Quantum Computing 量子運算

Constant function

A constant function always maps to either 1 or 0.

b (CNOT gate)

target or target input

CNOT gate

the quantum analog to the classical XOR gate

Balanced function

A balanced function maps to 1 for half of the inputs and maps to 0 for the other half.

Linear algorithm

A linear growth rate is less than a polynomial or exponential growth rate. Linear algorithm will generally require fewer resources for a system of very large size.

Two-qubit gate fidelity

At 99.91%, trapped ions have the highest two-qubit gate fidelity. This is followed by superconducting qubits at 99.4%.

cyphertext

Encryption (加密) takes raw data and translates it or encodes it into an unrecognizable message called a cyphertext (密文).

Exponential advantage

For N atoms, the classical resources scale as 2^N, whereas the quantum resources scale as N^c, where c generally ranges from 2 to 6. A change from exponential scaling to polynomial scaling represents an exponential improvement, or exponential advantage.

Gate fidelity

Gate fidelity is a measure of how closely the experimental gate operation matches - on average - the theoretically ideal version of that operation. It is a rigorous means to define how well a gate operation works.

Coherence time

It quantifies the robustness of a qubit. After the coherence time, the quantum state is predominantly lost. // The coherence time is a characteristic 1/e time scale during which -- on average -- the quantum state of a qubit is (partially) maintained. // After several coherence times, the qubit has essentially completely decohered; the state information is lost, but the qubit itself is still physically present.

Gate time

It quantifies the time required to perform a quantum operation.

Quantum computation

Quantum computers utilize certain unique properties of subatomic particles in conjunction with the theories of computer science to pro- and store information. This merging of quantum mechanics and computer science has been extensively explored during the last three decades, and has led to the development of techniques for a class of computational problems, for example, deciphering codes, factoring large numbers, searching an unsorted collection etc. that can be solved much more efficiently using a quantum computer. Such advances in information processing capability can be attrib- uted to the fact that the data bits in a quantum computer, unlike their counterparts in classical computers can simultaneously exist in more than one state at a time and can be manipulated simultaneously. Information in conventional digital representation uses a sequence of bits. Each bit is basically the charge of an electron. If the electron is charged, the bit is assumed to carry a value 1; alternatively the bit car- ries a value 0 if the electron is not charged. Thus a bit also known as a classical bit can be in state 0 or state 1, and measuring a bit at any time results in one of two possible outcomes.

Quantum key distribution

Quantum key distribution (QKD) is a secure communication method which implements a cryptographic protocol involving components of quantum mechanics. QKD provides a means to securely transmit and share such a secret key. The secret key can then be used to encrypt and decrypt information.

Quantum teleportation

Quantum teleportation is a technique for transferring quantum information from a sender at one location to a receiver some distance away.

Qubit lifetime

Qubits with long lifetimes tend to be more weakly coupled to their environment; have less sensitivity to noise; be more weakly coupled to control fields. If a qubit is less coupled to its environment, it is less sensitive to noise and thus tends to have a longer lifetime. Control fields may be thought of as intentional electromagnetic fields, in contrast to the unintentional ones of a noisy environment. If a qubit is weakly coupled and predominantly insensitive to environmental noise, it is likely that it is also similarly insensitive to intentionally applied control fields. This means that the amplitude of the control field must be made larger to compensate the insensitivity in order to respond as quickly as, for example, a qubit that is more strongly coupled to its environment and control fields.

Shor's algorithm

Shor's algorithm is a quantum algorithm for integer factorization that features an exponential speed up compared to the best known classical algorithms, and it has application to cryptanalysis (密碼破譯).

Superdense coding

Superdense coding (密集編碼) is a quantum communication protocol in which two bits of information can be communicated by only modifying and transmitting one qubit. It requires an entangled pair of qubits be prepared in advance and shared between the sender and the receiver. // Classical communication channels are not strictly required. Only one qubit needs to be transmitted. All of the information transmitted is contained in the quantum correlations between the two qubits, and so an entangled qubit pair is necessary. No information is encrypted in a superdense coding protocol. A quantum superposition by itself is not enough to perform a superdense coding protocol; entanglement of two qubits is necessary. // The superdense coding protocol enables one to send two classical bits of information per each transmitted qubit. This requires the sender and receiver to pre-share an entangled qubit pair.

No-cloning theorem

The no-cloning theorem is one of the three theorems on which the potential promise of quantum communication is based. If you prepare a qubit in a known state, you can prepare additional qubits in the same state. However, if you have a qubit in an unknown quantum state, you can't make exact copies of it. In short, the non-cloning theorem states that unknown quantum states can't be copied.

Quantum Supremacy

The point at which a quantum computer can perform calculations faster than the largest foreseeable classical computers.

Quantum advantage

The term "quantum advantage" is used to describe how a quantum computer may be able to outperform a classical computer. Quantum advantage serves as a kind of conceptual example of how much better quantum computers can be at various tasks and processes, and why quantum computing should be pursued as a frontier of IT.

ψ

actual state of a qubit (a vector)

Josephson Junctions

are thin oxide barriers sandwiched between two layers of superconductor.

Φ

azimuth angle

θ

polar angle

α

probability amplitude of 0 (a complex number)

β

probability amplitude of 1 (a complex number)

π

pulse

a (CNOT gate)

source or control input

X gate

the quantum analog of the classical NOT gate. X | 0 > ＝ | 1 > and X | 1 > ＝ | 0 >

U

unitary operator

spin-up

| 0 > or | ↑ >

spin-down

| 1 > or | ↓ >

量子運算

量子電腦結合電腦科學理論，利用亞原子粒子的某些獨特屬性來存儲和存儲信息。 在過去的三十年中，對量子力學和電腦科學的這種融合進行了廣泛的探索，並導致了針對一類計算問題的技術的發展，例如，解密代碼，分解大量因數，搜索未分類的集合等。 使用量子電腦可以更有效地解決問題。 信息處理能力的這種進步可以歸因於這樣一個事實，即量子電腦中的數據位與傳統電腦中的數據位不同，它們一次可以同時以一種以上狀態存在，並且可以同時被操縱。 常規數字表示中的信息使用比特序列。 每一位基本上都是電子的電荷。 如果電子帶電，則假定該位的值為1；否則為0。 或者，如果電子不帶電，則該位的值為0。 因此，也稱為經典位的位可以處於狀態0或狀態1，並且隨時測量位會導致兩種可能的結果之一。

OR gate

雙0為0

NOR gate

雙0為1

NAND gate

雙1為0

AND gate

雙1為1

XOR gate

鴛鴦為1