Why does a controlled gate not constitute a measurement?

Why does a controlled gate not constitute a measurement? Ask Question Asked 6 years, 5 months ago Modified today Viewed 1k times 7 I have recently listened to a talk on quantum computing and was fascinated to learn about IBM Q Experience. Between the explanations in the User Guide and in Nielsen's book, I came to the following question: Why does a controlled gate not act as a measurement? In the common example of creating a Bell pair, we first bring a two qubit state from |ψ⟩=|00⟩ | 𝜓 ⟩ = | 00 ⟩ to 1 2 √ (|00⟩+|10⟩) 1 2 ( | 00 ⟩ + | 10 ⟩ ) with a Hadamard gate. So far so good. But now we flip the second qubit only if the first is in state |1⟩ | 1 ⟩ . This turns the state of the two-qubit system into 1 2 – √ (|00⟩+|11⟩). 1 2 ( | 00 ⟩ + | 11 ⟩ ) . How does that work without measuring the state of the first qubit? quantum-gatemeasurement Share Improve this question Follow asked Oct 19, 2019 at 8:30 DK2AX 1735 5 bronze badges 1 Hi, welcome to QCSE. It's not as if the CNOT C N O T gate "looks" at the two qubits in their different states. A somewhat unsatisfactory answer is that the qubits must maintain coherence in order to apply the CNOT C N O T gate - the quantum gate is designed to specifically maintain coherence of the control and target qubit, for as long as possible. Maybe a better answer would explain how devices like IBM's are able to apply 2 2 -qubit gate while maintaining coherence. –  Mark Spinelli Commented Oct 19, 2019 at 12:42 Maybe a little late to the party but I want to drop a comment. It is not like your unitary checks that your qubit is in 0 or 1 and then puts it in 1 or 0 respectively when we apply X. Should ask the same question for other gates too, how they are able to convert the states without looking at them. In the case of the CNOT gate, it's doing the unitary transformation but it appears that one qubit is controlling the other's state. It does, in a way, but not the way we are thinking right now. It is doing the same rotations but results look different for different two qubit states. –  Prabhat Commented Jan 18, 2023 at 10:16 Add a comment 3 Answers Sorted by: Highest score (default) Date modified (newest first) Date created (oldest first) 4 How it works depends on the choice of quantum system used for computation. For any choice of quantum system, the common theme is that CNOT CNOT does not collapse the wavefunction, i.e. force a choice between |0⟩ | 0 ⟩ and |1⟩ | 1 ⟩ , while a measurement does. A simple example (oversimplified here) uses a non-linear Kerr medium to create a CNOT CNOT gate with two photons acting as qubits. In this case a Hadamard gate ( H 𝐻 ) is created with phase shifters (slabs of transparent media with index of refraction ≠1 ≠ 1 ) and beam splitters (partially silvered glass), which produce the superposition of states. The Kerr effect is a change in refractive index based on the presence of an electric field in the Kerr medium, and when two photons pass through a Kerr medium they can experience cross-phase modulation. In other words the atoms in the Kerr medium mediate an interaction between the two photons (qubits). The upshot is that the system can be tuned such that the Kerr medium acts as the gate K= ⎡ ⎣ ⎢ ⎢ ⎢ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 −1 ⎤ ⎦ ⎥ ⎥ ⎥ . 𝐾 = [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 − 1 ] . With access to K 𝐾 and H 𝐻 , the CNOT CNOT gate ( U c 𝑈 𝑐 ) is simply U c =(I⊗H)K(I⊗H)= ⎡ ⎣ ⎢ ⎢ ⎢ 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 ⎤ ⎦ ⎥ ⎥ ⎥ . 𝑈 𝑐 = ( 𝐼 ⊗ 𝐻 ) 𝐾 ( 𝐼 ⊗ 𝐻 ) = [ 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 ] . In this manner the U c 𝑈 𝑐 gate is implemented without collapsing the wavefunction. Conversely, when a photon interacts with a photon detector (measurement) it is absorbed and converted to current or voltage, collapsing the wavefunction and forcing it to choose one definite state. As noted above, this is an oversimplified explanation. Since you already have Nielsen and Chuang, you can see a much more rigorous treatment of this example in Section 7.4.2, as well as constructions of CNOT CNOT in the context of ion traps (7.6.3) and nuclear magnetic resonance (7.7.3). Share Improve this answer Follow edited Oct 19, 2019 at 19:43 answered Oct 19, 2019 at 19:36 Jonathan Trousdale 3,50210 10 silver badges 21 21 bronze badges Add a comment 0 A mechanistic way of looking at it that is sure to infuriate any genuine physicists in the discussion :) is that a CNOT is two supercooled transmons interacting as described in the Open Pulse documentation and that the mystical "observation" does not occur until there is