Quantum Integrated Sensing and Computation with Indefinite Causal Order

TL;DR

This paper investigates whether sensing and computation can be performed under indefinite causal order (ICO) by unifying them into a single quantum-state framework. It introduces a variational scheme where an $N$-qubit state acts as an agent that senses input $x$ via a unitary $U(x)$ and predicts $y=f(x)$ using a parametric circuit $U_\theta$, trained by minimizing a loss function. The ICO extension uses a quantum SWITCH with an order qubit to create a superposition of two processing orders, yielding a new effective operation $U_\theta(x_k)$ and allowing simultaneous consideration of observation-first and computation-first pathways. Experimental validation on a magnetic-navigation task shows ICO can achieve small training and testing losses and faster convergence than a definite-order benchmark, highlighting potential for quantum-integrated sensing and computation while acknowledging practical challenges such as SWITCH implementation and decoherence.

Abstract

Quantum operations with indefinite causal order (ICO) represent a framework in quantum information processing where the relative order between two events can be indefinite. In this paper, we investigate whether sensing and computation, two canonical tasks in quantum information processing, can be carried out within the ICO framework. We propose a scheme for integrated sensing and computation that uses the same quantum state for both tasks. The quantum state is represented as an agent that performs state observation and learns a function of the state to make predictions via a parametric model. Under an ICO operation, the agent experiences a superposition of orders, one in which it performs state observation and then executes the required computation steps, and another in which the agent carries out the computation first and then performs state observation. This is distinct from prevailing information processing and machine intelligence paradigms where information acquisition and learning follow a strict causal order, with the former always preceding the latter. We provide experimental results and we show that the proposed scheme can achieve small training and testing losses on a representative task in magnetic navigation.

Figures (2)

• Figure 1: Quantum integrated sensing and computation with linear causal order (left) and ICO (right). In the proposed framework, sensing and computation are carried out using the same quantum state $\ket{\psi}$. Under ICO, the agent effectively experiences a superposition of orders, one in which it observes the state and then computes, and another where the agent carries out the computation and then observes the state.
• Figure 2: Accrued training loss (left) and testing loss (right) over training epochs. We use a hardware-efficient model $U_{\theta}$ comprised of single qubit parametric gates and entangling CNOT gates with cyclical connectivity. The ansatz is comprised of $15$ layers and $N=3$ qubits. We use an additional qubit as an order qubit in the ICO scheme.