Efficient classical simulation of noisy random quantum circuits in one dimension

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.Comment: 27 pages, 9 figures, accepted for publication in Quantu

Enhanced energy-constrained quantum communication over bosonic Gaussian channels

Quantum communication is an important branch of quantum information science, promising unconditional security to classical communication and providing the building block of a future large-scale quantum network. Noise in realistic quantum communication channels imposes fundamental limits on the communication rates of various quantum communication tasks. It is therefore crucial to identify or bound the quantum capacities of a quantum channel. Here, we consider Gaussian channels that model energy loss and thermal noise errors in realistic optical and microwave communication channels and study their various quantum capacities in the energy-constrained scenario. We provide improved lower bounds to various energy-constrained quantum capacities of these fundamental channels and show that higher communication rates can be attained than previously believed. Specifically, we show that one can boost the transmission rates of quantum information and private classical information by using a correlated multi-mode thermal state instead of the single-mode thermal state of the same energy

Efficient classical simulation of noisy random quantum circuits in one dimension

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

Dissipative self-interference and robustness of continuous error-correction to miscalibration

We derive an effective equation of motion within the steady-state subspace of a large family of Markovian open systems (i.e., Lindbladians) due to perturbations of their Hamiltonians and system-bath couplings. Under mild and realistic conditions, competing dissipative processes destructively interfere without the need for fine-tuning and produce no dissipation within the steady-state subspace. In quantum error-correction, these effects imply that continuously error-correcting Lindbladians are robust to calibration errors, including miscalibrations consisting of operators undetectable by the code. A similar interference is present in more general systems if one implements a particular Hamiltonian drive, resulting in a coherent cancellation of dissipation. On the opposite extreme, we provide a simple implementation of universal Lindbladian simulation