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A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits.…
By exploiting a symmetric scheme for coupling $N$ spin-1/2 constituents (the physical qubits) to states with total angular momentum $N/2-1$, we construct rotationally invariant logical qudits of dimension $d=N-1$. One can encode all qudit…
We consider the task of performing quantum state tomography on a $d$-level spin qudit, using only measurements of spin projection onto different quantization axes. After introducing a basis of operators closely related to the spherical…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…
In some quantum algorithms, arithmetic operations are of utmost importance for resource estimation. In binary quantum systems, some efficient implementation of arithmetic operations like, addition/subtraction, multiplication/division,…
Reversible logic has attracted much research interest over the last few decades, especially due to its application in quantum computing. In the construction of reversible gates from basic gates, ancilla bits are commonly used to remove…
We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large…
Quantum-dot Cellular Automata (QCA) is one of the emerging nanotechnologies, promising alternative to CMOS technology due to faster speed, smaller size, lower power consumption, higher scale integration and higher switching frequency. Also,…
In this paper, we present a direct quantum adaptation of the classical shifted power method. The method is very similar to the iterative phase estimation algorithm; however, it does not require any initial estimate of an eigenvector and as…
Most of the work on implementing arithmetic on a quantum computer has borrowed from results in classical reversible computing (e.g. [VBE95], [BBF02], [DKR04]). These quantum networks are inherently classical, as they can be implemented with…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
In general, a quantum circuit is constructed with elementary gates, such as one-qubit gates and CNOT gates. It is possible, however, to speed up the execution time of a given circuit by merging those elementary gates together into larger…
The paper discusses various applications of permutation group theory in the synthesis of reversible logic circuits consisting of Toffoli gates with negative control lines. An asymptotically optimal synthesis algorithm for circuits…
Quantum computations are typically compiled into a circuit of basic quantum gates. Just like for classical circuits, a quantum compiler should optimize the quantum circuit, e.g. by minimizing the number of required gates. Optimizing quantum…
We theoretically investigate electron spin operations driven by applied electric fields in a semiconductor double quantum dot (DQD). Our model describes a DQD formed in semiconductor nanowire with longitudinal potential modulated by local…
The preparation of $n$-qubit quantum states is a cross-cutting subroutine for many quantum algorithms, and the effort to reduce its circuit complexity is a significant challenge. In the literature, the quantum state preparation algorithm by…
The Quantum Approximate Optimisation Algorithm is a $p$ layer, time-variable split operator method executed on a quantum processor and driven to convergence by classical outer loop optimisation. The classical co-processor varies individual…
Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic…
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method…
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…