control in arbitrary finite dimensions. Moreover, we show that the requirement of two-photon driving can be relaxed. We present two novel schemes, one based on Trotter-Suzuki decomposition, and another using gradient-based optimization to find control pulses for a desired gate. These schemes utilize large displacements while circumventing the need for considering large photon number states, thus taking advantage of the nonlinear effects while keeping the computation tractable.

[1] A. Lingenfelter, D. Roberts, and A. A. Clerk, Unconditional Fock State Generation Using Arbitrarily Weak Photonic Nonlinearities, arXiv:2103.12041 [quant-ph] (2021).   

Coherent Control of Stabilized Entangled States

Dissipative state stabilization is an approach for rapid preparation of complex quantum states by introducing engineered dissipation via coupling the system to a lossy bath. Several methods have been demonstrated that use fixed-amplitude parametric driving to induce stabilization [1,2]. The use of parametric interactions, however, affords us the opportunity to even modulate the system parameters in a time-dependent fashion at rates faster than the convergence time of the CW stabilization protocol. This provides a new axis of control over the stabilization process which may allow for further optimization of the overall stabilization performance. Moreover, after stabilization has completed, the time-dependent modulation of the drives can allow for coherent control within the stabilized manifold. In this talk, I will discuss theoretical and experimental prospects of open-loop quantum control in a multipartite system.

[1] High fidelity dissipation engineering using parametric interactions, Phys. Rev. Research 2, 023370 (2020)

[2] Trade off-Free Entanglement Stabilization in a Superconducting Qutrit-Qubit System, arXiv:2107.13579v2 (2021)   

Atomic state preparation using coherent feedback control.

Initializing a qubit in a desired state with high fidelity is important in quantum information. The existing protocols achieve this task by rotating the qubit from a known initial state to the desired state. In atomic systems these rotations require resonant pulses with precise control over phase and shape of the amplitude of the pulse.  Also the atom has to be prepared in a known initial state (typically a ground state).

Here we propose a scheme to prepare an atom in an arbitrary state using coherent control feedback protocol.  In this scheme, the superposition state is obtained by interacting the atom with a sequence of controller photons. The proposed scheme works even with off-resonant pulses and doesn’t require any information about the initial state. We show that the fidelity can be brought close to unity by increasing the number of controller photons. We also discuss possible implementations of this scheme using the existing experimental setups.   

Canonical phase measurement enabled by quantum feedback control

In addition to extracting information, measurements of quantum systems are a resource for enhancing control and precision. They can be used to alter what we are detecting and allow access to new observables. Current hardware can perform near-ideal measurements of photon number or field amplitude, the ability to perform an ideal phase measurement is still lacking, even in principle. We implement a single-shot canonical phase measurement on a one-photon wave packet, which surpasses the current standard of heterodyne detection and is optimal for single-shot phase estimation. By applying quantum feedback to a Josephson parametric amplifier, our system adaptively changes its measurement basis during photon arrival to suppress amplitude information. We validate the detector’s performance by tracking the quantum state of the photon source. These results demonstrate that quantum feedback can enable access to new classes of physical observables.   

Optimal controls in many-body quantum metrology

Quantum metrology is the subject of improving the precision of parameter estimation using quantum effects. Quantum controls come into play in quantum metrology in that they can engineer the dynamics and therefore alter the generator for parameter estimation. Assuming controls Hamiltonians are freely available, there has been a mature theory developed for applying quantum control in quantum metrology. However, how to apply optimal quantum controls in quantum metrology when certain control Hamiltonians are not available? In this talk, we answer this question by deriving optimal control equations using the variational approach. When the estimation Hamiltonian is time-independent, we show that one can apply the high-frequency expansion to recover the Heisenberg scaling for time-independent Hamiltonians. For example, for a spin chain with interactions up to local three-body interactions, assuming one-body and two-body controls are at hand, one can cancel the effect of local three-body interactions with high-frequency drives consisting of local two-body interactions. Our results open the door to investigate quantum metrology with a constrained set of available controls, which can be very practical for many-body quantum metrology.   

Weak-link-based nonreciprocal devices

We introduce a coupling scheme based on weak-link junctions that breaks time-reversal symmetry without the need of external drives. Exploiting this idea, we present the design of a dissipationless gyrator that can be used as a building block for the GKP qubit [1]. We moreover extend these concepts to other nonreciprocal devices and discuss applications to quantum information processing.

[1] Rymarz, M., Bosco, S., Ciani, A., & DiVincenzo, D. (2021). Hardware-Encoding Grid States in a Nonreciprocal Superconducting Circuit. Phys. Rev. X, 11, 011032.   

Preparation and stabilization of cavity Fock state superpositions with deep reinforcement learning

Photon number superposition states inside a microwave cavity are an essential resource for hardware efficient quantum computing, such as the binomial or cat codes frameworks. Their preparation and stabilization, however, usually require controls relying on second-order interactions to generate the non-classicality of the Wigner function.

Here, we propose instead a protocol based on state-of-the-art off-policy deep distributional reinforcement learning, to obtain heralded state preparation fidelities above 97% on average for a variety of bosonic states. Optimizing with respect to the distribution of returns, rather than their mean, was found to be instrumental in implementing a stable training procedure.

The approach relies on using a coherent displacement as linear control and quantum back action from weak measurements as the only non-linearity implemented with Ramsey type interferometry. Such measurements stabilize subspaces of Fock state superpositions, where by keeping track of the quantum state, our scheme is able to counteract the cavity decoherence rate, recovering from photon loss events in real time. Moreover, the reinforcement learning approach overcomes local minima in the stabilized subspace, reaching higher fidelities than conventional classical feedback protocols.   

