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Universal digital photonic single-qubit quantum channel simulator

Lu He, Chang Liu, Dongsheng Wang, Luo-Kan Chen, Zheng-Da Li, Xing-Can Yao, Li Li, Nai-Le Liu, Cheng-Zhi Peng, Barry C. Sanders, Yu-Ao Chen, Jian-Wei Pan

Published May 12, 2015• 3 citations
OpenAlex

Abstract

Quantum simulators, which exploit quantum effects to reveal unknown or difficult-to-compute properties of a model of interest, play a significant role in quantum information science. Quantum simulation of the dynamics of many-body system has been widely studied for various quantum computing systems, including cold atoms, trapped ions and photons. However, simulation of quantum channels, which describes one of the most general quantum processes in realistic systems, has not yet been fully explored, even for single-qubit channels. Here we report the first experimental digital quantum simulator of arbitrary single-qubit channels. We built this simulator with a set of single-qubit gates together with a single two-qubit entangling gate. We show that any single-qubit channel can be efficiently and accurately programmed and compiled by our simulator. Our scheme generalizes Hamiltonian-based simulators to channel-based digital quantum simulators, which could have important applications in quantum computation and quantum simulation.

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Quantum simulators, which exploit quantum effects to reveal unknown or difficult-to-compute properties of a model of interest, play a significant role in quantum information science. Quantum simulation of the dynamics of many-body system has been widely studied for various quantum computing systems, including cold atoms, trapped ions and photons. However, simulation of quantum channels, which describes one of the most general quantum processes in realistic systems, has not yet been fully explored, even for single-qubit channels. Here we report the first experimental digital quantum simulator of arbitrary single-qubit channels. We built this simulator with a set of single-qubit gates together with a single two-qubit entangling gate. We show that any single-qubit channel can be efficiently and accurately programmed and compiled by our simulator. Our scheme generalizes Hamiltonian-based simulators to channel-based digital quantum simulators, which could have important applications in quantum computation and quantum simulation.
Quantum channels describe general transformations of the state of a physical system and play a fundamental role in many fields. It promises wide range of applications, because any physical process can be represented as a quantum channel transforming an initial state into a final state. The evolution of system undergoing a quantum channel is not necessary unitary which makes it unrealisable without ancillary system. Inspired by the method performing non-unitary operator by the linear combination of unitary operations, we proposed a quantum algorithm for the simulation of universal single-qubit channel, described by a convex combination of two generalized extreme channels corresponding to four Kraus operators, and is scalable to arbitrary higher dimension. We demonstrate the whole algorithm experimentally using the universal IBM cloud quantum computer and study properties of different qubit quantum channels. We illustrate the quantum capacity of the general qubit quantum channels, which quantifies the amount of quantum information that can be protected. There is a general agreement between the theoretical predictions and the experiments, which strongly supported our method. By realizing arbitrary qubit channel, this work provides a universal way to explore various properties of quantum channel and novel prospect of quantum communication.
Quantum simulation is of great importance in quantum information science. Here, we report an experimental quantum channel simulator imbued with an algorithm for imitating the behavior of a general class of quantum systems. The reported quantum channel simulator consists of four single-qubit gates and one controlled-not gate. All types of quantum channels can be decomposed by the algorithm and implemented on this device. We deploy our system to simulate various quantum channels, such as quantum-noise channels and weak quantum measurement. Our results advance experimental quantum channel simulation, which is integral to the goal of quantum information processing.
A digital quantum simulator is an envisioned quantum device that can be programmed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions. With sequences of up to 100 gates and 6 qubits, the full time dynamics of a range of spin systems are digitally simulated. Interactions beyond those naturally present in our simulator are accurately reproduced, and quantitative bounds are provided for the overall simulation quality. Our results demonstrate the key principles of digital quantum simulation and provide evidence that the level of control required for a full-scale device is within reach.
Digital-analog quantum computing with two-level systems is a computational paradigm that combines an analog Hamiltonian with single-qubit gates to achieve universality. We extend this framework to ddd-level systems by conjugating an analog Hamiltonian block with single-qudit gates drawn from the Weyl-Heisenberg basis, which provides a natural set of operations for qudit architectures. More specifically, we propose a protocol to simulate arbitrary two-body Hamiltonians with at most O(d4n2)O(d^4 n^2)O(d4n2) analog blocks. The power of this approach is illustrated by the simulation of many-body qudit spin Hamiltonians including magnetic quadrupolar terms.
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here, we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully-connected set of gate operations that are native to the hardware and have a mean fidelity of 98 %. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa (DJ) and Bernstein-Vazirani (BV) algorithms with average success rates of 95 % and 90 %, respectively. We also perform a coherent quantum Fourier transform (QFT) on five trappedion qubits for phase estimation and period finding with average fidelities of 62 % and 84 %, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.
This study presents a roadmap towards utilizing a single arbitrary gate for universal quantum computing. Since two decades ago, it has been widely accepted that almost any single arbitrary gate with qubit number >2>2>2 is universal. Utilizing a single arbitrary gate for compiling is beneficial for systems with limited degrees of freedom, e.g. the scattering based quantum computing schemes. However, how to efficiently compile the wanted gate with a single arbitrary gate, and finally achieve fault-tolerant quantum computing is unknown. In this work, we show almost any target gate can be compiled to precision εεε with a circuit depth of approximately log⁡(ε−1)\log(ε^{-1})log(ε−1) with an improved brute-force compiling method. Under the assumption of reasonable classical resource, we show the gate imperfection can be lowered to 10−310^{-3}10−3. By treating the imperfection as coherent error, we show that the error can be further reduced by roughly two orders of magnitude with a measurement-free quantum error correction method.