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Register a new userDesign of a Quantum-Repeater using Quantum-Circuits and benchmarking its performance on an IBM Quantum-Computer
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Quantum communication relies on the existence of entanglement between two nodes of a network. Since, entanglement can only be produced using local quantum operations, distribution of parts of this entangled system between different nodes becomes necessary. However, due to the extremely fragile nature of entanglement and the presence of losses in the communication channel, the direct distribution of entanglement over large distances is nearly impossible. Quantum repeaters have been proposed to solve this problem. These enable one to establish long-range entanglement by dividing the link into smaller parts, creating entanglement between each part and connecting them up to form the full link. As researchers race to establish entanglement over larger and larger distances, it becomes essential to gauge the performance and robustness of the different protocols that go into designing a quantum repeater, before deploying them in real life. Present day noisy quantum computers are ideal for this task as they can emulate the noisy environment in a quantum communication channel and provide a benchmark for how the protocols will perform on real-life hardware. In this paper, we report the circuit-level implementation of the complete architecture of a Quantum Repeater. All the protocols of the repeater have been bench-marked on IBM Q, the worlds first publicly available cloud quantum computer. The results of our experiment provide a measure for the fidelity of entanglement current repeaters can establish. In addition, the repeater protocol provides a robust benchmark for the current state-of-the-art of quantum computing hardware.
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Uncovering the origin of the arrow of time remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the second law of thermodynamics, which declares that entropy growth proceeds from the systems entanglement with the environment. It remains to be seen, however, whether the irreversibility of time is a fundamental law of nature or whether, on the contrary, it might be circumvented. Here we show that, while in nature the complex conjugation needed for time reversal is exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state. Using this algorithm on an IBM quantum computer enables us to experimentally demonstrate a backward time dynamics for an electron scattered on a two-level impurity.
The field of quantum computing has grown from concept to demonstration devices over the past 20 years. Universal quantum computing offers efficiency in approaching problems of scientific and commercial interest, such as factoring large numbers, searching databases, simulating intractable models from quantum physics, and optimizing complex cost functions. Here, we present an 11-qubit fully-connected, programmable quantum computer in a trapped ion system composed of 13 $^{171}$Yb$^{+}$ ions. We demonstrate average single-qubit gate fidelities of 99.5$%$, average two-qubit-gate fidelities of 97.5$%$, and state preparation and measurement errors of 0.7$%$. To illustrate the capabilities of this universal platform and provide a basis for comparison with similarly-sized devices, we compile the Bernstein-Vazirani (BV) and Hidden Shift (HS) algorithms into our native gates and execute them on the hardware with average success rates of 78$%$ and 35$%$, respectively. These algorithms serve as excellent benchmarks for any type of quantum hardware, and show that our system outperforms all other currently available hardware.
Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters $K$ and $d$ of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most $d$ with at most $K$ qubits of inter-cluster quantum communication. We propose a cluster simulation scheme that can simulate any $(K,d)$-clustered quantum circuit on a $d$-qubit machine in time roughly $2^{O(K)}$, with further speedups possible when taking more fine-grained circuit structure into account. We show how our scheme can be used to simulate clustered quantum systems -- such as large molecules -- that can be partitioned into multiple significantly smaller clusters with weak interactions among them. By using a suitable clustered ansatz, we also experimentally demonstrate that a quantum variational eigensolver can still achieve the desired performance for estimating the energy of the BeH$_2$ molecule while running on a physical quantum device with half the number of required qubits.
Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time-evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter is the celebrated Heath-Jarrow-Morton framework, in which its dynamics is entirely specified by volatility factors. On its multifactor version, this model considers several noisy components to capture at best the dynamics of several time-maturing forward rates. However, as no general analytical solution is available, there is a trade-off between the number of noisy factors considered and the computational time to perform a numerical simulation. Here, we employ the quantum principal component analysis to reduce the number of noisy factors required to accurately simulate the time evolution of several time-maturing forward rates. The principal components are experimentally estimated with the $5$-qubit IBMQX2 quantum computer for $2times 2$ and $3times 3$ cross-correlation matrices, which are based on historical data for two and three time-maturing forward rates. This manuscript is a first step towards the design of a general quantum algorithm to fully simulate on quantum computers the Heath-Jarrow-Morton model for pricing interest-rate financial derivatives. It shows indeed that practical applications of quantum computers in finance will be achievable in the near future.
A new class of protocols called mirror benchmarking was recently proposed to measure the system-level performance of quantum computers. These protocols involve circuits with random sequences of gates followed by mirroring, that is, inverting each gate in the sequence. We give a simple proof that mirror benchmarking leads to an exponential decay of the survival probability with sequence length, under the uniform noise assumption, provided the twirling group forms a 2-design. The decay rate is determined by a quantity that is a quadratic function of the error channel, and for certain types of errors is equal to the unitarity. This result yields a new method for estimating the coherence of noise. We present data from mirror benchmarking experiments run on the Honeywell System Model H1. This data constitutes a set of performance curves, indicating the success probability for random circuits as a function of qubit number and circuit depth.
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