Related papers: Universality Classes of Stabilizer Code Hamiltonia…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to…
This paper investigates the thermodynamics of a large class of non-Hermitian, $PT$-symmetric oscillators, whose energy spectrum is entirely real. The spectrum is estimated by second-order WKB approximation, which turns out to be very…
Hamiltonian quantum computing, such as the adiabatic and holonomic models, can be protected against decoherence using an encoding into stabilizer subspace codes for error detection and the addition of energy penalty terms. This method has…
Quantum computers now show the promise of surpassing any possible classical machine. However, errors limit this ability and current machines do not have the ability to implement error correcting codes due to the limited number of qubits and…
We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an…
In this essay, we first sketch the development of ideas on the extraordinary dynamics of integrable classical nonlinear and quantum many body Hamiltonians. In particular, we comment on the state of mathematical techniques available for…
The ubiquity of stabilizer circuits in the design and operation of quantum computers makes techniques to verify their correctness essential. The simulation of stabilizer circuits, which aims to replicate their behavior using a classical…
Why is thermalisation a universal phenomenon? How does a quantum system reach thermodynamical equilibrium? These questions are not new, dating even from the very birth of quantum theory and have been the subject of a renewed interest over…
We show how certain suitably modified N-modular diagrams of integer partitions provide a nice combinatorial interpretation for the general term of Zeilberger's KOH identity. This identity is the reformulation of O'Hara's famous proof of the…
Understanding how microscopic few-body interactions give rise to thermal behavior in isolated quantum many-body systems remains a central challenge in nonequilibrium statistical mechanics. While individual energy eigenstates are expected to…
We investigate variational problems in quantum thermodynamics at positive temperature, in which admissible states are constrained by prescribed outcomes of a finite set of measurements. We solve a problem raised by the recent work [Liu,…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
Let G be a symplectic or orthogonal complex Lie group with Lie algebra g. As a G-module, the decomposition of the symmetric algebra S(g) into its irreducible components can be explicitely obtained by using identities due to Littlewood. We…
$\textit{Normalizer circuits}$ [1,2] are generalized Clifford circuits that act on arbitrary finite-dimensional systems $\mathcal{H}_{d_1}\otimes ... \otimes \mathcal{H}_{d_n}$ with a standard basis labeled by the elements of a finite…
We study a mechanism whereby quantum information present in the initial state of a quantum many-body system can be protected for arbitrary times due to a combination of symmetry and spatial locality. Remarkably, the mechanism is…
We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the…
We introduce a random variable approach to investigate the dynamics of a dissipative two-state system. Based on an exact functional integral description, our method reformulates the problem as that of the time evolution of a quantum state…
Hamiltonian inverse engineering enables the design of protocols for specific quantum evolutions or target state preparation. Perfect state transfer (PST) and remote entanglement generation are notable examples, as they serve as key…
In this paper, we explicitly construct (Abelian) anyonic excitations of arbitrary stabilizer Hamiltonians which are local on a 2D lattice of qubits. This leads directly to the conclusion that, in the presence of local thermal noise, such…