Then $p$ is the probability that you are completely misunderstood.Ī good connection or a relatively unimportant question will result in $pP_a$. And similarly a 'no' is transformed into 'yes'. For simplicity, let's imagine a case where a garbled 'yes' doesn't simply sound like nonsense, but sounds like a 'no'. If you are being asked a question on which someone's life depends, however, $P_a$ will be much lower.įor the second we can use $p$, the probability that your answer is garbled by a bad connection. If you are being asked to confirm a preference for ice cream flavours, and don't mind too much if you get vanilla rather than chocolate, $P_a$ might be quite high. For the first, we can use $P_a$, the maximum acceptable probability of being misunderstood. How important is it that you are understood correctly?īoth of these can be parameterized with probabilities.If someone asks you a question to which the answer is 'yes' or 'no', the way you give your response will depend on two factors: This allows us to begin by considering a very straightforward example: speaking on the phone.

The basic ideas behind error correction are the same for quantum information as for classical information. We will also see how it can be run on current prototype devices. Though not a true example of quantum error correction - it uses physical qubits to encode a logical bit, rather than a qubit - it serves as a simple guide to all the basic concepts in any quantum error correcting code. In this chapter we will look at a particular example of error correction: the repetition code. So when benchmarking our progress towards fault-tolerant quantum computation, we must keep track of how well our devices perform error correction. The operations on the logical qubits required to implement quantum computation will be performed by essentially making small perturbations to this procedure.īecause of the vast amount of effort required for this process, most operations performed in fault-tolerant quantum computers will be done to serve the purpose of error detection and correction. Auxiliary degrees of freedom are also constantly measured, to detect signs of errors and allow their effects to be removed. The encoding is maintained by constantly putting the physical qubits through a highly entangling circuit. This will be done through the process of quantum error correction, in which logical qubits are encoded in a large number of physical qubits. For the future era of fault-tolerance, however, we must find ways to build logical qubits from physical qubits. In the current era of quantum computing, we seek to use physical qubits despite their imperfections, by designing custom algorithms and using error mitigation effects. Instead, we refer to them as physical qubits. These qubits will always be much too imprecise to serve directly as logical qubits. However, the imperfections can never be removed entirely. The last few decades have also seen great advances in finding physical systems that behave as qubits, with better quality qubits being developed all the time. Qubits that obey these assumptions are often known as logical qubits. Most quantum algorithms developed over the past few decades have assumed that these qubits are perfect: they can be prepared in any state we desire, and be manipulated with complete precision. Quantum computing requires us to encode information in qubits. Quantum Simulation as a Search AlgorithmĮstimating Pi Using Quantum Phase Estimation Algorithm Grover's search with an unknown number of solutions Investigating Quantum Hardware Using Microwave PulsesĮxploring the Jaynes-Cummings Hamiltonian with Qiskit Pulse

Introduction to Quantum Error Correction using Repetition Codes Investigating Quantum Hardware Using Quantum Circuits Solving the Travelling Salesman Problem using Phase Estimation Quantum Edge Detection - QHED Algorithm on Small and Large Images Quantum Image Processing - FRQI and NEQR Image Representations Implementations of Recent Quantum Algorithms Hybrid quantum-classical Neural Networks with PyTorch and Qiskit Solving Satisfiability Problems using Grover's Algorithm Solving combinatorial optimization problems using QAOA Solving Linear Systems of Equations using HHL Classical Computation on a Quantum Computer

Types of quantum error