146 research outputs found
Graph-theoretic simplification of quantum circuits with the ZX-calculus
We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations graphically. Then, using the rules of the ZX-calculus, we give a simplification strategy for ZX-diagrams based on the two graph transformations of local complementation and pivoting and show that the resulting reduced diagram can be transformed back into a quantum circuit. While little is known about extracting circuits from arbitrary ZX-diagrams, we show that the underlying graph of our simplified ZX-diagram always has a graph-theoretic property called generalised flow, which in turn yields a deterministic circuit extraction procedure. For Clifford circuits, this extraction procedure yields a new normal form that is both asymptotically optimal in size and gives a new, smaller upper bound on gate depth for nearest-neighbour architectures. For Clifford+T and more general circuits, our technique enables us to to `see around' gates that obstruct the Clifford structure and produce smaller circuits than naïve `cut-and-resynthesise' methods
Enumerating all bilocal Clifford distillation protocols through symmetry reduction
Entanglement distillation is an essential building block in quantum
communication protocols. Here, we study the class of near-term implementable
distillation protocols that use bilocal Clifford operations followed by a
single round of communication. We introduce tools to enumerate and optimise
over all protocols for up to (not necessarily equal) Bell-diagonal states
using a commodity desktop computer. Furthermore, by exploiting the symmetries
of the input states, we find all protocols for up to copies of a Werner
state. For the latter case, we present circuits that achieve the highest
fidelity. These circuits have modest depth and number of two-qubit gates. Our
results are based on a correspondence between distillation protocols and double
cosets of the symplectic group, and improve on previously known protocols.Comment: 13 pages main text, 5 pages appendices, 8 figure
Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates II: Single-Copy Measurements
Recent work has shown that -qubit quantum states output by circuits with
at most single-qubit non-Clifford gates can be learned to trace distance
using time and samples. All prior
algorithms achieving this runtime use entangled measurements across two copies
of the input state. In this work, we give a similarly efficient algorithm that
learns the same class of states using only single-copy measurements.Comment: 22 pages. arXiv admin note: text overlap with arXiv:2305.1340
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