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/2304.1048101302nas a2200133 4500008004100000245005800041210005800099260001300157520089200170100002101062700002701083700002101110856003701131 2023 eng d00aError Mitigation Thresholds in Noisy Quantum Circuits0 aError Mitigation Thresholds in Noisy Quantum Circuits c2/8/20233 a

Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the performance of such strategies when the noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the existence of an error mitigation threshold for random spatially local circuits in spatial dimensions D≥2: characterization disorder below the threshold rate allows for error mitigation up to times that scale with the number of qubits. For one-dimensional circuits, by contrast, mitigation fails at an O(1) time for any imperfection in the characterization of disorder. We discuss implications for tests of quantum computational advantage, fault-tolerant probes of measurement-induced phase transitions, and quantum algorithms in near-term devices.

1 aNiroula, Pradeep1 aGopalakrishnan, Sarang1 aGullans, Michael uhttps://arxiv.org/abs/2302.0427801590nas a2200217 4500008004100000245004000041210004000081260001400121520100000135100002101135700001601156700001501172700002201187700002001209700001901229700001901248700002101267700002201288700002501310856003701335 2023 eng d00aQuantum Sensing with Erasure Qubits0 aQuantum Sensing with Erasure Qubits c10/2/20233 a

The dominant noise in an "erasure qubit" is an erasure -- a type of error whose occurrence and location can be detected. Erasure qubits have potential to reduce the overhead associated with fault tolerance. To date, research on erasure qubits has primarily focused on quantum computing and quantum networking applications. Here, we consider the applicability of erasure qubits to quantum sensing and metrology. We show theoretically that, for the same level of noise, an erasure qubit acts as a more precise sensor or clock compared to its non-erasure counterpart. We experimentally demonstrate this by artificially injecting either erasure errors (in the form of atom loss) or dephasing errors into a differential optical lattice clock comparison, and observe enhanced precision in the case of erasure errors for the same injected error rate. Similar benefits of erasure qubits to sensing can be realized in other quantum platforms like Rydberg atoms and superconducting qubits

1 aNiroula, Pradeep1 aDolde, Jack1 aZheng, Xin1 aBringewatt, Jacob1 aEhrenberg, Adam1 aCox, Kevin, C.1 aThompson, Jeff1 aGullans, Michael1 aKolkowitz, Shimon1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2310.0151201741nas a2200181 4500008004100000245006600041210006300107260001300170520118700183100001801370700002301388700002401411700002101435700002001456700002501476700002101501856003701522 2023 eng d00aA sharp phase transition in linear cross-entropy benchmarking0 asharp phase transition in linear crossentropy benchmarking c5/8/20233 a

Demonstrations of quantum computational advantage and benchmarks of quantum processors via quantum random circuit sampling are based on evaluating the linear cross-entropy benchmark (XEB). A key question in the theory of XEB is whether it approximates the fidelity of the quantum state preparation. Previous works have shown that the XEB generically approximates the fidelity in a regime where the noise rate per qudit ε satisfies εN≪1 for a system of N qudits and that this approximation breaks down at large noise rates. Here, we show that the breakdown of XEB as a fidelity proxy occurs as a sharp phase transition at a critical value of εN that depends on the circuit architecture and properties of the two-qubit gates, including in particular their entangling power. We study the phase transition using a mapping of average two-copy quantities to statistical mechanics models in random quantum circuit architectures with full or one-dimensional connectivity. We explain the phase transition behavior in terms of spectral properties of the transfer matrix of the statistical mechanics model and identify two-qubit gate sets that exhibit the largest noise robustness.

1 aWare, Brayden1 aDeshpande, Abhinav1 aHangleiter, Dominik1 aNiroula, Pradeep1 aFefferman, Bill1 aGorshkov, Alexey, V.1 aGullans, Michael uhttps://arxiv.org/abs/2305.0495401469nas a2200133 4500008004100000245007900041210006900120260001500189520102500204100002101229700002701250700002101277856003701298 2023 eng d00aThresholds in the Robustness of Error Mitigation in Noisy Quantum Dynamics0 aThresholds in the Robustness of Error Mitigation in Noisy Quantu c10/30/20233 a

Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the robustness of such strategies when the noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the existence of a threshold in the robustness of error mitigation for random spatially local circuits in spatial dimensions D≥2: noise characterization disorder below the threshold rate allows for error mitigation up to times that scale with the number of qubits. For one-dimensional circuits, by contrast, mitigation fails at an O(1) time for any imperfection in the characterization of disorder. As a result, error mitigation is only a practical method for sufficiently well-characterized noise. We discuss further implications for tests of quantum computational advantage, fault-tolerant probes of measurement-induced phase transitions, and quantum algorithms in near-term devices.

