Related papers: Generalized Conditional Displacement
Practical utilization of Gottesman-Kitaev-Preskill (GKP) qubits requires not only the preparation of logical basis states, but also the ability to prepare and evaluate arbitrary logical qubit superpositions. Currently, this is typically…
Encoding a qubit in a larger Hilbert space of an oscillator is an efficient way to protect its quantum information against decoherence. Promising examples of such bosonic encodings are the Gottesman-Kitaev-Preskill (GKP) codes. In this…
We propose local strategies to protect global quantum information. The protocols, which are quantum error correcting codes for dissipative systems, are based on environment measurements, direct feedback control and simple encoding of the…
A critical component of any quantum error-correcting scheme is detection of errors by using an ancilla system. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information.…
We propose two distinct methods of improving quantum computing protocols based on surface codes. First, we analyze the use of dislocations instead of holes to produce logical qubits, potentially reducing spacetime volume required.…
It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum…
Long distance quantum communication will require the use of quantum repeaters to overcome the exponential attenuation of signal with distance. One class of such repeaters utilizes quantum error correction to overcome losses in the…
Structured sparsity is an important modeling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design. In this paper we investigate the…
In continuous-variable quantum computing, autonomous quantum error correction (QEC) can dissipatively steer a noisy quantum state into a target state or manifold, enabling robust quantum information processing without explicit syndrome…
We characterize generalized derivatives of the solution operator of the obstacle problem. This precise characterization requires the usage of the theory of so-called capacitary measures and the associated solution operators of relaxed…
Measurements play an important role in quantum computing (QC), by either providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly…
We introduce a novel formulation of a Generalized Gottesman-Kitaev-Preskill (GKP) state that resolves all of its foundational pathologies, such as infinite energy, non-normalizability, and orthogonality. We demonstrate that these issues are…
In this paper we introduce a universal operator theoretic framework for quantum fault tolerance. This incorporates a top-down approach that implements a system-level criterion based on specification of the full system dynamics, applied at…
A modification of the generalized shift-splitting (GSS) method is presented for solving singular saddle point problems. In this kind of modification, the diagonal shift matrix is replaced by a block diagonal matrix which is symmetric…
Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum…
In this study, we explore the universality of Selective Number-dependent Arbitrary Phase (SNAP) and Displacement gates for quantum control in qudit-based systems. However, optimizing the parameters of these gates poses a challenging task.…
The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.
Gottesman, Kitaev and Preskill have formulated a way of encoding a qubit into an oscillator such that the qubit is protected against small shifts (translations) in phase space. The idea underlying this encoding is that error processes of…
Large-amplitude squeezed cat and high-quality Gottesman-Kitaev-Preskill (GKP) states are powerful resources for quantum error correction. However, previous schemes in optics are limited to low success probabilities, small amplitudes, and…
Bosonic encoding of quantum information into harmonic oscillators is a hardware efficient approach to battle noise. In this regard, oscillator-to-oscillator codes not only provide an additional opportunity in bosonic encoding, but also…