01467nas a2200193 4500008004100000245005900041210005900100260001400159520089600173100002101069700003001090700001901120700001801139700001601157700002401173700001801197700002101215856003701236 2024 eng d00aPhase transition in magic with random quantum circuits0 aPhase transition in magic with random quantum circuits c4/11/20243 a

Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards efficient and practical fault-tolerant computation. We observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic, which we characterize through analytic, numeric and experimental probes. Below a critical error rate, stabilizer syndrome measurements remove the accumulated magic in the circuit, effectively protecting against coherent errors; above the critical error rate syndrome measurements concentrate magic. A better understanding of such rich behavior in the resource theory of magic could shed more light on origins of quantum speedup and pave pathways for more efficient magic state generation.

1 aNiroula, Pradeep1 aWhite, Christopher, David1 aWang, Qingfeng1 aJohri, Sonika1 aZhu, Daiwei1 aMonroe, Christopher1 aNoel, Crystal1 aGullans, Michael uhttps://arxiv.org/abs/2304.1048101229nas a2200157 4500008004100000245007900041210006900120260001300189520074400202100001900946700001700965700001300982700002100995700001801016856003701034 2023 eng d00aEver more optimized simulations of fermionic systems on a quantum computer0 aEver more optimized simulations of fermionic systems on a quantu c3/6/20233 a

Despite using a novel model of computation, quantum computers break down programs into elementary gates. Among such gates, entangling gates are the most expensive. In the context of fermionic simulations, we develop a suite of compilation and optimization techniques that massively reduce the entangling-gate counts. We exploit the well-studied non-quantum optimization algorithms to achieve up to 24\% savings over the state of the art for several small-molecule simulations, with no loss of accuracy or hidden costs. Our methodologies straightforwardly generalize to wider classes of near-term simulations of the ground state of a fermionic system or real-time simulations probing dynamical properties of a fermionic system. 

1 aWang, Qingfeng1 aCian, Ze-Pei1 aLi, Ming1 aMarkov, Igor, L.1 aNam, Yunseong uhttps://arxiv.org/abs/2303.0346001894nas a2200301 4500008004100000245006400041210006300105260001400168520102800182100001601210700001701226700001801243700002101261700002201282700001601304700001701320700002201337700003001359700002201389700001901411700002101430700001801451700001801469700002301487700002101510700002401531856003701555 2021 eng d00aCross-Platform Comparison of Arbitrary Quantum Computations0 aCrossPlatform Comparison of Arbitrary Quantum Computations c7/27/20213 a

As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information for a single QC. On the other hand, a comparison between different QCs on the same arbitrary circuit provides a lower-bound for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform fidelities.

1 aZhu, Daiwei1 aCian, Ze-Pei1 aNoel, Crystal1 aRisinger, Andrew1 aBiswas, Debopriyo1 aEgan, Laird1 aZhu, Yingyue1 aGreen, Alaina, M.1 aAlderete, Cinthia, Huerta1 aNguyen, Nhung, H.1 aWang, Qingfeng1 aMaksymov, Andrii1 aNam, Yunseong1 aCetina, Marko1 aLinke, Norbert, M.1 aHafezi, Mohammad1 aMonroe, Christopher uhttps://arxiv.org/abs/2107.1138702349nas a2200313 4500008004100000245007100041210006900112260001400181520145100195100001601646700003401662700001701696700001801713700001301731700001801744700001901762700002101781700001401802700002201816700001601838700002501854700001801879700001901897700002001916700002001936700001801956700002401974856003701998 2021 eng d00aInteractive Protocols for Classically-Verifiable Quantum Advantage0 aInteractive Protocols for ClassicallyVerifiable Quantum Advantag c12/9/20213 a

Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output is itself classically intractable. On the other hand, certain quantum algorithms (e.g. prime factorization via Shor's algorithm) are efficiently verifiable, but require more resources than what is available on near-term devices. One way to bridge the gap between verifiability and implementation is to use "interactions" between a prover and a verifier. By leveraging cryptographic functions, such protocols enable the classical verifier to enforce consistency in a quantum prover's responses across multiple rounds of interaction. In this work, we demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer. We execute two complementary protocols -- one based upon the learning with errors problem and another where the cryptographic construction implements a computational Bell test. To perform multiple rounds of interaction, we implement mid-circuit measurements on a subset of trapped ion qubits, with subsequent coherent evolution. For both protocols, the performance exceeds the asymptotic bound for classical behavior; maintaining this fidelity at scale would conclusively demonstrate verifiable quantum advantage.

1 aZhu, Daiwei1 aKahanamoku-Meyer, Gregory, D.1 aLewis, Laura1 aNoel, Crystal1 aKatz, Or1 aHarraz, Bahaa1 aWang, Qingfeng1 aRisinger, Andrew1 aFeng, Lei1 aBiswas, Debopriyo1 aEgan, Laird1 aGheorghiu, Alexandru1 aNam, Yunseong1 aVidick, Thomas1 aVazirani, Umesh1 aYao, Norman, Y.1 aCetina, Marko1 aMonroe, Christopher uhttps://arxiv.org/abs/2112.0515602193nas a2200157 4500008004100000245010400041210006900145260001400214490000600228520169000234100001901924700001301943700002401956700001801980856003701998 2021 eng d00aResource-Optimized Fermionic Local-Hamiltonian Simulation on Quantum Computer for Quantum Chemistry0 aResourceOptimized Fermionic LocalHamiltonian Simulation on Quant c7/21/20210 v53 a

The ability to simulate a fermionic system on a quantum computer is expected to revolutionize chemical engineering, materials design, nuclear physics, to name a few. Thus, optimizing the simulation circuits is of significance in harnessing the power of quantum computers. Here, we address this problem in two aspects. In the fault-tolerant regime, we optimize the $\rzgate$ and $\tgate$ gate counts along with the ancilla qubit counts required, assuming the use of a product-formula algorithm for implementation. We obtain a savings ratio of two in the gate counts and a savings ratio of eleven in the number of ancilla qubits required over the state of the art. In the pre-fault tolerant regime, we optimize the two-qubit gate counts, assuming the use of the variational quantum eigensolver (VQE) approach. Specific to the latter, we present a framework that enables bootstrapping the VQE progression towards the convergence of the ground-state energy of the fermionic system. This framework, based on perturbation theory, is capable of improving the energy estimate at each cycle of the VQE progression, by about a factor of three closer to the known ground-state energy compared to the standard VQE approach in the test-bed, classically-accessible system of the water molecule. The improved energy estimate in turn results in a commensurate level of savings of quantum resources, such as the number of qubits and quantum gates, required to be within a pre-specified tolerance from the known ground-state energy. We also explore a suite of generalized transformations of fermion to qubit operators and show that resource-requirement savings of up to more than 20% is possible.

1 aWang, Qingfeng1 aLi, Ming1 aMonroe, Christopher1 aNam, Yunseong uhttps://arxiv.org/abs/2004.04151