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The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these…
Protecting quantum information through quantum error correction (QEC) is a cornerstone of future fault-tolerant quantum computation. However, current QEC-protected logical qubits have only achieved coherence times about twice those of their…
We investigate an efficient quantum error correction of a fully correlated noise. Suppose the noise is characterized by a quantum channel whose error operators take fully correlated forms given by $\sigma_x^{\otimes n}$, $\sigma_y^{\otimes…
Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. As a novel approach, quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the…
Quantum resources can, in principle, enable Heisenberg-limited (HL) sensing, yet no-go theorems imply that HL scaling is generically unattainable in realistic noisy devices. While quantum error correction (QEC) can suppress noise, its use…
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…
Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are…
When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free…
Noise poses a challenge for any real-world implementation in quantum information science. The theory of quantum error correction deals with this problem via methods to encode and recover quantum information in a way that is resilient…
Constructing an efficient and robust quantum memory is central to the challenge of engineering feasible quantum computer architectures. Quantum error correction codes can solve this problem in theory, but without careful design it can…
We present a generalization of quantum error correction to infinite-dimensional Hilbert spaces. The generalization yields new classes of quantum error correcting codes that have no finite-dimensional counterparts. The error correction…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
We consider quantum metrology in noisy environments, where the effect of noise and decoherence limits the achievable gain in precision by quantum entanglement. We show that by using tools from quantum error-correction this limitation can be…
Quantum error mitigation, a data processing technique for recovering the statistics of target processes from their noisy version, is a crucial task for near-term quantum technologies. Most existing methods require prior knowledge of the…
The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator is particularly appealing for fault-tolerant quantum computing with bosons because Gaussian operations on encoded Pauli eigenstates enable Clifford quantum…
Fault-tolerant quantum computation traditionally incurs substantial resource overhead, with both qubit and time overheads scaling polylogarithmically with the size of the computation. While prior work by Gottesman showed that constant qubit…
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been…
This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known…
Standard approaches to quantum error correction (QEC) require active maintenance using measurements and classical processing. Passive QEC, by contrast, has so far been established only in unphysical spatial dimensions. Here, we give an…
Quantum computation promises to advance a wide range of computational tasks. However, current quantum hardware suffers from noise and is too small for error correction. Thus, accurately utilizing noisy quantum computers strongly relies on…