Noise Mitigation Through Design and Optimization of Parametric Quantum Channels

Abstract

The primary aim of the thesis is to introduce and investigate an original protocol for the design and the optimization of parameterized noisy quantum channels, with the goal of mitigating hardware-induced noise. Significant attention is also devoted to the design of noise models, which are essential for emulation purposes. The protocol begins with the derivation of a noise model for a hardware gate, represented as a quantum channel, that can be simulated classically. This task is achieved through process tomography, a procedure that enables the characterization of the channel. It should be noted that such simulation is feasible on classical computers, since the optimization task concerns low-dimensional gates typically acting on 2–3 qubits. The noisy channel is then engineered by embedding it into a probabilistic ensemble of circuits, in which additional single-qubit parameterized gates — assumed to be noiseless — are introduced. Through this procedure, the noisy channel becomes parameterized and can be optimized according to an appropriate metric. Following a worst-case, agnostic perspective, we choose the diamond distance between the noisy channel and the target unitary channel as the cost function. This metric is generally considered the most suitable for distinguishing quantum channels. The resulting optimal ensemble of circuits can be implemented on real hardware under fixed calibration conditions, yielding a channel that approximates the target more closely than the original noisy channel. This approach can be interpreted as a noise mitigation strategy based on pre-processing design and optimization: rather than correcting errors after the computation, less noisy channels are employed during the computation itself. In this context, the protocol — within the noise-aware variational quantum compiling framework — shares with the randomized compiling the principle of circuit dressing to tailor noise during execution. The methodology is validated on two toy models of the single-qubit identity with amplitude damping noise, combining both analytical and numerical approaches. The analysis highlights the role of convexity in the space of quantum channels, with explicit demonstrations of optimal convex combinations and connections to encoding-decoding and dynamical decoupling strategies. The analysis of these simple models is intended as a proof-of-principle of the protocol in a controlled and well-characterized environment. In addition, this thesis introduces the design of random noise models that are constrained to maintain a fixed diamond distance from a target quantum channel. The controlled addition of random noise to a unitary channel represents a significant and — to our knowledge — previously unexplored approach within noise modeling. Indeed, in principle, the currently available built-in noise models may limit the expressivity of the emulation. The task was achieved by enriching the noise spectrum through the addition of random Kraus operators and small systematic rotations. To assess the effects of hardware-induced noise, we proposed an experimental design aimed at simulating the time evolution of a triangular Ising model in a transverse field. Our approach employs Trotterization, adapted to the topology and connectivity of a certain quantum processing unit (QPU) profile. Building on the noisy native gates of the QPU profile, we propose the emulation, engineering and optimization of a noisy CZ gate, subsequently employed within sequences of non-native gates. Using the designed noise models, we perform several emulations aimed at evaluating the effectiveness of the protocol in the presence of progressively dominant systematic rotations, and at comparing it with Pauli twirling, a technique of randomized compiling.