Related papers: Linear growth of quantum circuit complexity
We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…
We characterize the expressive power of quantum circuits with the pseudo-dimension, a measure of complexity for probabilistic concept classes. We prove pseudo-dimension bounds on the output probability distributions of quantum circuits; the…
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a…
Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full $n$-qubit group, one often resorts to $t$-designs. Unitary…
We introduce magic-augmented Clifford circuits -- architectures in which Clifford circuits are preceded and/or followed by constant-depth circuits of non-Clifford (``magic") gates -- as a resource-efficient way to realize approximate…
As experimental platforms for quantum information processing continue to mature, characterization of the quality of unitary gates that can be applied to their quantum bits (qubits) becomes essential. Eventually, the quality must be…
The problem of the quantitative degradation of the performance of a quantum computer due to noisy unitary gates (imperfect external control) is studied. It is shown that quite general conclusions on the evolution of the fidelity can be…
As quantum circuits become more integrated and complex, additional error sources that were previously insignificant start to emerge. Consequently, the fidelity of quantum gates benchmarked under pristine conditions falls short of predicting…
The Gottesman-Knill theorem asserts that quantum circuits composed solely of Clifford gates can be efficiently simulated classically. This theorem hinges on the fact that Clifford gates map Pauli strings to other Pauli strings, thereby…
There is currently a significant need for robust and efficient methods for characterizing quantum devices. While there has been significant progress in this direction, there remains a crucial need to precisely determine the strength and…
Cryptography depends on truly unpredictable numbers, but physical sources emit biased or correlated bits. Quantum mechanics enables the amplification of imperfect randomness into nearly perfect randomness, but prior demonstrations have…
Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have…
The concrete schemes to realize three types of basic quantum logical gates using linear quadripartite cluster states of optical continuous variables are proposed. The influences of noises and finite squeezing on the computation precision…
Quantum computation using electron spins in three coupled dot with different size is proposed. By using the energy selectivity of both photon assisted tunneling and spin rotation of electrons, logic gates are realized by static and…
Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…
Quantifying the complexity of quantum states is a longstanding key problem in various subfields of science, ranging from quantum computing to the black-hole theory. The lower bound on quantum pure state complexity has been shown to grow…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
Fault-tolerant quantum computing hinges on efficient logical compilation, in particular, translating high-level circuits into code-compatible implementations. Gate-by-gate compilation often yields deep circuits, requiring significant…
Our goal in this paper is to construct optimal topological generators for compact unitary Lie groups, extending the work of a letter of Sarnak and arXiv:1704.02106 on golden and super-golden gates to higher dimensions. To do so we consider…
The success probability of a quantum algorithm constructed from noisy quantum gates cannot be accurately predicted from single parameter metrics that compare noisy and ideal gates. We illustrate this concept by examining a system with…