an interaction outside that environment. Share Improve this answer Follow answered Oct 19, 2019 at 15:01 Jack Woehr 594 4 bronze badges Add a comment 0 A CNOT gate is a REVERSIBLY TRANSFORMATIVE 2-qubit conditional gate operation. How to create a 1-qubit conditional gate? Let's start simple with a single qubit conditional gate before we jump to two qubits. I find photonics are the easiest to understand intuitively; specifically, let's look at a Polarized Beam Splitter (PBS). If we shoot a beam of photons into a PBS, the beam will be directed onto path A or B based on the polarization of the photons. A PBS effectively works as an 'if' statement without "measurement:" if a photon is vertically polarized (|𝑉⟩), then reflect it into Path B; else, transmit it into Path A Measurement: we don't know which path it took until we measure at the end, thus preserving the quantum state. Reversibility: you can also imagine if we had a second PBS, we could redirect the beam back into the original path without having changed anything. In fact, in linear optics, a PBS is often used to implement a "trivial" version of a CNOT gate. How to create a 2-qubit conditional gate? If we stick with photonics, we would need to add another tool, in addition to the beam splitter: phase interference. Two photons can interact based on interference without any measurement necessary. We can leverage tools like polarization, interference, and other more complex systems to create logic that is conditional without disrupting the quantum state of the system. See this paper here. How does IBM create a 2-qubit conditional gate? IBM uses a clever combination of cross resonant behavior and gate logic. Here's a simplified explanation... Setup: We need two qubits: a Control Qubit (QC) and a Target Qubit (QT) Both qubits are in close proximity physically Both qubits are coupled/connected in a way that allows them to interact (cross resonance) Step 1: Apply a microwave pulse to the QC qubit at the resonant frequency of the QT. Due to the coupling, this induces a rotation on the QT that depends on the state of the control qubit (ZX rotation). Long story short: if the QC is |0>, we induce a +X rotation on the QT if the QC is |1>, we induce a -X rotation on the QT The cleverness: the IBM engineers use this phenomenon to induce a π/2 rotation (x-axis) on the QT. Step 2: Next, we perform an RX[-π/2] gate directly on QT. The results either add constructively or destructively to Step 1 to create a full rotation or cancel out completely; effectively, conditionally flipping a bit without ever "measuring" it. We can picture this on the Bloch Sphere; however, since we're only using two axis, we only need to picture a clock. For the sake of simplicity, let's say the QT starts at |0>. In the image below, the two columns show two possible states of the QC and the effect of the 2 steps on the QT. Step 1: If the QC is |0>, it induces a π/2 rotation which would leave QT at 3 o’clock. If the QC is |1>, it induces a -π/2 rotation which would leave QT at 9 o’clock. Step 2: We rotate (RX) the QT by -π/2. If QT is at 9 o’clock, a -π\2 rotation would leave it at 6 o’clock (|1> - bit flipped). If QT was at 3 o’clock, a -π/2 rotation would leave it at 12 o’clock (|0> - back where we started). The actual implementation is slightly more complex and includes some additional steps for error correction. Please note: I am not a physicist and this is simply my best attempt at understanding this fascinating topic! If you see anything amiss, please correct me. ❤️ Share Improve this answer Follow edited 3 hours ago answered 3 hours ago Ethan Strider 1011 1 bronze badge New contributor Add a comment Your Answer Sign up or log in Sign up using Google Sign up using Email and Password Post as a guest Name Email Required, but never shown Post Your Answer By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. Start asking to get answers Find the answer to your question by asking. Ask question Explore related questions quantum-gatemeasurement See similar questions with these tags. The Overflow Blog Prevent agentic identity theft Building shared coding guidelines for AI (and people too) Linked 5 How do we realise photonic gates? 2 What is quantum gate's correponding circuit implementation? Related 1 How does entangle qubits pass single qubit gate? 2 Can Shor's 9 Qubit Code Correct for a measurement on the first qubit? 