Guess, SWAP, Repeat : Capturing Quantum Snapshots in Classical Memory

TL;DR

The paper addresses the challenge of observing quantum states without destruction and storing them for later reuse. It introduces a fidelity-based quantum snapshot framework that uses SWAP-test feedback to non-destructively reconstruct states, with two estimation paradigms: gradient-based neural generation and gradient-free evolutionary strategies (QESwap). Real-device demonstrations on IBM hardware and extensive simulations show high fidelities for pure states (up to $\sim 1.0$) and practical robustness of the gradient-free method under noise, outlining a viable route toward classical-quantum memory and modular quantum workflows. While effective for pure states and small systems, the approach faces intrinsic limitations for mixed states due to the Hilbert-Schmidt inner product nature of the SWAP test, motivating future work on alternative fidelity estimators. Overall, the framework advances non-destructive quantum observation, circuit introspection, and memory-enabled quantum computing, with substantial implications for QRAM, debugging, and memory-assisted quantum architectures.

Abstract

We introduce a novel technique that enables observation of quantum states without direct measurement, preserving them for reuse. Our method allows multiple quantum states to be observed at different points within a single circuit, one at a time, and saved into classical memory without destruction. These saved states can be accessed on demand by downstream applications, introducing a dynamic and programmable notion of quantum memory that supports modular, non-destructive quantum workflows. We propose a hardware-agnostic, machine learning-driven framework to capture non-destructive estimates, or "snapshots," of quantum states at arbitrary points within a circuit, enabling classical storage and later reconstruction, similar to memory operations in classical computing. This capability is essential for debugging, introspection, and persistent memory in quantum systems, yet remains difficult due to the no-cloning theorem and destructive measurements. Our guess-and-check approach uses fidelity estimation via the SWAP test to guide state reconstruction. We explore both gradient-based deep neural networks and gradient-free evolutionary strategies to estimate quantum states using only fidelity as the learning signal. We demonstrate a key component of our framework on IBM quantum hardware, achieving high-fidelity (approximately 1.0) reconstructions for Hadamard and other known states. In simulation, our models achieve an average fidelity of 0.999 across 100 random quantum states. This provides a pathway toward non-volatile quantum memory, enabling long-term storage and reuse of quantum information, and laying groundwork for future quantum memory architectures.

Figures (8)

• Figure 1: Methodology for Non-Destructive Quantum State Observation ('Snapshot'): This figure illustrates the methodology behind the three primary processes for observing a quantum state with $n$ qubits. The approach begins with an unknown target circuit (marked in light blue) and a neural network model that generates an output representing either a state vector (Method 1), a unitary (Method 2), or a density matrix (Method 3). This output is used to construct a reconstructed circuit (marked in light purple). An ancilla qubit is initialized in the state $|0\rangle$, and a swap test is performed between the target and reconstructed circuits. The outcome is projected onto the ancilla qubit, and its measurement yields fidelity, a measure of similarity between the two states. A fidelity of 1 indicates a perfect match between the reconstructed and target states. If the fidelity is not sufficiently close to 1, the neural network’s model weights are updated using the fidelity value. This iterative process continues until the fidelity converges to a value very close to 1, ensuring accurate state reconstruction.
• Figure 2: Progression of reconstructed states towards target states for noiseless and noisy conditions: The left figure shows the noiseless case where the target unknown state remains fixed, allowing smooth convergence. In contrast, the right figure illustrates the noisy case, where the target state keeps shifting due to hardware noise, making convergence significantly more challenging.
• Figure 3: Entanglement entropy analysis of target and reconstructed states: (a) Distribution of target entanglement entropy across qubit counts. (b) Comparison of target and reconstructed entanglement entropy, sorted by circuit index, showing close alignment across different system sizes.
• Figure 4: Fidelity distributions for state vector reconstruction across qubit counts: (a) & (b) show results for the gradient-based (NN) method under noiseless and noisy settings; (c) & (d) show the same for the gradient-free (ES) method.
• Figure 5: Fidelity distributions for unitary matrix reconstruction under noiseless conditions. (a) Gradient-based (NN) method; (b) Gradient-free (ES) method.