1 aNiroula, Pradeep1 aGopalakrishnan, Sarang1 aGullans, Michael uhttps://arxiv.org/abs/2302.0427801622nas a2200145 4500008004100000245008500041210006900126260001400195520114800209100002201357700002101379700002101400700001801421856003701439 2021 eng d00aEfficient quantum programming using EASE gates on a trapped-ion quantum computer0 aEfficient quantum programming using EASE gates on a trappedion q c7/15/20213 a

Parallel operations in conventional computing have proven to be an essential tool for efficient and practical computation, and the story is not different for quantum computing. Indeed, there exists a large body of works that study advantages of parallel implementations of quantum gates for efficient quantum circuit implementations. Here, we focus on the recently invented efficient, arbitrary, simultaneously entangling (EASE) gates, available on a trapped-ion quantum computer. Leveraging its flexibility in selecting arbitrary pairs of qubits to be coupled with any degrees of entanglement, all in parallel, we show a n-qubit Clifford circuit can be implemented using 6log(n) EASE gates, a n-qubit multiply-controlled NOT gate can be implemented using 3n/2 EASE gates, and a n-qubit permutation can be implemented using six EASE gates. We discuss their implications to near-term quantum chemistry simulations and the state of the art pattern matching algorithm. Given Clifford + multiply-controlled NOT gates form a universal gate set for quantum computing, our results imply efficient quantum computation by EASE gates, in general.

1 aGrzesiak, Nikodem1 aMaksymov, Andrii1 aNiroula, Pradeep1 aNam, Yunseong uhttps://arxiv.org/abs/2107.0759101625nas a2200229 4500008004100000245008800041210006900129260001400198520092400212100001801136700002101154700001601175700002101191700001601212700002201228700001801250700002501268700002101293700002001314700002401334856003701358 2021 eng d00aObservation of measurement-induced quantum phases in a trapped-ion quantum computer0 aObservation of measurementinduced quantum phases in a trappedion c6/10/20213 a

Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the "pure" phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the "mixed" or "coding" phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge.

1 aNoel, Crystal1 aNiroula, Pradeep1 aZhu, Daiwei1 aRisinger, Andrew1 aEgan, Laird1 aBiswas, Debopriyo1 aCetina, Marko1 aGorshkov, Alexey, V.1 aGullans, Michael1 aHuse, David, A.1 aMonroe, Christopher uhttps://arxiv.org/abs/2106.0588101237nas a2200253 4500008004100000245004100041210004100082260001300123520055200136100001900688700002400707700002100731700002000752700002700772700001800799700001600817700001700833700002000850700002100870700001900891700001300910700002300923856003700946 2021 eng d00aQuantum Machine Learning for Finance0 aQuantum Machine Learning for Finance c9/9/20213 a

Quantum computers are expected to surpass the computational capabilities of classical computers during this decade, and achieve disruptive impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from Quantum Computing not only in the medium and long terms, but even in the short term. This review paper presents the state of the art of quantum algorithms for financial applications, with particular focus to those use cases that can be solved via Machine Learning.

1 aPistoia, Marco1 aAhmad, Syed, Farhan1 aAjagekar, Akshay1 aButs, Alexander1 aChakrabarti, Shouvanik1 aHerman, Dylan1 aHu, Shaohan1 aJena, Andrew1 aMinssen, Pierre1 aNiroula, Pradeep1 aRattew, Arthur1 aSun, Yue1 aYalovetzky, Romina uhttps://arxiv.org/abs/2109.0429801465nas a2200169 4500008004100000245007200041210006900113260001400182520093400196100002301130700002001153700002501173700002101198700002101219700001801240856003701258 2021 eng d00aTight bounds on the convergence of noisy random circuits to uniform0 aTight bounds on the convergence of noisy random circuits to unif c12/1/20213 a

We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we discuss recent barrier results for depth-agnostic and/or noise-agnostic proof techniques. We show that in certain depth regimes, noise-agnostic proof techniques might still work in order to prove an often-conjectured claim in the literature on quantum computational advantage, contrary to what was thought prior to this work. 

1 aDeshpande, Abhinav1 aFefferman, Bill1 aGorshkov, Alexey, V.1 aGullans, Michael1 aNiroula, Pradeep1 aShtanko, Oles uhttps://arxiv.org/abs/2112.0071602145nas a2200205 4500008004100000245005800041210005700099260001500156300001100171490000700182520152100189100002301710700002101733700002201754700002101776700002501797700002101822700002701843856006901870 2017 eng d00aEmergent equilibrium in many-body optical bistability0 aEmergent equilibrium in manybody optical bistability c2017/04/17 a0438260 v953 a

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.

1 aFoss-Feig, Michael1 aNiroula, Pradeep1 aYoung, Jeremy, T.1 aHafezi, Mohammad1 aGorshkov, Alexey, V.1 aWilson, Ryan, M.1 aMaghrebi, Mohammad, F. uhttps://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.043826