Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real, nonnegative amplitudes. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k-SAT problems, use k-local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n-body interactions. Here we present a new 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

1 aBringewatt, Jacob1 aDorland, William1 aJordan, Stephen, P.1 aMink, Alan uhttps://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.02232301422nas a2200241 4500008004100000245006700041210006500108520070100173100001800874700002200892700002500914700002400939700002500963700001800988700002101006700002001027700002501047700001601072700002101088700001501109700001901124856003701143 2018 eng d00aExperimental Low-Latency Device-Independent Quantum Randomness0 aExperimental LowLatency DeviceIndependent Quantum Randomness3 aApplications of randomness such as private key generation and public randomness beacons require small blocks of certified random bits on demand. Device-independent quantum random number generators can produce such random bits, but existing quantum-proof protocols and loophole-free implementations suffer from high latency, requiring many hours to produce any random bits. We demonstrate device-independent quantum randomness generation from a loophole-free Bell test with a more efficient quantum-proof protocol, obtaining multiple blocks of 512 bits with an average experiment time of less than 5 min per block and with certified error bounded by 2−64≈5.42×10−20.

1 aZhang, Yanbao1 aShalm, Lynden, K.1 aBienfang, Joshua, C.1 aStevens, Martin, J.1 aMazurek, Michael, D.1 aNam, Sae, Woo1 aAbellĂˇn, Carlos1 aAmaya, Waldimar1 aMitchell, Morgan, W.1 aFu, Honghao1 aMiller, Carl, A.1 aMink, Alan1 aKnill, Emanuel uhttps://arxiv.org/abs/1812.0778602638nas a2200265 4500008004100000245009500041210006900136260001500205300001200220490000800232520186000240100002102100700001902121700001802140700001802158700001502176700002002191700001902211700001602230700002502246700001802271700002402289700002202313856003702335 2018 eng d00aExperimentally Generated Randomness Certified by the Impossibility of Superluminal Signals0 aExperimentally Generated Randomness Certified by the Impossibili c2018/04/11 a223-2260 v5563 aFrom dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge with random number generators is that it is hard to ensure that their outputs are unpredictable. For a random number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model describing the underlying physics is required to assert unpredictability. Such a model must make a number of assumptions that may not be valid, thereby compromising the integrity of the device. However, it is possible to exploit the phenomenon of quantum nonlocality with a loophole-free Bell test to build a random number generator that can produce output that is unpredictable to any adversary limited only by general physical principles. With recent technological developments, it is now possible to carry out such a loophole-free Bell test. Here we present certified randomness obtained from a photonic Bell experiment and extract 1024 random bits uniform to within 10−12. These random bits could not have been predicted within any physical theory that prohibits superluminal signaling and allows one to make independent measurement choices. To certify and quantify the randomness, we describe a new protocol that is optimized for apparatuses characterized by a low per-trial violation of Bell inequalities. We thus enlisted an experimental result that fundamentally challenges the notion of determinism to build a system that can increase trust in random sources. In the future, random number generators based on loophole-free Bell tests may play a role in increasing the security and trust of our cryptographic systems and infrastructure.

1 aBierhorst, Peter1 aKnill, Emanuel1 aGlancy, Scott1 aZhang, Yanbao1 aMink, Alan1 aJordan, Stephen1 aRommal, Andrea1 aLiu, Yi-Kai1 aChristensen, Bradley1 aNam, Sae, Woo1 aStevens, Martin, J.1 aShalm, Lynden, K. uhttps://arxiv.org/abs/1803.0621901575nas a2200217 4500008004100000245010100041210006900142260001500211520089600226100002101122700001901143700001801162700001501180700002401195700001901219700001601238700002501254700001801279700002201297856003801319 2017 eng d00aExperimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling0 aExperimentally Generated Random Numbers Certified by the Impossi c2017/02/163 aRandom numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtained 256 new random bits, uniform to within 0.001.

1 aBierhorst, Peter1 aKnill, Emanuel1 aGlancy, Scott1 aMink, Alan1 aJordan, Stephen, P.1 aRommal, Andrea1 aLiu, Yi-Kai1 aChristensen, Bradley1 aNam, Sae, Woo1 aShalm, Lynden, K. uhttps://arxiv.org/abs/1702.05178#