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Register a new userUniversal quantum computing with twist-free and temporally encoded lattice surgery
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Added by
Christopher Chamberland
Publication date
2021
fields
Physics
and research's language is
English
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Lattice surgery protocols allow for the efficient implementation of universal gate sets with two-dimensional topological codes where qubits are constrained to interact with one another locally. In this work, we first introduce a decoder capable of correcting spacelike and timelike errors during lattice surgery protocols. Afterwards, we compute logical failure rates of a lattice surgery protocol for a full biased circuit-level noise model. We then provide a new protocol for performing twist-free lattice surgery. Our twist-free protocol reduces the extra circuit components and gate scheduling complexities associated with the measurement of higher weight stabilizers when using twists. We also provide a protocol for temporally encoded lattice surgery that can be used to reduce both runtimes and the total space-time costs of quantum algorithms. Lastly, we propose a layout for a quantum processor that is more efficient for surface codes exploiting noise bias, and which is compatible with the other techniques mentioned above.
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In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect- based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance 3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.
We present a linear optics quantum computation scheme with a greatly reduced cost in resources compared to KLM. The scheme makes use of elements from cluster state computation and achieves comparable resource usage to those schemes while retaining the circuit based approach of KLM.
A single qubit may be represented on the Bloch sphere or similarly on the $3$-sphere $S^3$. Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of $3$-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes to be a $3$-manifold $M^3$. More precisely, the $d$-dimensional POVMs defined from subgroups of finite index of the modular group $PSL(2,mathbb{Z})$ correspond to $d$-fold $M^3$- coverings over the trefoil knot. In this paper, one also investigates quantum information on a few universal knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy. Further connections between POVMs based UQC and $M^3$s obtained from Dehn fillings are explored.
When calculating the overhead of a quantum algorithm made fault-tolerant using the surface code, many previous works have used defects and braids for logical qubit storage and state distillation. In this work, we show that lattice surgery reduces the storage overhead by over a factor of 4, and the distillation overhead by nearly a factor of 5, making it possible to run algorithms with $10^8$ T gates using only $3.7times 10^5$ physical qubits capable of executing gates with error $psim 10^{-3}$. These numbers strongly suggest that defects and braids in the surface code should be deprecated in favor of lattice surgery.
Future quantum computers will require quantum error correction for faithful operation. The correction capabilities come with an overhead for performing fault-tolerant logical operations on the encoded qubits. One of the most resource efficient ways to implement logical operations is lattice surgery, where groups of physical qubits, arranged on lattices, can be merged and split to realize entangling gates and teleport logical information. Here, we report on the experimental realization of lattice surgery between two topologically encoded qubits in a 10-qubit ion trap quantum information processor. In particular, we demonstrate entanglement between two logical qubits and we implement logical state teleportation.
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