Related papers: Linear-Depth Quantum Circuits for n-qubit Toffoli …
We propose a direct (non-recursive) algorithm for applying a rotation $R_{\theta^\ast}$, $\epsilon$-close to a desired rotation $R_\theta$, to a single qubit using the Clifford+Toffoli gate set. Our algorithm does not rely on repeatedly…
The prime objective of this study is to seek a circuit diagram for a multi-inputs Toffoli gate including only single qubit gates and CNOTs. In this regard, we have developed two variational quantum algorithms that can be used to implement a…
We present improved circuits for the control-control-phase (Toffoli) gate and the control-swap (Fredkin) gate using three and four global two-qubit gates, respectively. This is a nearly double speed-up compared to the conventional circuits,…
QAC$^0$ is the class of constant-depth quantum circuits with polynomially many ancillary qubits, where Toffoli gates on arbitrarily many qubits are allowed. In this work, we show that the parity function cannot be computed in QAC$^0$,…
Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations…
Discrete-time quantum walks with position-dependent coin operators have numerous applications. For a position dependence that is sufficiently smooth, it has been provided in Ref. [1] an approximate quantum-circuit implementation of the coin…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
We put forward a strategy to encode a quantum operation into the unmodulated dynamics of a quantum network without the need of external control pulses, measurements or active feedback. Our optimization scheme, inspired by supervised machine…
We propose a linear-size synthesis of the multi-controlled Toffoli gate on qudits with at most one borrowed ancilla. This one ancilla can even be saved when the qudit dimension is odd. Our synthesis leads to improvements in various quantum…
Low depth measurement-based quantum computation with qudits ($d$-level systems) is investigated and a precise relationship between this powerful model and qudit quantum circuits is derived in terms of computational depth and size…
We design quantum circuits by using the standard cell approach borrowed from classical circuit design, which can speed-up the layout of circuits with a regular structure. Our standard cells are general and can be used for all types of…
Decoherence -- in the current physical implementations of quantum computers -- makes depth reduction a vital task in quantum-circuit design. Moore and Nilsson (SIAM Journal of Computing, 2001) demonstrated that additional qubits -- known as…
We present protocols for preparing two-dimensional abelian and non-abelian topologically ordered states by employing finite depth unitary circuits composed of long-ranged, simultaneous, and mutually commuting two-qubit gates. Our protocols…
The depth of quantum circuits is a critical factor when running them on state-of-the-art quantum devices due to their limited coherence times. Reducing circuit depth decreases noise in near-term quantum computations and reduces overall…
The efficient decomposition of multi-controlled gates is a significant factor in quantum compiling, both in circuit depth and T-gate count. Recent work has demonstrated that qudits have the potential to reduce resource requirements from…
The problem of finding efficient decompositions of multi-qubit gates is of importance for quantum computing, especially, in application to existing noisy intermediate-scale quantum devices, whose resources are substantially limited. Here we…
Implementing many important sub-circuits on near-term quantum devices remains a challenge due to the high levels of noise and the prohibitive depth on standard nearest-neighbour topologies. Overcoming these barriers will likely require…
In this paper we present a generic construction to obtain an optimal T depth quantum circuit for any arbitrary $n$-input $m$-output Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}^m$ having algebraic degree $k\leq n$, and it achieves an…
While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can…
Quantum gates based on geometric phases possess intrinsic noise-resilience features and therefore attract much attention. However, the implementations of previous geometric quantum computation typically require a long pulse time of gates.…