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To understand what the sum of histories is, we visualize the evolution of a quantum state given a quantum circuit as a tree. The root is the input | 0 ⊗ n {\displaystyle |0\rangle ^{\otimes n}} , and each node in the tree has 2 n {\displaystyle 2^{n}} children, each representing a state in C n {\displaystyle \mathbb {C} ^{n}} .
Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics. It studies the hardness of computational problems in relation to these complexity classes, as well as the relationship between quantum complexity ...
In a quantum circuit, the vectors are used to represent the state of the qubits and different matrices are used to represent the gate that is applied on the qubits. Since linear algebra is a major component of the quantum simulation, Field Programmable Gate Arrays ( FPGAs ) could be used to accelerate the simulation of quantum computing.
However, the computationally equivalent quantum circuit is a more common model. [51] [52]: 2 Qubit A qubit (/ ˈ k juː b ɪ t /) or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device.
Quantum random circuits (QRC) is a concept of incorporating an element of randomness into the local unitary operations and measurements of a quantum circuit.The idea is similar to that of random matrix theory which is to use the QRC to obtain almost exact results of non-integrable, hard-to-solve problems by averaging over an ensemble of outcomes.
This is a list of quantum computing terminology. Qubit. [1] [2] Quantum circuit. [3] [4] Quantum logic gate. [5] [6] [7] Topological quantum computer. [8] [9 ...
The term DQC1 has been used to instead refer to decision problems solved by a polynomial time classical circuit that adaptively makes queries to polynomially many DQC1 circuits. [6] In this sense of use, the class naturally contains all of BPP, and the power of the class is focused on the "inherently quantum" power.
Quantum advantage comes in the form of time complexity rather than computability, and quantum complexity theory shows that some quantum algorithms are exponentially more efficient than the best-known classical algorithms. A large-scale quantum computer could in theory solve computational problems unsolvable by a classical computer in any ...