5 How Does the Qiskit Reset Gate Affect Other Entangled Qubits 3 Measuring in the computational basis in the single qubit gate QFT implementation 2 How does a generic controlled-U operation work? 2 Is it necessary to apply CNOT for the sole purpose of "establishing a correlation" between two qubits 3 How does syndrome extraction in bit-flip codes using stabilizers work? 0 Connection between a Pauli measurement and the corresponding Pauli gate? 1 How exactly does measuring a syndrome operator work for 'non-discrete' errors? Hot Network Questions feature generating strategy Number of Solutions to Equations involving Floor Function Getting accurate estimates of TSA line lengths? Check out these rebuses Get index of aperiodic number I built a database. What should I do next? Speed of light as limit of information or limit of energy transfer Compare & Contrast Genesis 9:22's idiom phrase "saw the nakedness of his father" with Ezekiel 22:10's phrase "have uncovered their fathers’ nakedness" "Surprising" clause in a Swiss car rental contract? If an emoji renders differently on two devices due to compatibility issues, whose interpretation is valid? What is reservation in anticipation of demand? Colleague doesn't work on any task unless request specifically comes from the boss If *wh-movement* is blocked by a syntactic island, how can we form an interrogative clause? How long do valves last? Decoding keylock from sys.dm_os_waiting_tasks.resource_description How long will it take the remaining cleaners? Ignoring the tail of the letter "g" in setting the baseline of text in nodes of a tikz diagram What is the physics behind how welding works? What are these straps on these common pressure suits? 41 years of confusing Windows version naming What is the difference between "Что случается?" and "Что происходит?" To what extent did the evacuation of Soviet factories to the Urals apply to those in the Moscow region? Local travel info related to NBJ (Dr. António Agostinho Neto International Airport)? How idiomatic is the term "library person" in this context? Question feed By continuing to use this website, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. By exiting this window, default cookies will be accepted. To reject cookies, select an option from below. Customize settings Cookie Consent Preference Center When you visit any of our websites, it may store or retrieve information on your browser, mostly in the form of cookies. This information might be about you, your preferences, or your device and is mostly used to make the site work as you expect it to. The information does not usually directly identify you, but it can give you a more personalized experience. Because we respect your right to privacy, you can choose not to allow some types of cookies. Click on the different category headings to find out more and manage your preferences. Please note, blocking some types of cookies may impact your experience of the site and the services we are able to offer. Cookie Policy Accept all cookies Manage Consent Preferences Strictly Necessary Cookies Always Active These cookies are necessary for the website to function and cannot be switched off in our systems. They are usually only set in response to actions made by you which amount to a request for services, such as setting your privacy preferences, logging in or filling in forms. You can set your browser to block or alert you about these cookies, but some parts of the site will not then work. These cookies do not store any personally identifiable information. Targeting Cookies Targeting Cookies These cookies are used to make advertising messages more relevant to you and may be set through our site by us or by our advertising partners. They may be used to build a profile of your interests and show you relevant advertising on our site or on other sites. They do not store directly personal information, but are based on uniquely identifying your browser and internet device. Performance Cookies Performance Cookies These cookies allow us to count visits and traffic sources so we can measure and improve the performance of our site. They help us to know which pages are the most and least popular and see how visitors move around the site. All information these cookies collect is aggregated and therefore anonymous. If you do not allow these cookies we will not know when you have visited our site, and will not be able to monitor its performance. Functional Cookies Functional Cookies These cookies enable the website to provide enhanced functionality and personalisation. They may be set by us or by third party providers whose services we have added to our pages. If you do not allow these cookies then some or all of these services may not function properly. Cookie List Clear checkbox label label Apply Cancel Consent Leg.Interest checkbox label label checkbox label label checkbox label label Necessary cookies only Confirm My Choices