As an application of fault-tolerant quantum computers, we consider radiation transport calculations in this study. Radiation transport calculation using Monte Carlo calculation can obtain a solution to even a problem difficult to solve analytically. However, it is time-consuming depending on the scale and precision of the problem. Because it is known that the computational complexity of Monte Carlo calculation can be square rooted by quantum amplitude estimation, acceleration can be expected if radiation transport calculation is run on a quantum computer. In this study, we designed and investigated a quantum circuit for a simplified transport calculation in which the reaction is only forward scattering or absorption and the energy and time do not change as well as showed the possibility of acceleration the calculation. Further, we estimated the number of logical qubits required to solve practical problems based on the quantum circuit.
As an application of fault-tolerant quantum computers, we consider radiation transport calculations in this study. Radiation transport calculation using Monte Carlo calculation can obtain a solution to even a problem difficult to solve analytically. However, it is time-consuming depending on the scale and precision of the problem. Because it is known that the computational complexity of Monte Carlo calculation can be square rooted by quantum amplitude estimation, acceleration can be expected if radiation transport calculation is run on a quantum computer. In this study, we designed and investigated a quantum circuit for a simplified transport calculation in which the reaction is only forward scattering or absorption and the energy and time do not change as well as showed the possibility of acceleration the calculation. Further, we estimated the number of logical qubits required to solve practical problems based on the quantum circuit.
Quantum computing performance simulators are needed to provide practical metrics for the effectiveness of executing theoretical quantum information processing protocols on physical hardware. In this work, we present a tool to simulate the execution of fault-tolerant quantum computation by automating the tracking of common fault paths for error propagation through an encoded circuit block and quantifying the failure probability of each encoded qubit throughout the circuit. Our simulator runs a fault path counter on encoded circuit blocks to determine the probability that two or more errors remain on the encoded qubits after each block is executed, and it combines errors from all the encoded blocks to estimate performance metrics such as the logical qubit failure probability, the overall circuit failure probability, the number of qubits used, and the time required to run the overall circuit. Our technique efficiently estimates the upper bound of the error probability and provides a useful measure of the error threshold at low error probabilities where conventional Monte Carlo methods are ineffective. We describe a way of simplifying the fault-tolerant measurement process in the Steane code to reduce the number of error correction steps necessary. We present simulation results comparing the execution of quantum adders, which constitute a major part of Shor’s algorithm.
The radiation transfer equation is widely used for simulations, for example, heat transfer in engineering, diffuse optical tomography in healthcare, and radiation hydrodynamics in astrophysics. By combining the lattice Boltzmann method, we propose a quantum algorithm for radiative transfer. This algorithm encompasses all the essential physical processes of radiative transfer: absorption, scattering, and emission. Although a sufficient number of measurements are required to precisely estimate the quantum state, and the initial encoding of the quantum state remains a challenging problem, our quantum algorithm exponentially accelerates radiative-transfer calculations compared to classical algorithms. In order to verify the quantum algorithm, we perform quantum circuit simulation using IBM Qiskit Aer and find good agreement between our numerical result and the exact solution. The algorithm paves the way for applications, such as fault-tolerant quantum computers for plasma engineering, telecommunications, nuclear-fusion technology, healthcare, and astrophysics. Published by the American Physical Society 2024
Computing the ground-state properties of quantum many-body systems is a promising application of near-term quantum hardware with a potential impact in many fields. The conventional algorithm quantum phase estimation uses deep circuits and requires fault-tolerant technologies. Many quantum simulation algorithms developed recently work in an inexact and variational manner to exploit shallow circuits. In this work, we combine quantum Monte Carlo with quantum computing and propose an algorithm for simulating the imaginary-time evolution and solving the ground-state problem. By sampling the real-time evolution operator with a random evolution time according to a modified Cauchy-Lorentz distribution, we can compute the expected value of an observable in imaginary-time evolution. Our algorithm approaches the exact solution given a circuit depth increasing polylogarithmically with the desired accuracy. Compared with quantum phase estimation, the Trotter step number, i.e. the circuit depth, can be thousands of times smaller to achieve the same accuracy in the ground-state energy. We verify the resilience to Trotterisation errors caused by the finite circuit depth in the numerical simulation of various models. The results show that Monte Carlo quantum simulation is promising even without a fully fault-tolerant quantum computer.
