Related papers: Counting unitaries of T-depth one

While implementing a quantum algorithm it is crucial to reduce the quantum resources, in order to obtain the desired computational advantage. For most fault-tolerant quantum error-correcting codes the cost of implementing the non-Clifford…

We present a simple algorithm that implements an arbitrary $n$-qubit unitary operator using a Clifford+T circuit with T-count $O(2^{4n/3} n^{2/3})$. This improves upon the previous best known upper bound of $O(2^{3n/2} n)$, while the best…

We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive…

We present a quantum algorithm for multiplying two $n$-bit integers with overall circuit depth and $T$-depth both bounded by $O(\log^{2} n)$, while using $O(n^{2})$ gates and ancillary qubits. Our construction generates partial products via…

We show that any $n$-qubit Clifford unitary can be implemented using at most $2n$ multi-qubit joint measurements. All the multi-qubit joint measurements used for implementing the Clifford unitary can be chosen to form at most two sets of…

We describe a new method for approximating an arbitrary $n$ qubit unitary with precision $\varepsilon$ using a Clifford and T circuit with $O(4^{n}n(\log(1/\varepsilon)+n))$ gates. The method is based on rounding off a unitary to a unitary…

A unitary t-design is a set of unitaries that is "evenly distributed" in the sense that the average of any t-th order polynomial over the design equals the average over the entire unitary group. In various fields -- e.g. quantum information…

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…

Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing…

We develop the concept of a unitary t-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group U(2^n) on n qubits. In particular, sets of unitaries forming…

We prove that random quantum circuits on any geometry, including a 1D line, can form approximate unitary designs over $n$ qubits in $\log n$ depth. In a similar manner, we construct pseudorandom unitaries (PRUs) in 1D circuits in…

We give a Clifford+T representation of the Toffoli gate of T-depth 1, using four ancillas. More generally, we describe a class of circuits whose T-depth can be reduced to 1 by using sufficiently many ancillas. We show that the cost of…

In this paper, we show the equivalence of the set of unitaries computable by the circuits over the Clifford and T library and the set of unitaries over the ring $\mathbb{Z}[\frac{1}{\sqrt{2}},i]$, in the single-qubit case. We report an…

We propose a method of compiling that permits to identify quantum circuits able to simulate arbitrary $n$-qubit unitary operations via the adjustment of angles in single-qubit gates therein. The method of compiling itself extends older…

Let $n\geq 8$ be divisible by 4. The Clifford-cyclotomic gate set $\mathcal{G}_n$ is the universal gate set obtained by extending the Clifford gates with the $z$-rotation $T_n = \mathrm{diag}(1,\zeta_n)$, where $\zeta_n$ is a primitive…

Since an n-qubit circuit consisting of CNOT gates can have up to $\Omega(n^2/\log{n})$ CNOT gates, it is natural to expect that $\Omega(n^2/\log{n})$ Toffoli gates are needed to apply a controlled version of such a circuit. We show that the…

We seek to develop better upper bound guarantees on the depth of quantum CZ gate, CNOT gate, and Clifford circuits than those reported previously. We focus on the number of qubits $n\,{\leq}\,$1,345,000 [1], which represents the most…

We consider the notion of unitary transformations forming bases for subspaces of $M(d,\mathbb{C})$ such that the square of Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case,…

We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov and Mosca. Their algorithm takes as input an exactly synthesizable single-qubit…

We present an algorithm for performing quantum process tomography on an unknown $n$-qubit unitary $C$ from the Clifford group. Our algorithm uses Bell basis measurements to deterministically learn $C$ with $4n + 3$ queries, which is the…