# Tag Info

41

When we talk about quantum computers, we usually mean fault-tolerant devices. These will be able to run Shor's algorithm for factoring, as well as all the other algorithms that have been developed over the years. But the power comes at a cost: to solve a factoring problem that is not feasible for a classical computer, we will require millions of qubits. This ...

28

An oracle (at least in this context) is simply an operation that has some property that you don't know, and are trying to find out. The term "black box" is used equivalently, to convey the idea that it's just a box that you can't see inside, and hence you don't know what it's doing. All you know is that you can supply inputs and receive outputs. In the ...

22

The church of the larger (or higher, or greater) Hilbert space is just a trick that some people like (myself included) for rewriting some operations. The most general operations that you can write down for a system are described by completely positive maps, while we like describing things with unitaries, which you can always do by moving from the original ...

20

"Postselection" refers to the process of conditioning on the outcome of a measurement on some other qubit. (This is something that you can think of for classical probability distributions and statistical analysis as well: it is not a concept special to quantum computation.) Postselection has featured quite often (up to this point) in quantum mechanics ...

18

The terminology of 'surface code' is a little bit variable. It might refer to a whole class of things, variants of the Toric code on different lattices, or it might refer to the Planar code, the specific variant on a square lattice with open boundary conditions. The Toric Code I'll summarise some of the basic properties of the Toric code. Imagine a square ...

14

The surface codes are a family of quantum error correcting codes defined on a 2D lattice of qubits. Each code within this family has stabilizers that are defined equivalently in the bulk, but differ from one another in their boundary conditions. The members of the surface code family are sometimes also described by more specific names: The toric code is a ...

13

There are a few things to distinguish here, which are often conflated by experts because we're using these terms quickly and informally to convey intuitions rather than in the way that would be most transparent to novices. A "qubit" can refer to a small system, which has a quantum mechanical state. The states of a quantum mechanical system form a vector ...

12

The qsphere is a way of representing multi-qubit states. So it could be used for 5 qubit states, but it could also be used for any other number. It could also be used for just one qubit. But in this case it is important to note that the single qubit qsphere is not the same as the Bloch sphere, which is our standard way of representing single qubit states. ...

11

Quantum computing deals (mostly) with finite-dimensional quantum systems called qubits. If you know basic quantum mechanics then you know that the Hilbert space of a qubit is $\mathbb{C}^2$, i.e., the two-dimensional complex Hilbert space over $\mathbb{C}$ (for the more technical people, the Hilbert space is actually $\mathbb{C}P^1$). Therefore, to ...

10

Code spaces and code-words A quantum error correcting code is often identified with the code-space (Nielsen & Chuang certainly seem to do so). The code space $\mathcal C$ of e.g. an $n$-qubit quantum error correction code is a vector subspace $\mathcal C \subseteq \mathcal H_2^{\otimes n}$. A code word (terminology which was borrowed from the ...

10

Preliminary - The DiVincenzo criteria for a 'normal' quantum computer The DiVincenzo criteria, as originally proposed by DiVincenzo, are $5$ criteria that he originally proposed in his seminal 2000 paper. In this paper, he proposed five criteria, which are widely considered to be the five (sufficient and necessary) criteria that any physical quantum computer ...

9

When translating a classical circuit into a quantum circuit, you often need to introduce extra qubits simply because quantum computers only implement reversible logic. Such extra qubits are ancilla (or ancillary qubits). One way to spot which qubits are ancilla is to look for those qubits that typically need to be "uncomputed" when using the quantum circuit ...

9

T2 is so-called dephasing time. It describes how long the phase of a qubit stays intact. In your words, it is time from $|+\rangle= \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ to $|-\rangle= \frac{1}{\sqrt{2}}(|0\rangle - |1\rangle)$, or conversely. Just note that both T1 and T2 are not actually "time from state x to state y" but rather decay ...

9

Slight correction to Martin Vesely's answer: $T_2$ is not the (decay constant) time after which an initial state $|+\rangle$ will necessarily switch to the state $|-\rangle$. If it were, then error correction would be easy. Instead, it's the (decay constant) time after which an initial state $|+\rangle$ will evolve into an equal classical probabilistic ...

8

No, the computational basis does not have any special meaning, it is just the basis that is "most natural" in a given context, and is conventionally denoted with $|0\rangle$ and $|1\rangle$ in the case of qubits. To give a few examples: If the qubits are encoded into the polarization of single photons, the computational basis is typically the basis formed ...