Quantum performance simulators can provide practical metrics for the effectiveness of executing theoretical quantum information processing protocols on physical hardware. In this work we present a scheme to simulate the performance of fault tolerant quantum computation by automating the tracking of common fault paths for error propagation through a circuit and quantifying the fidelity of each qubit throughout the computation. Our simulation tool outputs the expected execution time, required number of qubits and the final error rate of running common fault tolerant protocols on a universal hardware, assumed to be a network of qubits with full connectivity. Our technique efficiently estimates the upper bound of error probability and provides a useful performance measure of the error threshold at low error rates where conventional Monte Carlo methods are ineffective. To verify the proposed simulator, we present simulation results comparing the execution of quantum adders which constitute a major part of Shor's algorithm.
Solid state quantum computer architectures are often touted as inherently scalable on the basis of proven classical architecture miniaturisation - i.e. through sheer ease of component replication. However, this weak scaling argument misses the vast complexity of the implementation of fault-tolerant quantum protocols required to protect quantum information processing against errors. In a successful design of strongly scalable quantum computer architecture, highly non-trivial requirements such as qubit transport, logic gates for physically separated qubits, fast read-out and resources for classical processing and error correction must be incorporated. We review a new adiabatic scheme coherent (spin) transport by adiabatic passage (CTAP) for physical qubit transport particularly suited to atomic and solid-state systems. The tunnelling rates, transfer times and the effects of decoherence are calculated for CTAP using phosphorous donors in silicon. Using CTAP qubit transport we have proposed a bi-linear donor electron spin architecture with potential for scale-up to fault-tolerant operation. This architecture allows for the distribution of interaction, storage and readout regions and incorporates non-nearest-neighbour interactions between qubits. The transport rails which provide these non-local interactions, also provide alternative pathways to avoid non-functioning regions. The key questions under investigation are whether one can: perform fault-tolerant quantum computation on such an architecture, and determine quantitative estimates of the fault-tolerant threshold.
Quantum algorithms are often represented in terms of quantum circuits operating on ideal (logical) qubits. However, the practical implementation of these algorithms poses significant challenges. Many quantum algorithms require a substantial number of logical qubits, and the inherent susceptibility to errors of quantum computers require quantum error correction. The integration of error correction introduces overhead in terms of both space (physical qubits required) and runtime (how long the algorithm needs to be run for). This paper addresses the complexity of comparing classical and quantum algorithms, primarily stemming from the additional quantum error correction overhead. We propose a comprehensive framework that facilitates a direct and meaningful comparison between classical and quantum algorithms. By acknowledging and addressing the challenges introduced by quantum error correction, our framework aims to provide a clearer understanding of the comparative performance of classical and quantum computing approaches. This work contributes to understanding the practical viability and potential advantages of quantum algorithms in real-world applications. We apply our framework to quantum cryptanalysis, since it is well known that quantum algorithms can break factoring and discrete logarithm based cryptography and weaken symmetric cryptography and hash functions. In order to estimate the real-world impact of these attacks, apart from tracking the development of fault-tolerant quantum computers it is important to have an estimate of the resources needed to implement these quantum attacks. This analysis provides state-of-the art snap-shot estimates of the realistic costs of implementing quantum attacks on these important cryptographic algorithms, assuming quantum fault-tolerance is achieved using surface code methods, and spanning a range of potential error rates. These estimates serve as a guide for gauging the realistic impact of these algorithms and for benchmarking the impact of future advances in quantum algorithms, circuit synthesis and optimization, fault-tolerance methods and physical error rates.