相关论文: Implementing unitary operators in quantum computat…
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a…
Quantum Hamiltonians containing nonseparable products of non-commuting operators, such as $\hat{\bf x}^m \hat{\bf p}^n$, are problematic for numerical studies using split-operator techniques since such products cannot be represented as a…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…
Ab initio studies of atomic nuclei are based on Hamiltonians including one-, two- and three-body operators with very complicated structures. Traditionally, matrix elements of such operators are expanded on a Harmonic Oscillator…
We propose a protocol to realize quantum simulation and computation in spin systems with long-range interactions. Our approach relies on the local addressing of single spins with external fields parametrized by Walsh functions. This enables…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
We show how to divide a coupled multi-spin system into a small subset of ``active'' spins that evolve under chemical shift or scalar coupling operators, and a larger subset of ``spectator'' spins which are returned to their initial states,…
We demonstrate that quantum Hamiltonian operator for a free transverse field within the framework of the second quantization reveals an alternative set of states satisfying the eigenstate functional equations. The construction is based upon…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
We present a direct basis formalism for using nonorthogonal basis sets in the second quantization framework. As an alternative to the dual basis formalism, a direct basis retains the Hermiticity relation between the creation and…
In the last years, we have been witnessing a tremendous push to demonstrate that quantum computers can solve classically intractable problems. This effort, initially focused on the hardware, progressively included the simplification of the…
We consider a bipartite quantum object, composed of a quantum system and a quantum actuator which is periodically reset. We show that the reduced dynamics of the system approaches unitarity as the reset frequency of the actuator is…
We present a systematic perturbative construction of the most general metric operator (and positive-definite inner product) for quasi-Hermitian Hamiltonians of the standard form, H= p^2/2 + v(x), in one dimension. We show that this problem…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
A new model of quantum computing has recently been proposed which, in analogy with a classical lambda-calculus, exploits quantum processes which operate on other quantum processes. One such quantum meta-operator takes N unitary…
We show how the basic operations of quantum computing can be expressed and manipulated in a clear and concise fashion using a multiparticle version of geometric (aka Clifford) algebra. This algebra encompasses the product operator formalism…
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…
The common spin Hamiltonians such as the Ising, XY, or Heisenberg model do not have ground states that are the graph states needed in measurement-based quantum computation. Various highly-entangled many-body states have been suggested as a…