Efficient learning of quantum states prepared with few fermionic
non-Gaussian gates
- URL: http://arxiv.org/abs/2402.18665v1
- Date: Wed, 28 Feb 2024 19:18:27 GMT
- Title: Efficient learning of quantum states prepared with few fermionic
non-Gaussian gates
- Authors: Antonio Anna Mele and Yaroslav Herasymenko
- Abstract summary: We present an efficient algorithm for learning states on $n$ fermion modes prepared by any number of Gaussian gates.
Our work sheds light on the structure of states prepared with few non-Gaussian gates and offers an improved upper bound on their circuit complexity.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The experimental realization of increasingly complex quantum states
underscores the pressing need for new methods of state learning and
verification. In one such framework, quantum state tomography, the aim is to
learn the full quantum state from data obtained by measurements. Without prior
assumptions on the state, this task is prohibitively hard. Here, we present an
efficient algorithm for learning states on $n$ fermion modes prepared by any
number of Gaussian and at most $t$ non-Gaussian gates. By Jordan-Wigner
mapping, this also includes $n$-qubit states prepared by nearest-neighbour
matchgate circuits with at most $t$ SWAP-gates. Our algorithm is based
exclusively on single-copy measurements and produces a classical representation
of a state, guaranteed to be close in trace distance to the target state. The
sample and time complexity of our algorithm is $\mathrm{poly}(n,2^t)$; thus if
$t=O(\log(n))$, it is efficient. We also show that, if $t$ scales slightly more
than logarithmically, any learning algorithm to solve the same task must be
inefficient, under common cryptographic assumptions. We also provide an
efficient property testing algorithm that, given access to copies of a state,
determines whether such state is far or close to the set of states for which
our learning algorithm works. Beyond tomography, our work sheds light on the
structure of states prepared with few non-Gaussian gates and offers an improved
upper bound on their circuit complexity.
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