01667nas a2200157 4500008004100000245007000041210006800111260001400179520117400193653002701367653003101394100001601425700001801441700001301459856003701472 2022 eng d00aComputational self-testing of multi-qubit states and measurements0 aComputational selftesting of multiqubit states and measurements c1/31/20223 a

Self-testing is a fundamental technique within quantum information theory that allows a classical verifier to force (untrusted) quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under standard computational assumptions. In this work, we generalize their techniques to give the first protocol that self-tests N EPR pairs and measurements in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ϵ must be poly(N,ϵ)-close to being honest in the appropriate sense. In particular, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a cloud quantum computer, on which we cannot enforce spatial separation, using only classical communication.

10aFOS: Physical sciences10aQuantum Physics (quant-ph)1 aFu, Honghao1 aWang, Daochen1 aZhao, Qi uhttps://arxiv.org/abs/2201.1343002428nas a2200217 4500008004100000245010600041210006900147260001400216520171900230653004301949653002701992653002902019653003102048100001702079700001502096700001302111700001702124700001602141700001602157856003702173 2022 eng d00aEfficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning0 aEfficient and practical quantum compiler towards multiqubit syst c4/14/20223 a

Efficient quantum compiling tactics greatly enhance the capability of quantum computers to execute complicated quantum algorithms. Due to its fundamental importance, a plethora of quantum compilers has been designed in past years. However, there are several caveats to current protocols, which are low optimality, high inference time, limited scalability, and lack of universality. To compensate for these defects, here we devise an efficient and practical quantum compiler assisted by advanced deep reinforcement learning (RL) techniques, i.e., data generation, deep Q-learning, and AQ* search. In this way, our protocol is compatible with various quantum machines and can be used to compile multi-qubit operators. We systematically evaluate the performance of our proposal in compiling quantum operators with both inverse-closed and inverse-free universal basis sets. In the task of single-qubit operator compiling, our proposal outperforms other RL-based quantum compilers in the measure of compiling sequence length and inference time. Meanwhile, the output solution is near-optimal, guaranteed by the Solovay-Kitaev theorem. Notably, for the inverse-free universal basis set, the achieved sequence length complexity is comparable with the inverse-based setting and dramatically advances previous methods. These empirical results contribute to improving the inverse-free Solovay-Kitaev theorem. In addition, for the first time, we demonstrate how to leverage RL-based quantum compilers to accomplish two-qubit operator compiling. The achieved results open an avenue for integrating RL with quantum compiling to unify efficiency and practicality and thus facilitate the exploration of quantum advantages.

10aFOS: Computer and information sciences10aFOS: Physical sciences10aMachine Learning (cs.LG)10aQuantum Physics (quant-ph)1 aChen, Qiuhao1 aDu, Yuxuan1 aZhao, Qi1 aJiao, Yuling1 aLu, Xiliang1 aWu, Xingyao uhttps://arxiv.org/abs/2204.0690402559nas a2200193 4500008004100000245008700041210006900128260001400197520194300211653002102154653002702175653003302202653003102235100001302266700001802279700001802297700001302315856003702328 2022 eng d00aA theory of quantum differential equation solvers: limitations and fast-forwarding0 atheory of quantum differential equation solvers limitations and  c11/9/20223 a

We study the limitations and fast-forwarding of quantum algorithms for solving linear ordinary differential equation (ODE) systems with particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the ODE is inhomogeneous. On the one hand, for generic homogeneous linear ODEs, by proving worst-case lower bounds, we show that quantum algorithms suffer from computational overheads due to two types of ``non-quantumness'': real part gap and non-normality of the coefficient matrix. We then show that ODEs in the absence of both types of ``non-quantumness'' are equivalent to quantum dynamics, and reach the conclusion that quantum algorithms for quantum dynamics work best. We generalize our results to the inhomogeneous case and find that existing generic quantum ODE solvers cannot be substantially improved. To obtain these lower bounds, we propose a general framework for proving lower bounds on quantum algorithms that are amplifiers, meaning that they amplify the difference between a pair of input quantum states. On the other hand, we show how to fast-forward quantum algorithms for solving special classes of ODEs which leads to improved efficiency. More specifically, we obtain quadratic to exponential improvements in terms of the evolution time T and the spectral norm of the coefficient matrix for the following classes of ODEs: inhomogeneous ODEs with a negative definite coefficient matrix, inhomogeneous ODEs with a coefficient matrix having an eigenbasis that can be efficiently prepared on a quantum computer and eigenvalues that can be efficiently computed classically, and the spatially discretized inhomogeneous heat equation and advection-diffusion equation. We give fast-forwarding algorithms that are conceptually different from existing ones in the sense that they neither require time discretization nor solving high-dimensional linear systems.

10aFOS: Mathematics10aFOS: Physical sciences10aNumerical Analysis (math.NA)10aQuantum Physics (quant-ph)1 aAn, Dong1 aLiu, Jin-Peng1 aWang, Daochen1 aZhao, Qi uhttps://arxiv.org/abs/2211.0524601535nas a2200181 4500008004100000022001400041245005100055210005100106260001400157490000800171520104700179100001501226700001701241700001501258700001301273700001401286856005301300 2021 eng d a1079-711400aQuantum Simulation with Hybrid Tensor Networks0 aQuantum Simulation with Hybrid Tensor Networks c8/31/20210 v1273 a

Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors, inheriting both their distinct features in efficient representation of many-body wave functions. With the example of hybrid tree tensor networks, we demonstrate efficient quantum simulation using a quantum computer whose size is significantly smaller than the one of the target system. We numerically benchmark our method for finding the ground state of 1D and 2D spin systems of up to 8×8 and 9×8 qubits with operations only acting on 8+1 and 9+1 qubits,~respectively. Our approach sheds light on simulation of large practical problems with intermediate-scale quantum computers, with potential applications in chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.

1 aYuan, Xiao1 aSun, Jinzhao1 aLiu, Junyu1 aZhao, Qi1 aZhou, You uhttp://dx.doi.org/10.1103/PhysRevLett.127.040501