Certified Random Number Generation using Quantum Computers

TL;DR

This work tackles the problem of generating certified quantum randomness using current quantum computers without requiring spatially separated devices. It employs a temporal analogue of Bell tests, the Leggett-Garg inequality (LGI), along with No Signaling In Time (NSIT) to certify randomness from a single-qubit source in a semi-device-independent manner. The authors implement low-depth circuits on IBMQ backends, demonstrating LGI violation while satisfying NSIT and extracting genuine randomness bounded by $H_\infty(AB|XY) \ge -\log_2\left(\frac{1 + \alpha + \sqrt{1-2\alpha}}{2}\right)$ with $\alpha = I-1$, achieving practical randomness generation on real hardware. They perform a thorough noise analysis, apply M3 readout mitigation to improve results, and discuss limitations and potential upgrades toward fully loophole-free implementations. The work provides a practical framework for using quantum computers as semi-device-independent randomness generators and as benchmarks for quantum-device performance.

Abstract

In recent decades, quantum technologies have made significant strides toward achieving quantum utility. However, practical applications are hindered by challenges related to scaling the number of qubits and the depth of circuits. In this paper, we investigate how current quantum computers can be leveraged for practical applications, particularly in generating secure random numbers certified by Quantum Mechanics. While random numbers can be generated and certified in a device-independent manner through the violation of Bell's inequality, this method requires significant spatial separation to satisfy the no-signaling condition, making it impractical for implementation on a single quantum computer. Instead, we employ temporal correlations to generate randomness by violating the Leggett-Garg inequality, which relies on the No-Signaling in Time condition to certify randomness, thus overcoming spatial constraints. By applying this protocol to existing quantum computers, we demonstrate the feasibility of secure, semi-device-independent random number generation using low-depth circuits with single-qubit gates.

Figures (15)

• Figure 1: The circuits for different measurement setting $t_1t_2$, $t_1t_3$ and $t_2t_3$. $U_1$ and $U_2$ denotes the rotation operators with angles $\theta_1$ and $\theta_2$
• Figure 2: Circuits for correlation measurements of $t_1t_2$, $t_2t_3$ and $t_1t_3$ transpiled in the IBMQ Brussels backend. The Unitaries for rotation operators involving the angles $\theta_1$ and $\theta_2$ are decomposed in terms of the $R_Z$ and $SX$ gates available in the backend. The qubit 12 was selected after analyzing the best possible layout for our circuit using the mapomatic algorithm.
• Figure 3: Circuit for computing the one time probabilities at $t_2$ and $t_3$. These circuits are utilized in the verification of the NSIT conditions and are not used in generating random bits. These circuits also can be decomposed in terms of the $SX$ and $R_Z$ gates followed by a single measurement.
• Figure 4: LGI violation experiment in IBMQ Brussels. We repeated the experiment for each value $10$ times, each of the experiment was run for $50,000$ shots. We observe that for all cases the experimental results are slightly lower than the expected values, which is due to the noise factors in the backend as demonstrated later.
• Figure 5: Genuine Randomness vs LGI violation plotted alongside the theoretical analytical bound for the experiment in IBMQ Brussels. The genuine randomness spread is a bit lower than the expected lower bound because the results of the LGI values in the experiment were lower than the expected values.