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Quantum states have high affinity for errors and hence error correction is of utmost importance to realise a quantum computer. Laflamme showed that 5 qubits are necessary to correct a single error on a qubit. In a Pauli error model, four…
Pure quantum states are often approximately encoded as classical bit strings such as those representing probability amplitudes and those describing circuits that generate the quantum states. The crucial quantity is the minimum length of…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
The sensitivity of classical and quantum sensing is impaired in a noisy environment. Thus, one of the main challenges facing sensing protocols is to reduce the noise while preserving the signal. State of the art quantum sensing protocols…
We propose a sampling-based simulation for fault-tolerant quantum error correction under coherent noise. A mixture of incoherent and coherent noise, possibly due to over-rotation, is decomposed into Clifford channels with a quasiprobability…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
As quantum computers approach the fault tolerance threshold, diagnosing and characterizing the noise on large scale quantum devices is increasingly important. One of the most important classes of noise channels is the class of Pauli…
We derive the effective channel for a logical qubit protected by an arbitrary quantum error-correcting code, and derive the map between channels induced by concatenation. For certain codes in the presence of single-bit Pauli errors, we…
A formulation for evaluating the performance of quantum error correcting codes for a general error model is presented. In this formulation, the correlation between errors is quantified by a Hamiltonian description of the noise process. We…
Quantum states are inherently fragile, making their storage a major concern for many practical applications and experimental tests of quantum mechanics. The field of quantum memories is concerned with how this storage may be achieved,…
The standard quantum error correction protocols use projective measurements to extract the error syndromes from the encoded states. We consider the more general scenario of weak measurements, where only partial information about the error…
We first present a useful characterization of additive (stabilizer) quantum error-correcting codes. Then we present several examples of We first present a useful characterization of additive (stabilizer) quantum error--correcting codes.…
Quantum noise constitutes a fundamental obstacle to realizing practical quantum technologies. To address the pivotal challenge of identifying quantum systems least affected by noise, we introduce the purest quantum state identification,…
Fault-tolerant quantum computations require alternating quantum and classical computations, where the classical computations prove vital in detecting and correcting errors in the quantum computation. Recently, interest in using these…
We study the fundamental design automation problem of equivalence checking in the NISQ (Noisy Intermediate-Scale Quantum) computing realm where quantum noise is present inevitably. The notion of approximate equivalence of (possibly noisy)…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
The demonstration of quantum error correction (QEC) is one of the most important milestones in the realization of fully-fledged quantum computers. Toward this, QEC experiments using the surface codes have recently been actively conducted.…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…