More Like this

1. Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers

   https://doi.org/10.1039/d0cp05444e  

   Wang, David Z.; Gauthier, Aidan Q.; Siegmund, Ashley E.; Hunt, Katharine L. (March 2021, Physical Chemistry Chemical Physics)

   null (Ed.)

   This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A , B , and C , with a fixed angle θ between A and B and a range of angles θ ′ between B and C . For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser–Horne–Shimony–Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M . We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M , whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ ′. 

   more » « less
2. Quantum Query Complexity of Entropy Estimation

   https://doi.org/10.1109/TIT.2018.2883306  

   Li, Tongyang; Wu, Xiaodi (April 2019, IEEE Transactions on Information Theory)

   Estimation of Shannon and Rényi entropies of unknown discrete distributions is a fundamental problem in statistical property testing. In this paper, we give the first quantum algorithms for estimating α-Rényi entropies (Shannon entropy being 1-Rényi entropy). In particular, we demonstrate a quadratic quantum speedup for Shannon entropy estimation and a generic quantum speedup for α-Rényi entropy estimation for all α ≥ 0, including tight bounds for the Shannon entropy, the Hartley entropy (α = 0), and the collision entropy (α = 2). We also provide quantum upper bounds for estimating min-entropy (α = +∞) as well as the Kullback-Leibler divergence. We complement our results with quantum lower bounds on α- Rényi entropy estimation for all α ≥ 0. Our approach is inspired by the pioneering work of Bravyi, Harrow, and Hassidim (BHH) [1], however, with many new technical ingredients: (1) we improve the error dependence of the BHH framework by a fine-tuned error analysis together with Montanaro’s approach to estimating the expected output of quantum subroutines [2] for α = 0, 1; (2) we develop a procedure, similar to cooling schedules in simulated annealing, for general α ≥ 0; (3) in the cases of integer α ≥ 2 and α = +∞, we reduce the entropy estimation problem to the α-distinctness and the ⌈log n⌉-distinctness problems, respectively. 

   more » « less
3. Efficient classical simulation of noisy random quantum circuits in one dimension

   https://doi.org/10.22331/q-2020-09-11-318  

   Noh, Kyungjoo; Jiang, Liang; Fefferman, Bill (September 2020, Quantum)

   Understanding the computational power of noisy intermediate-scale quantum (NISQ) devices is of both fundamental and practical importance to quantum information science. Here, we address the question of whether error-uncorrected noisy quantum computers can provide computational advantage over classical computers. Specifically, we study noisy random circuit sampling in one dimension (or 1D noisy RCS) as a simple model for exploring the effects of noise on the computational power of a noisy quantum device. In particular, we simulate the real-time dynamics of 1D noisy random quantum circuits via matrix product operators (MPOs) and characterize the computational power of the 1D noisy quantum system by using a metric we call MPO entanglement entropy. The latter metric is chosen because it determines the cost of classical MPO simulation. We numerically demonstrate that for the two-qubit gate error rates we considered, there exists a characteristic system size above which adding more qubits does not bring about an exponential growth of the cost of classical MPO simulation of 1D noisy systems. Specifically, we show that above the characteristic system size, there is an optimal circuit depth, independent of the system size, where the MPO entanglement entropy is maximized. Most importantly, the maximum achievable MPO entanglement entropy is bounded by a constant that depends only on the gate error rate, not on the system size. We also provide a heuristic analysis to get the scaling of the maximum achievable MPO entanglement entropy as a function of the gate error rate. The obtained scaling suggests that although the cost of MPO simulation does not increase exponentially in the system size above a certain characteristic system size, it does increase exponentially as the gate error rate decreases, possibly making classical simulation practically not feasible even with state-of-the-art supercomputers. 

   more » « less
4. Entanglement capacity of fermionic Gaussian states

   https://doi.org/10.1088/1751-8121/acfc06  

   Huang, Youyi; Wei, Lu (October 2023, Journal of Physics A: Mathematical and Theoretical)

   Abstract We study the capacity of entanglement as an alternative to entanglement entropies in estimating the degree of entanglement of quantum bipartite systems over fermionic Gaussian states. In particular, we derive the exact and asymptotic formulas of average capacity of two different cases—with and without particle number constraints. For the later case, the obtained formulas generalize some partial results of average capacity in the literature. The key ingredient in deriving the results is a set of new tools for simplifying finite summations developed very recently in the study of entanglement entropy of fermionic Gaussian states. 

   more » « less
5. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays

   https://doi.org/10.1126/science.aax9743  

   Omran, A.; Levine, H.; Keesling, A.; Semeghini, G.; Wang, T. T.; Ebadi, S.; Bernien, H.; Zibrov, A. S.; Pichler, H.; Choi, S.; et al (August 2019, Science)

   Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging because such states are extremely fragile. Using a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states, we demonstrate the creation of “Schrödinger cat” states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits. Our approach is based on engineering the energy spectrum and using optimal control of the many-body system. We further demonstrate entanglement manipulation by using GHZ states to distribute entanglement to distant sites in the array, establishing important ingredients for quantum information processing and quantum metrology. 

   more » « less