Related papers: Error correction schemes for fully correlated quan…
The low-energy subspace of a conformal field theory (CFT) can serve as a quantum error correcting code, with important consequences in holography and quantum gravity. We consider generic 1+1D CFT codes under extensive local dephasing…
Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations,…
From the set of operators for errors and its correction code, we introduce the so-called complete unitary transformation. It can be used for encoding while the inverse of it can be applied for correcting the errors of the encoded qubit. We…
In multi-qubit system, correlated errors subject to unwanted interactions with other qubits is one of the major obstacles for scaling up quantum computers to be applicable. We present two approaches to correct such noise and demonstrate…
In order to reduce errors, error correction codes (ECCs) need to be implemented fast. They can correct the errors corresponding to the first few orders in the Taylor expansion of the Hamiltonian of the interaction with the environment. If…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
We present a universal fault-tolerant quantum computing architecture based on identical particle qubits (IPQs), where we find that the first-order IPQ - bath interaction fundamentally differs from the conventional first-order qubit-bath…
We present a set of efficiently implementable logical multi-qubit gates in concatenated quantum error correction codes using parity qubits. In particular, we show how fault-tolerant high-weight rotation gates of arbitrary angle can be…
I give a pedagogical account of Shor's nine-bit code for correcting arbitrary errors on single qubits, and I review work that determines when it is possible to maintain quantum coherence by reversing the deleterious effects of open-system…
Homomorphic quantum error correction aims to protect quantum data against both unauthorized access and environmental noise during server-based processing. We investigate the algebraic compatibility between quantum homomorphic encryption and…
The errors that arise in a quantum channel can be corrected perfectly if and only if the channel does not decrease the coherent information of the input state. We show that, if the loss of coherent information is small, then approximate…
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4…
Error filtration is a hardware scheme that mitigates noise by exploiting auxiliary qubits and entangling gates. Although both signal and ancillas are subject to local noise, constructive interference(and in some cases post-selection) allows…
We show that quantum feedback control can be used as a quantum error correction process for errors induced by weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per…
Polynomial multiplication stands out as a highly demanding arithmetic process in the development of post-quantum cryptosystems. The importance of the number-theoretic transform (NTT) extends beyond post-quantum cryptosystems, proving…
Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to…
Fault-tolerant quantum computers which can solve hard problems rely on quantum error correction. One of the most promising error correction codes is the surface code, which requires universal gate fidelities exceeding the error correction…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
A frequently encountered source of systematic error in quantum computations is imperfections in the control pulses which are the classical fields that control qubit gate operations. From an analysis of the quantum mechanical time-evolution…
We construct a universal set of high fidelity quantum gates to be used on a sparse bipartite lattice with always-on Ising couplings. The gates are based on dynamical decoupling sequences using shaped pulses, they protect against…