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Representation of (H C n , I, O). Input qubits are shown by i1, i2, ..., in and squared vertices represent output qubits.
Source publication
In measurement-based quantum computation (MBQC), a special highly-entangled state (called a resource state) allows for universal quantum computation driven by single-qubit measurements and post-measurement corrections. Physical realisations of this model have been achieved in various physical systems for low numbers of qubits. The large number of q...
Contexts in source publication
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... Theorem 4, min QR is determined for open graphs with flow. + 1, m), where m is the whole num- ber of qubits in the pattern. ...
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... n }, n outputs, {v 1 , v 2 , ..., v n }, and (m−2n) = 0 intermedi- ate qubits, {v n+1 , v n+2 , ..., v m }, where m = m − n. Rather than specifying the edges of H n directly, we instead specify the edges of the graph H C n ob- tained by edge complement of H n . This is for simplicity since H n will be highly connected. The graph H C n , shown in Fig. 1, has the following edges: {i j , v j } for j ∈ {1, 2, ..., n − 2}, {v n+j , v n+j+1 } for j ∈ {0, 1, ..., m − n − 1}, and {i n−1 , v m ...
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... gflow on H n can be found by applying the algorithm proposed in Ref. [36], which yields the following: g(i j ) = {v j , v n−1 } for j ∈ {1, ..., n − 2}, g(v j ) = {v j−2 , v j−1 } for j ∈ {n + 1, ..., m }, g(i n−1 ) = {v m −1 , v m } and g(i n ) = v m . Since from Fig. 1 the maximum degree of H C n can easily be seen to be 2, the minimal degree of H n must be equal to m − 3. Starting from a qubit w in a partial or- der induced by a gflow on this open graph, we ...
Citations
... If the physical qubits employed, which should have long coherence times, can be rapidly re-initialized, the BOQC protocol can be optimized to use fewer resources; this optimization is similar to the scheme in [24]. Assuming that Bob's qubits are reused after being measured, Alice and Oscar alternately perform a complete computation round; pictorially this means using the order denoted with gray numbers in Figure 1, where the last layer of F j is left unmeasured, becoming the input of G j -thus, the last unmeasured layer of G j is the input of F j+1 . ...
... The main challenges for physical implementation are the sizable physical resources -we need 97 qubits to run 3-qubit BEQS -and the high fidelity transmission of encrypted qubits from Alice or Oscar to Bob. We think that these challenges can be at least largely overcome: To deal with the large size, we note the possibility of "reusing" the qubits [24]. To accomplish reliable transmission, we propose using remote state preparation (RSP) [6] as a quantum channel. ...
Here we extend the concept of blind client-server quantum computation, in which a client with limited quantum power controls the execution of a quantum computation on a powerful server, without revealing any details of the computation. Our extension is to introduce a three-node setting in which an oracular quantum computation can be executed blindly. In this Blind Oracular Quantum Computation (BOQC), the oracle (Oscar) is another node, with limited power, who acts in cooperation with the client (Alice) to supply quantum information to the server so that the oracle part of the quantum computation can also be executed blindly. We develop tests of this protocol using two- and three-qubit versions of the exact Grover algorithm (i.e., with database sizes $4\leq N\leq 8$), obtaining optimal implementations of these algorithms within a gate array scheme and the blinded cluster-state scheme. We discuss the feasibility of executing these protocols in state-of-the-art three-node experiments using NV-diamond electronic and nuclear qubits.
