Related papers: Catalytic $z$-rotations in constant $T$-depth
Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the…
Large-scale quantum computers rely on quantum error correction to protect the fragile quantum information. Among the possible candidates of quantum computing devices, silicon-based spin qubits hold a great promise due to their compatibility…
We introduce the parity-unfolded architecture, a fault-tolerant quantum computing scheme that relies on direct preparation and teleportation of small-angle rotations $ Z^{1/2^{k}}$ rather than approximating them with the conventional…
Rotation gates are widely used in various quantum algorithms. To implement fault-tolerant rotation gates, state distillation or gate synthesis is typically employed. However, the overhead of these schemes scales rapidly with increasing…
We study the encoding complexity for quantum error correcting codes with large rate and distance. We prove that random Clifford circuits with $O(n \log^2 n)$ gates can be used to encode $k$ qubits in $n$ qubits with a distance $d$ provided…
We consider a unitary transformation which maps any given state of an $n$-qubit quantum register into another one. This transformation has applications in the initialization of a quantum computer, and also in some quantum algorithms.…
The fidelity of certain gates on noisy quantum computers may be improved when they are implemented using more than two levels of the involved transmons. The main impediments to achieving this potential are the dynamic gate phase errors that…
For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary…
The quantum Toffoli gate allows universal reversible classical computation. It is also an important primitive in many quantum circuits and quantum error correction schemes. Here we demonstrate the realization of a Toffoli gate with three…
With recent advancements in quantum computing technology, optimizing quantum circuits and ensuring reliable quantum state preparation have become increasingly vital. Traditional methods often demand extensive expertise and manual…
We investigate the problem of synthesizing T-depth optimal quantum circuits over the Clifford+T gate set. First we construct a special subset of T-depth 1 unitaries, such that it is possible to express the T-depth-optimal decomposition of…
Single-step implementations of multi-qubit gates are generally believed to provide a simpler design, a faster operation, and a lower decoherence. For coupled three qubits interacting with a photon field, a realizable scheme for a…
The quantum Fourier transform (QFT) is a crucial subroutine in many quantum algorithms. In this paper, we study the exact lower bound problem of CNOT gate complexity for fault-tolerant QFT. First, we consider approximating the ancilla-free…
We identify a novel qudit gate which we call the $\sqrt[d]{Z}$ gate. This is an alternate generalization of the qutrit $T$ gate to any odd prime dimension $d$, in the $d^{\text{th}}$ level of the Clifford hierarchy. Using this gate which is…
We show that any 2D scalar field theory compactified on a cylinder and with a Fourier expandable potential $V$ is equivalent, in the small coupling limit, to a 1D theory involving a massless particle in a potential $V$ and an infinite tower…
We consider a four-state pure bipartite system consisting of four qubits shared among two parties using the same Schmidt basis, two qubits per party. In some cases, transformation between two known pure states may not be possible using LOCC…
Adaptive quantum circuits employ unitary gates assisted by mid-circuit measurement, classical computation on the measurement outcome, and the conditional application of future unitary gates based on the result of the classical computation.…
Efficient synthesis of arbitrary quantum states and unitaries from a universal fault-tolerant gate-set e.g. Clifford+T is a key subroutine in quantum computation. As large quantum algorithms feature many qubits that encode coherent quantum…
Random quantum states have various applications in quantum information science. We discover a new ensemble of quantum states that serve as an $\epsilon$-approximate state $t$-design while possessing extremely low entanglement, magic, and…
We prove that a unitary matrix has an exact representation over the Clifford+T gate set with local ancillas if and only if its entries are in the ring Z[1/sqrt(2),i]. Moreover, we show that one ancilla always suffices. These facts were…