Kaushik Chakraborty

Cryptography depends on truly unpredictable numbers, but physical sources emit biased or correlated bits. Quantum mechanics enables the amplification of imperfect randomness into nearly perfect randomness, but prior demonstrations have required physically co-located, loophole-free Bell tests, constraining the feasibility of remote operation. Here we realize certified randomness amplification across a network by dynamically probing large, entangled quantum states on Quantinuum's 98-qubit Helios trapped-ion quantum processor. Our protocol is secure even if the remote device acts maliciously or is compromised by an intercepting adversary, provided the samples are generated quickly enough to preclude classical simulation of the quantum circuits. We stream quantum gates in real time to the quantum processor, maintain quantum state coherence for $\approx 0.9$ seconds, and then reveal the measurement bases to the quantum processor only milliseconds before measurement. This limits the time for classical spoofing to 30 ms and constrains the location of hypothetical adversaries to a $4{,}500$ km radius. We achieve a fidelity of 0.586 on random circuits with 64 qubits and 276 two-qubit gates, enabling the amplification of realistic imperfect randomness with a low entropy rate into nearly perfect randomness.

While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers, realizing this potential remains a challenge. One such task is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy. Certified randomness has many applications but is fundamentally impossible to achieve solely by classical computation. In this work, we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations: a client generates quantum "challenge" circuits using a small randomness seed, sends them to an untrusted quantum server to execute, and verifies the server's results. We analyze the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of $1.1\times10^{18}$ floating-point operations per second across multiple supercomputers, we certify $71,313$ bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of today's quantum computers.

Gate-based quantum computers hold enormous potential to accelerate classically intractable computational tasks. Random circuit sampling (RCS) is the only known task that has been able to be experimentally demonstrated using current-day NISQ devices. However, for a long time, it remained challenging to demonstrate the quantum utility of RCS on practical problems. Recently, leveraging RCS, an interactive protocol generating certified randomness was demonstrated using a trapped ion quantum computer, advancing the practical utility of near-term gate-based quantum computers. In this work, we establish a strong connection between certified randomness and another quantum computation classical communication primitive, classically verifiable position verification (CVPV), which circumvents the practical challenges that may arise from long-distance quantum communications. We provide a new generic compiler that can convert any single-round proof of quantumness based certified randomness protocol into a secure classical communication-based position verification scheme. Later, we extend our compiler to different types of multi-round protocols. Notably, our compiler can be applied to any multi-round certified randomness protocol that can be analyzed using the entropy accumulation theorem, making its applicability very general. Moreover, we show that CVPV is equivalent to a relaxed variant of certified randomness that we define. We instantiate each of our compilers using existing certified randomness protocols. In particular, building on the work of Aaronson and Hung (STOC '23), we give a NISQ-friendly instantiation based on RCS, which was experimentally demonstrated by Liu et al.. Hence, we show that CVPV is another application within reach of NISQ devices.