Log In Sign Up

Lower bound the T-count via unitary stabilizer nullity

by   Jiaqing Jiang, et al.

We introduce magic measures for multi-qubit quantum gates and establish lower bounds on the non-Clifford resources for fault-tolerant quantum computation. First, we introduce the stabilizer nullity of an arbitrary multi-qubit unitary, which is based on the subgroup of the quotient Pauli group associated with the unitary. This unitary stabilizer nullity extends the state stabilizer nullity by Beverland et al. to a dynamic version. We in particular show this magic measure has desirable properties such as sub-additivity under composition and additivity under tensor product. Second, we prove that a given unitary's stabilizer nullity is a lower bound for the T-count, utilizing the above properties in gate synthesis. Third, we compare the state and the unitary stabilizer nullity, proving that the lower bounds for the T-count obtained by the unitary stabilizer nullity are never less than the state stabilizer nullity. Moreover, we show an explicit n-qubit unitary family of unitary stabilizer nullity 2n, which implies that its T-count is at least 2n. This gives an example where the bounds derived by the unitary stabilizer nullity strictly outperform the state stabilizer nullity by a factor of 2. We further connect the unitary stabilizer nullity and the state stabilizer nullity with auxiliary systems, showing that adding auxiliary systems and choosing proper stabilizer states can strictly improving the lower bound obtained by the state stabilizer nullity.


page 1

page 2

page 3

page 4


Explicit lower bounds on strong simulation of quantum circuits in terms of T-gate count

We investigate Clifford+T quantum circuits with a small number of T-gate...

A Converse for Fault-tolerant Quantum Computation

With improvements in achievable redundancy for fault-tolerant quantum co...

Lower Bounds for Function Inversion with Quantum Advice

Function inversion is that given a random function f: [M] → [N], we want...

The composition complexity of majority

We study the complexity of computing majority as a composition of local ...

Multi-User Distillation of Common Randomness and Entanglement from Quantum States

We construct new protocols for the tasks of converting noisy multipartit...

Quantum Lower Bounds for 2D-Grid and Dyck Language

We show quantum lower bounds for two problems. First, we consider the pr...

Interruptible Algorithms for Multiproblem Solving

In this paper we address the problem of designing an interruptible syste...