A Thorough Study of State Leakage Mitigation in Quantum Computing with One-Time Pad

TL;DR

This work addresses horizontal state leakage in cloud-based quantum computing due to noisy reset operations. It proposes using classical (COTP) and quantum (QOTP) one-time pads before resets to randomize post-reset states and prevent leakage, and analyzes when COTP suffices vs QOTP under different measurement axes and reset implementations. The study models state evolution with density matrices and quantum channels, and quantifies leakage using an SNR metric across real devices and simulators, revealing that QOTP effectively achieves a maximally mixed state and thus universal protection, while COTP's effectiveness is conditional. The findings provide practical design guidance for secure reset procedures in cloud quantum computing and contribute to the broader security of NISQ-era quantum workloads.

Abstract

The ability for users to access quantum computers through the cloud has increased rapidly in recent years. Despite still being Noisy Intermediate-Scale Quantum (NISQ) machines, modern quantum computers are now being actively employed for research and by numerous startups. Quantum algorithms typically produce probabilistic results, necessitating repeated execution to produce the desired outcomes. In order for the execution to begin from the specified ground state each time and for the results of the prior execution not to interfere with the results of the subsequent execution, the reset mechanism must be performed between each iteration to effectively reset the qubits. However, due to noise and errors in quantum computers and specifically these reset mechanisms, a noisy reset operation may lead to systematic errors in the overall computation, as well as potential security and privacy vulnerabilities of information leakage. To counter this issue, we thoroughly examine the state leakage problem in quantum computing, and then propose a solution by employing the classical and quantum one-time pads before the reset mechanism to prevent the state leakage, which works by randomly applying simple gates for each execution of the circuit. In addition, this work explores conditions under which the classical one-time pad, which uses fewer resources, is sufficient to protect state leakage. Finally, we study the role of various errors in state leakage, by evaluating the degrees of leakage under different error levels of gate, measurement, and sampling errors. Our findings offer new perspectives on the design of reset mechanisms and secure quantum computing systems.

Figures (7)

• Figure 1: Schematic of the threat model. (a) Without OTP, the state of the victim circuit is leaked to the attacker circuit; (b) with OTP, the state leakage can be mitigated.
• Figure 2: Schematic of how states are transformed with OTP. The pink vector shows an arbitrary state, while others show the state after applying gates of OTP. (a) With COTP, the final states (the orange vector) are along the axis of the generalized Pauli-$X$ gate; (b) with QOTP, the final states (no show in the figure) are the original points.
• Figure 3: $P(-1)$, the probability of attackers measuring $-1$ on ibmq_jakarta on IBM Quantum. The state leakage is shown in (a) and (c) without OTP (black lines) by the apparent dependence of $P(-1)$ on $\alpha$. (a) The reset operation is 250 ns delay (default value on IBM Quantum) and the measurement axis is the $Z$ axis; (b) the reset operation is 250 ns delay and the measurement is the $X$ axis; (c) the reset operation is 250 ns delay and the measurement axis is the $X$ axis. (c) the reset operation is the default reset instruction and the measurement axis is the $Z$ axis; (d) the reset operation is the default reset instruction and the measurement axis is the $X$ axis.
• Figure 4: $P(-1)$, the probability of attackers measuring $-1$ on the simulator. (a) The reset operation is 250 ns delay (default value on IBM Quantum) and $T_1 = T_2 = 100$ ns; (b) the reset operation is the reset instruction and $M_{10} = 0.05, M_{01} = 0.10$ and no error on Pauli-$X$. (c) The reset operation is the measurement-less reset instruction and $p_r = 0.1$.
• Figure 5: SNR on the simulator with different $\gamma_1$ and $\gamma_2$, the ratio of 250 ns to the decoherence time $T_1$ and $T_2$ defined in Section \ref{['sec:thermal']}. Note $\gamma_1 \leq 2\gamma_2$ due to $T_2 \leq 2T_1$. (a) The measurement axis is along the $Z$ axis; (b) the measurement axis is along the $X$ axis.