01493nas a2200193 4500008004100000245007800041210006900119260001400188490000600202520090100208100002201109700001401131700002101145700002401166700002301190700002401213700002501237856003701262 2020 eng d00aEntanglement Bounds on the Performance of Quantum Computing Architectures0 aEntanglement Bounds on the Performance of Quantum Computing Arch c9/22/20200 v23 a

There are many possible architectures for future quantum computers that designers will need to choose between. However, the process of evaluating a particular connectivity graph's performance as a quantum architecture can be difficult. In this paper, we establish a connection between a quantity known as the isoperimetric number and a lower bound on the time required to create highly entangled states. The metric we propose counts resources based on the use of two-qubit unitary operations, while allowing for arbitrarily fast measurements and classical feedback. We describe how these results can be applied to the evaluation of the hierarchical architecture proposed in Phys. Rev. A 98, 062328 (2018). We also show that the time-complexity bound we place on the creation of highly-entangled states can be saturated up to a multiplicative factor logarithmic in the number of qubits.

1 aEldredge, Zachary1 aZhou, Leo1 aBapat, Aniruddha1 aGarrison, James, R.1 aDeshpande, Abhinav1 aChong, Frederic, T.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1908.0480201600nas a2200145 4500008004100000245005700041210005700098260001500155490000800170520117800178100002101356700002401377700001601401856003701417 2017 eng d00aExtracting entanglement geometry from quantum states0 aExtracting entanglement geometry from quantum states c2017/10/060 v1193 a

Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network - and hence the geometry - is largely fixed a priori by the choice of tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of non-interacting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.

1 aHyatt, Katharine1 aGarrison, James, R.1 aBauer, Bela uhttps://arxiv.org/abs/1704.01974