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tation, a pair of qubits from the source quantum computer quality of matter qubits is a trade-off. Therefore, the quantum |
to the destination quantum computer is transferred for local architectures, including quantum algorithms, need to be well- |
operations and measurements before decoherence, the loss of designedandwell-resolvedtoachievethecommunicationand |
the shared entangled qubits. However, errors and failures in- local operations for generating matter qubits. |
curred in quantum teleportation preserve the entangled qubits |
C. QuantumAlgorithmsandDistributedQuantumAlgorithms |
of quantum computers. To guarantee the Bell state of the |
shared pair of qubits, an entanglement distillation procedure The quantum algorithms to be executed in quantum com- |
is developed to iteratively increase fidelity or the probability puterscanbeofseveraltypesdependingonthecomputational |
that the qubit will be transferred without changing its state. paradigm. The key issues on quantum algorithms and dis- |
However, quantum teleportation requires a lot of iterations, tributed quantum algorithms are as follows. |
time,andresourcestoachievetheBellstateofapairofqubits. 1) QuantumAlgorithm: Numerousstudieshavefocusedon |
Additionally, the qubits of the shared Bell pairs are called quantumalgorithmsoperatingatexponentiallyfasterspeedson |
entangled-qubits (or eqbits), which are stored in quantum quantumcomputersimplementedonquantumcircuits[12].We |
memories. discuss the most prevalent quantum algorithms as follows: |
2) Distributed Quantum Circuits: Required quantum cir- • Shor’s algorithm was devised to factor prime numbers in |
cuitscanbesplitanddistributedamongmultiplequantumpro- polynomial time, which cannot be done polynomially by |
cessors of quantum computers, with each quantum computer classical algorithms. The factoring problem is suggested |
executing a fragment of quantum circuits. The architecture to be reformulated as the finding-period problem and |
of the quantum circuits executes non-local quantum gates solved through quantum phase estimation, which esti- |
for the shared entangled qubits. A logically identical set of mates phases or eigenvalues of eigenvectors of unitary |
instructions is used to coordinate the additional operations operators. |
required for the non-local operation to replace the multiple • Grover’salgorithmsolvesasearchingproblemforanun- |
qubit operations. In particular, a partitioning of quantum structured database, which provides quadratically speed- |
circuits to achieve the least number of qubits among quantum up computation. An equal superposition of all possible |
processors must be determined remotely by exchanging non- solutions is employed as inputs that result in the same |
local operations with other quantum gates. amplitudes. The inputs are passed and processed through |
3) Distributed Quantum Architectures: Multiple quantum theoraclediffusertoboosttheamplitudesandthenreflect |
processing units (QPUs) can be executed for computations thesolutionintermsofthegreatestamountofamplitudes. |
in parallel with each other universally to achieve distributed The Grover’s algorithm can be used as a generic algorithm |
quantum computing. Qubits are prepared as input data by the to address a variety of problems due to the independence of |
the algorithm and the internal structure of lists. As a result, |
Oracle diffuser |
executing Grover’s algorithm gives many classical problems a operator Quantum gates |
quadratic speed-up computation. |0⟩ |
2) Distributed Quantum Algorithm: Despite the fact that |
|0⟩ |
quantumcomputingissignificantlymoreadvancedthanclassi- |
cal computing, only small quantum computers (with a limited |0000⟩ |0⟩ |
number of qubits) have so far been constructed due to the |
noiseanddepthofquantumcircuits.Asanalternativetolarge- |0⟩ |
scale monolithic designs, a distributed grid of small quan- |
Measurement |
tum computers has been proposed to help advance quantum |
computing. In particular, as distributed quantum computing (a) |
necessitates sharing the superposition state among quantum Oracle diffuser |
computers, quantum networks through entanglement need to Quantum Computer 1 operator Quantum gates |
|0⟩ |
be considered in the implementation. In addition, swap gates |
are implemented in order to teleport qubits between a pair |0⟩ |
of two quantum computers. We discuss the most prevalent |
Quantum teleportation |
distributed quantum algorithms as follows: |0000⟩ Quantum Computer 2 |
|0⟩ |
• Distributed Shor’s algorithm was implemented to solve |
factorization problems by small-capacity quantum com- |0⟩ |
puters. The architecture of quantum circuits to per- Measurement |
form collaboratively is designed to handle quantum |
(b) |
teleportation and simulate a large capacity quantum |
computer [3]. The complexity of distributed Shor’s Fig. 2: A procedure of computing the required four-qubits |
algorithm is O((logN)2), while Shor’s algorithm re- quantumtask;(a)onequantumcomputerwithfourqubitsand |
quires O(cid:0) (logN)2(loglogN)(logloglogN)(cid:1) , where N (b) two quantum computers with two qubits per each. |
denotes the integer to be factored. |
• Distributed Grover’s algorithm was also developed to |
linksbetweentwointerconnectedquantumcomputersenabling |
address the unstructured search problem. According to |
quantum teleportation are oriented and have a static capacity. |
the expensive query time in Grover’s algorithm, the |
However, the number of quantum computers, the number of |
distributedGrover’salgorithmcanreducequerytimes[4]. |
qubitsofeachquantumcomputer,andthecapacityofquantum |
Functions that needs to be computed can be divided into |
2k subfunctions by the distributed Grover’s algorithm, networks are limited and static. Therefore, the allocation of |
these resources needs to provide sufficient quantum deploy- |
which then computes one of the usable subfunctions to |
ments to support quantum tasks in the distributed quantum |
findthesolutiontotheoriginalfunction.Incomparisonto |
computing framework. |
the original Grover’s algorithm, distributed Grover’s al- |
gorithm can significant speed up queries. A procedure of |
B. System Model, Decisions, and Costs |
Grover’s algorithm solving a four-qubit quantum task for |
AsshowninFig.1,thequantumcomputeroperatorchooses |
quantum computing and distributed quantum computing |
between two alternative stages for allocating resources for |
using two quantum computers is shown in Fig. 2. |
distributed quantum computing, i.e., utilizing the reserved |
Among distributed quantum algorithms, the grid of dis- |
quantum computers and deploying on-demand quantum com- |
tributed quantum circuits has to be well-designed to make the |
puters. To use the reserved quantum computer, the quantum |
best utilization of the constrained resources in quantum com- |
computeroperatorfollowsinstructionsofthedistributedquan- |
puters.Therefore,itbecomesincreasinglyimportanttoaddress |
tum computers to complete the quantum task. However, the |
resource allocation in distributed quantum computing to solve |
reserved quantum computers may not be sufficient to accom- |
resource constraints in quantum computing environments. |
plishalarge-scalequantumcomputationaltask.Therefore,the |
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