01951nas a2200217 4500008004100000245008300041210006900124260001500193490000600208520129200214100002001506700002301526700001701549700002201566700002401588700002301612700001301635700002301648700002501671856003701696 2022 eng d00aImplementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions0 aImplementing a Fast Unbounded Quantum Fanout Gate Using PowerLaw c10/27/20220 v43 a
The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/rα in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor's algorithm to be performed on a D-dimensional lattice in time logarithmic in the number of qubits for interactions with α≤D. As a corollary, we show that power-law systems with α≤D are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a new technique to give a general lower bound, linear in the size of the system, on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than is possible with previously available techniques.
1 aGuo, Andrew, Y.1 aDeshpande, Abhinav1 aChu, Su-Kuan1 aEldredge, Zachary1 aBienias, Przemyslaw1 aDevulapalli, Dhruv1 aSu, Yuan1 aChilds, Andrew, M.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2007.0066201561nas a2200169 4500008004100000245007300041210006900114260001300183490000800196520105300204100001901257700001701276700001301293700002301306700002501329856003701354 2020 eng d00aDestructive Error Interference in Product-Formula Lattice Simulation0 aDestructive Error Interference in ProductFormula Lattice Simulat c6/4/20200 v1243 aQuantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of n sites for time t using the first-order product formula with r time slices is O(nt/r+nt3/r2) when nt2/r is less than a small constant. Given an error tolerance ε, the error bound yields an estimate of max{O(n2t/ε),O(n2t3/2/ε1/2)} for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [PNAS 115, 9456-9461 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.
1 aTran, Minh, C.1 aChu, Su-Kuan1 aSu, Yuan1 aChilds, Andrew, M.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1912.1104701434nas a2200193 4500008004100000245005500041210005500096260001500151490000800166520090200174100001701076700001601093700001701109700001801126700002101144700001701165700002101182856003701203 2019 eng d00aPhoton pair condensation by engineered dissipation0 aPhoton pair condensation by engineered dissipation c04/02/20190 v1233 aDissipation can usually induce detrimental decoherence in a quantum system. However, engineered dissipation can be used to prepare and stabilize coherent quantum many-body states. Here, we show that by engineering dissipators containing photon pair operators, one can stabilize an exotic dark state, which is a condensate of photon pairs with a phase-nematic order. In this system, the usual superfluid order parameter, i.e. single-photon correlation, is absent, while the photon pair correlation exhibits long-range order. Although the dark state is not unique due to multiple parity sectors, we devise an additional type of dissipators to stabilize the dark state in a particular parity sector via a diffusive annihilation process which obeys Glauber dynamics in an Ising model. Furthermore, we propose an implementation of these photon-pair dissipators in circuit-QED architecture.
1 aCian, Ze-Pei1 aZhu, Guanyu1 aChu, Su-Kuan1 aSeif, Alireza1 aDeGottardi, Wade1 aJiang, Liang1 aHafezi, Mohammad uhttps://arxiv.org/abs/1904.0001601611nas a2200205 4500008004100000245008100041210006900122260001500191490000800206520098000214100001701194700001601211700002401227700002201251700002501273700002401298700002101322700002501343856003701368 2019 eng d00aScale-Invariant Continuous Entanglement Renormalization of a Chern Insulator0 aScaleInvariant Continuous Entanglement Renormalization of a Cher c03/27/20190 v1223 aThe multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.
1 aChu, Su-Kuan1 aZhu, Guanyu1 aGarrison, James, R.1 aEldredge, Zachary1 aCuriel, Ana, Valdés1 aBienias, Przemyslaw1 aSpielman, I., B.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1807.1148601463nas a2200121 4500008004100000245007300041210006900114520107000183100001701253700001601270700001801286856003701304 2018 eng d00aTwo-Dimensional Dilaton Gravity Theory and Lattice Schwarzian Theory0 aTwoDimensional Dilaton Gravity Theory and Lattice Schwarzian The3 a