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Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full use of quantum mechanical speedup, more transformation should be implemented on amplitudes. Here we propose the notion of quantum amplitude arithmetic (QAA) that intent to evolve the quantum state by performing arithmetic operations on amplitude. Based on the basic design of multiplication and addition operations, QAA can be applied to solve the black-box quantum state preparation problem and the quantum linear system problem with fairly low complexity, and evaluate nonlinear functions on amplitudes directly. QAA is expected to find applications in a variety of quantum algorithms.
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We describe a general-purpose framework to design quantum algorithms relying upon an efficient handling of arrays. The corner-stone of the framework is the direct embedding of information into quantum amplitudes, thus avoiding the need to deal with square roots or encode the information in registers. We discuss the entire pipeline, from data loading to information extraction. Particular attention is devoted to the definition of an efficient tool-kit of quantum arithmetic operations on arrays. We comment on strong and weak points of the proposed manipulations, especially in relation to an effective exploitation of quantum parallelism. Eventually, we give explicit examples regarding the manipulation of generic oracles.
We evaluate the performance of quantum arithmetic algorithms run on a distributed quantum computer (a quantum multicomputer). We vary the node capacity and I/O capabilities, and the network topology. The tradeoff of choosing between gates executed remotely, through ``teleported gates on entangled pairs of qubits (telegate), versus exchanging the relevant qubits via quantum teleportation, then executing the algorithm using local gates (teledata), is examined. We show that the teledata approach performs better, and that carry-ripple adders perform well when the teleportation block is decomposed so that the key quantum operations can be parallelized. A node size of only a few logical qubits performs adequately provided that the nodes have two transceiver qubits. A linear network topology performs acceptably for a broad range of system sizes and performance parameters. We therefore recommend pursuing small, high-I/O bandwidth nodes and a simple network. Such a machine will run Shors algorithm for factoring large numbers efficiently.
In this paper we derive from simple and reasonable assumptions a Gaussian noise model for NISQ Quantum Amplitude Estimation (QAE). We provide results from QAE run on various IBM superconducting quantum computers and Honeywells H1 trapped-ion quantum computer to show that the proposed model is a good fit for real-world experimental data. We then give an example of how to embed this noise model into any NISQ QAE algorithm, such that the amplitude estimation is noise-aware.
Quantum entanglement is a critical resource for quantum information and quantum computation. However, entanglement of a quantum system is subjected to change due to the interaction with the environment. One typical result of the interaction is the amplitude damping that usually results in the reduction of the entanglement. Here we propose a protocol to protect quantum entanglement from the amplitude damping by applying Hadamard and CNOT gates. As opposed to some recently studied methods, the scheme presented here does not require weak measurement in the reversal process, leading to a faster recovery of entanglement. We propose a possible experimental implementation based on linear optical system.
Quantum gates are typically vulnerable to imperfections in the classical control fields applied to physical qubits to drive the gates. One approach to reduce this source of error is to break the gate into parts, known as textit{composite pulses} (CPs), that typically leverage the constancy of the error over time to mitigate its impact on gate fidelity. Here we extend this technique to suppress textit{secular drifts} in Rabi frequency by regarding them as sums of textit{power-law drifts} whose first-order effects on over- or under-rotation of the state vector add linearly. We show that composite pulses that suppress the power-law drifts $t^p$ for all $p leq n$ are also high-pass filters of textit{filter order} $n+1$ cite{ball_walsh-synthesized_2015}. We present sequences that satisfy our proposed textit{power law amplitude} $text{PLA}(n)$ criteria, obtained with this technique, and compare their simulated performance under time-dependent amplitude errors to some traditional composite pulse sequences. We find that there is a range of noise frequencies for which the $text{PLA}(n)$ sequences provide more error suppression than the traditional sequences, but in the low frequency limit, non-linear effects become more important for gate fidelity than frequency roll-off. As a result, the previously known $F_1$ sequence, which is one of the two solutions to the $text{PLA}(1)$ criteria and furnishes suppression of both linear secular drift and the first order nonlinear effects, is a better noise filter than any of the other $text{PLA}(n)$ sequences in the low frequency limit.
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