Entanglement control in two interacting asymmetric qubits coupled off-resonance to a radiation field

In previous works [1,2], we have studied the manipulation of entanglement sudden death (ESD) and asymptotic behavior in a system of two interacting identical atoms (qubits) coupled to radiation field. We showed how the interplay among the different system parameters can be used to tune the system dynamics and asymptotic behavior. In this work, we study a system of two interacting asymmetric atoms coupled to a radiation field at non-zero detuning. The two atoms are coupled through dipole-dipole and Ising interactions. We provide an exact analytic solution for the system dynamics that span the entire system parameter phase space starting from any initial state. We show how the asymmetry of the system can be utilized to avoid ESD and enhance its entanglement asymptotic value, when tuned with the other system parameters such as the non-zero detuning, and dipole-dipole and Ising couplings. This system can be realized in quantum dots (or Rydberg atoms) in optical cavities and superconducting (or hybrid) qubits in linear resonators, which is of special interest in the field of quantum information processing (QIP).

[1] Gehad Sadiek, Wiam Al-Drees and Sebawe Abdullah, Optics Express 27, 33799 (2019).

[2] Gehad Sadiek, Wiam Al-Drees, Salwa Shaglel and Hala Elhag, Entropy 23, 00629 (2021).   

Reinforcement Learning for Quantum Feedback in the Jaynes-Cummings Model and beyond

The Jaynes-Cummings model of a qubit coupled to a cavity represents one of the paradigmatic models of light-matter interaction, with experimental realizations in cavity and circuit quantum electrodynamics and phononic systems. The nonlinearity provided by the qubit can be exploited to prepare arbitrary quantum states of the cavity, and an explicit construction for the required control sequences has been provided by Law and Eberly. However, in the presence of noise and decoherence, this approach is not sufficient, and feedback strategies need to be invented. In this talk, we will show how suitably engineered techniques of reinforcement learning can efficiently discover such strategies. The same techniques can also be applied to a wide range of other settings.   

Design of a deep neural network suitable for real-time feedback strategies discovered via reinforcement learning on a quantum device

Real-time feedback for quantum systems is an essential ingredient in many quantum control tasks, such as quantum error correction and quantum state preparation. Two aspects make feedback challenging: First, a time far shorter than the coherence time is required. Second, it represents a complex decision making problem. The subfield of machine learning dealing with optimizing strategies for problems of this type is reinforcement learning, whose power has been convincingly demonstrated in areas ranging from robotics to video and board games.

In this work, we present and analyze the design of a neural network which can be implemented on a Field Programmable Gate Array (FPGA) to discover real-time feedback strategies for initialization of a superconducting qubit. Our network will be trained via reinforcement learning which is only based on data directly accessible in an experiment, such that precise knowledge of the underlying dynamics is not required. To address the challenge of low latency, we introduce a key idea: the network inference computation is interleaved with the simultaneous collection of measurement data.   

Feedback cooling and active qubit reset using FPGA-based feedback

In circuit QED feedback can be used for active qubit reset and feedback cooling. We present an efficient and general-purpose template-based feedback scheme working with direct digital synthesis and sampling. The feedback latency is limited almost entirely by converter latency. State discrimination can be based on measurements from multiple channels and feedback can be applied to multiple outputs. We demonstrate active qubit reset and feedback cooling on a two qubit sample. We also discuss the process of template optimization using the whole readout response rather than just the I/Q-quadratures.

The feedback is implemented and tested on a platform we call Presto which is based on a radio-frequency system-on-a-chip (RFSoC) from Xilinx. The platfrom has multiple outputs and inputs capable of direct digital synthesis and sampling in the 4-8 GHz band without using analog mixers, all phase-coherent and synchronized to a single master clock.   

Realizing a Reinforcement Learning Agent on a Field-Programmable Gate Array for Real-time Control of Superconducting Qubits

Real-time controllers of quantum systems process the outcome of intermediate measurements to determine which subsequent actions to apply to the quantum system. Realizing such adaptive control, on timescales much shorter than the coherence time, has a wide range of potential applications, such as in quantum error correction and in quantum state preparation. Here, we implement a deep neural network on a field-programmable gate array (FPGA) and investigate its use as a real-time reinforcement learning agent to efficiently initialize a transmon qubit into its ground state. The agent repeatedly measures the qubit and chooses after each cycle whether to idle, to apply a bit-flip gate, or to terminate. After the agent chooses to terminate the initialization process, we perform a validation measurement to infer the probability of having successfully initialized the ground state. To train the agent, we use model-free reinforcement learning that is based solely on measurement data.   

Engineering microwave-activated interactions for two-qubit gates and coherent-error suppression

Improving the extensibility of circuit-QED architectures is a necessary step towards developing functional large-scale quantum processors. In this context, the choice of two-qubit coupling and gate scheme is important, as it can place stringent design constraints at a larger scale. Tunable-qubit architectures offer some flexibility for mitigating frequency crowding and might have an edge in this respect. However, tunability often comes at the price of increased decoherence. In this talk, we introduce a transmon-qubit-based architecture that leverages always-on microwave drives to enhance or suppress multiqubit interactions. In the appropriate frame, the drive parameters appear as tunable knobs that are useful to enact two-qubit gates or idle with high-fidelity. We discuss ways to leverage such tunability alongside operating-regime tradeoffs that account for drive-induced decoherence.