Related papers: Shrinking of Operators in Quantum Error Correction…
Atom loss is a dominant error source in neutral-atom quantum processors, yet its correlated structure remains largely unexploited by existing quantum error correction decoders. We analyze the performance of the surface code equipped with…
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are…
We present a unified approach to quantum error correction, called operator quantum error correction. This scheme relies on a generalized notion of noiseless subsystems that is not restricted to the commutant of the interaction algebra. We…
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…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small…
The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of…
We construct a new class of differential operators that naturally act on AdS harmonic functions. These are weight shifting operators that change the spin and dimension of AdS representations. Together with CFT weight shifting operators, the…
We suggest that the principle of holographic duality can be extended beyond conformal invariance and AdS isometry. Such an extension is based on a special relation between functional determinants of the operators acting in the bulk and on…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
Fault-tolerant quantum computation with depolarization error often requires demanding error threshold and resource overhead. If the operations can maintain high noise bias -- dominated by dephasing error with small bit-flip error -- we can…
Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the…
We explore the connection between the operator product expansion (OPE) in the boundary and worldsheet conformal field theories in the context of AdS$_{d+1}$/CFT$_d$ correspondence. Considering single trace scalar operators in the boundary…
We develop the procedures of gauging and ungauging, reveal their operational meaning and propose their generalization in a systematic manner within the framework of quantum error-correcting codes. We demonstrate with an example of the…
Correlation functions of local operators in Quantum Field Theory (QFT) on hyperbolic space can be fully characterized by the set of QFT data $\lbrace \Delta_i,C_{ijk},b^{\hat{\mathcal{O}}}_j\rbrace$. These are the scaling dimensions of…
The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de…
Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these…
The AdS/CFT correspondence stipulates a duality between conformal field theories and certain theories of quantum gravity in one higher spatial dimension. However, probing this conjecture on contemporary classical or quantum computers is…
Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the…
We study the Casimir energy of bulk fields in AdS$_3$ and its relation to subleading terms in the central charge of the dual CFT$_2$. Computing both sides of the standard CFT$_2$ relation $E=-c/12$ independently we show that this relation…