8

When we have just one qubit, there's nothing particularly special about the computational basis; it's just nice to have a canonical basis. In practice you could think that first you implement a gate $Z$ with $Z^2 = I$ and $Z\neq I$, and then you say that the computational basis is the eigenbasis of this gate. However, when we talk about multi-qubit systems, ...

8

As the other answer conveyed (and to which I am just trying to provide some clarification), post-selection is about just looking at a subset of possible measurement outcomes. To my mind, this falls into two different cases, as below. Yes, they are different aspects of the same thing, but they are used very differently by two different communities. ...

8

"Church of the higher hilbert space" is a term coined by John Smolin. According to quantiki it is: for the dilation constructions of channels and states, which [...] provide a neat characterization of the set of permissible quantum operations and to quote wikipedia, it: describe[s] the habit of regarding every mixed state of a quantum system as a pure ...

7

The general meaning of ancilla in ancilla qubit is auxiliary. In particular, when people write about "constant input" what they mean is that, for a given algorithm -which has a purpose, such as finding the prime factors of an input number, or effecting a simple arithmetic operation between two input numbers the value of the ancilla qubits will be independent ...

7

I managed to get access to the paper mentioned in the question. Schrödinger in 1935 (the same year the original EPR paper was published) wrote in English: "By the interaction the two representatives (or $\psi$-functions) have become entangled." This was in the abstract. He also wrote later in the paper: "What constitutes the entanglement is that $\psi$ is ...

7

The difficulty with explaining quantum computing is that quantum objects and processes have no direct classical analogue; they're an entirely new ontological category. For example, you might have learned in high school physics that light "is both a particle and a wave" in an attempt to relate it to two classical objects you can intuitively understand. In ...

7

The spectral gap is pretty much independent of the promise gap. (First off, my feeling is that "promise gap" is a little bit misleading, though formally correct: What it really refers to, in essence, is the accuracy you are aiming for in determining the energy of the Hamiltonian. One way is to guarantee that the problem does not have a ground state ...

6

Talking about bases such as $\left|0\rangle\langle0\right|$ and $\left|1\rangle\langle1\right|$ (or the equivalent vector notation $\left|0\right>$ and $\left|1\right>$, which I'll use in this answer) at the same time as 'horizontal' and 'vertical' are, to a fair extent (pardon the pun) orthogonal concepts. On a Bloch sphere, there are 3 different ...

6

Is qsphere an actual term representing 5 qubits? If it is, it is not widely used. I claim this because I looked around in arXiv, a repository of electronic preprints of research articles, and found nothing. There are many other units of quantum information than just qubit though. All of the following appear at least occasionally in the relevant literature....

6

If you think of a electronic spin $S=1/2$, imagine measuring it on the z-axis to obtain $S_z=+1/2$ (or $S_z=-1/2$). This (the z projection of the spin magnetic moment) is a possible basis for the measurement. Or you could measure the spin on the x-axis, and they you will obtain $S_x=+1/2$ (or $S_x=-1/2$). This is a different basis. The measurements on Bell ...

6

Qubits are essentially quantum objects from which you can extract a bit. But there are different ways that this can be done, and the answer you get depends on the measurement you choose. If you qubit is an electron spin, the measurement basis corresponds to measuring spin in a particular direction. We use that picture more generally in the form of the Bloch ...

6

Basically, it means that the correlations could be used to send a message. Or simply that Bob’s measurement outcomes can reveal some details of Alice’s actions. This is impossible when Alice and Bob each hold one qubit of a Bell pair. Despite the entanglement present, as well as contextuality, signaling in this case would result faster than light ...

6

There is no standard name for a qudit for $d>3$. The community has mostly settled on the term qudit (but you will still find qunit or quNit, for example, using $n$ or $N$ instead of $d$ in some older papers). You will find the odd paper where an individual author will pick a name for the $d=4$ case. I’ve certainly seen ququad and ququart. But I think ...

6

I had forwarded this question to Dr. Lov Grover and received the following response. I guess inversion about average is a better name for the $\mathrm{W}\mathbb I_0\mathrm{W}$ transformation. When I initially did the algorithm, I called this the diffusion transform because I was familiar with classical diffusion and this is what this transform accomplished -...

6

Note that your current definitions of the projection matrices $\{P_{1},P_{2},...,P_{n}\}$ are actually not projection matrices, since $P_{i}^{2} = I \not= P_{i} \,\, \forall i$. What works 'better' is if you have something like: \begin{split} P_{1}^{+1} =& |0\rangle\langle 0 | \otimes I \otimes I....\otimes I \\ P_{1}^{-1} =& |1\...

Only top voted, non community-wiki answers of a minimum length are eligible