Related papers: Quantum simulation beyond Hamiltonian paradigm: ca…
Quantum computers have the potential to efficiently simulate the dynamics of many interacting quantum particles, a classically intractable task of central importance to fields ranging from chemistry to high-energy physics. However,…
This paper introduces a formalism that aims to describe the intricacies of quantum computation by establishing a connection with the mathematical foundations of tensor theory and multilinear maps. The focus is on providing a comprehensive…
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…
Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are…
With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
Phases of matter are sharply defined in the thermodynamic limit. One major challenge of accurately simulating quantum phase diagrams of interacting quantum systems is due to the fact that numerical simulations usually deal with the energy…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
A quantum algorithm of SU(N) Yang-Mills theory is formulated in terms of quantum circuits. It can nonperturbatively calculate the Dyson series and scattering amplitudes with polynomial complexity. The gauge fields in the interaction picture…
We present the generalization of the CNC formalism, based on closed and noncontextual sets of Pauli observables, to the setting of odd-prime-dimensional qudits. By introducing new CNC-type phase space point operators, we construct a…
We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in…
Quantum Computing (QC) refers to an emerging paradigm that inherits and builds with the concepts and phenomena of Quantum Mechanic (QM) with the significant potential to unlock a remarkable opportunity to solve complex and computationally…
We study $\mathrm{SU}(3)$ Yang-Mills theory in $(2+1)$ dimensions based on networks of Wilson lines. With the help of the $q$ deformation, networks respect the (discretized) $\mathrm{SU}(3)$ gauge symmetry as a quantum group, i.e.,…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…
Nuclear physics, whose underling theory is described by quantum gauge field coupled with matter, is fundamentally important and yet is formidably challenge for simulation with classical computers. Quantum computing provides a perhaps…
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…
The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to…