Gates · Pauli operator
Pauli-Y gate
The Pauli gate that combines a bit flip with a phase rotation around the y axis.
Exact & formalUpdated
A small worked example, computed in your browser. It is not a result from this record's papers.
Y flips the bit and turns the phase
One qubit starting at |0⟩. Y is the gate that does what X does and a phase as well.
Step 1 of 1 · Y
Probability of each outcome after this step
- 1100%
Takes |0⟩ to i|1⟩. The bit flips exactly as X would flip it, and the amplitude picks up a quarter turn of phase on the way. On this state that phase is global and unobservable; inside a larger circuit, where |0⟩ has amplitude too, it is what separates Y from X.
The whole state moves from 0 to 1 — one certain outcome before, one certain outcome after, no superposition either side.
Readout Measuring always gives 1. By this measurement alone Y is indistinguishable from X — the difference lives in a phase, and a phase needs something to be measured against.
Open in Studio- Steps1
- Wires1
- Qubits1
- Depth1 gate
- Outcomes1 per input
- Papers1
Pauli-Y rounds out the three Pauli generators and makes phase-sensitive basis changes explicit.
Takes1 qubitWhat joins here
Takes a 1-qubit register and states no assumption about what is on it. That is the whole condition: anything returning 1 qubits can feed it.
15 entries meet this end. Named below.
Returns1 qubitWhat joins here
Returns a 1-qubit register a next stage can take. This is the end that joins.
13 entries meet this end. Named below.
A unitary. The same register goes in and comes out, and this entry states no assumption about what is on it — which is what lets anything of the same width feed it. See all 29 →
Pauli- is , combining a bit flip with a phase. Directly: and , matching this record's basis-action check. Up to convention (equivalently ), which is why it behaves as the "odd one out" when composing and . is Hermitian and unitary with , so like and it is its own inverse — the identity this record's matrix square verifies. Its eigenstates have eigenvalues and correspond to a rotation of the Bloch sphere about the -axis. The imaginary prefactors are invisible to a single computational-basis measurement but matter as soon as acts inside a superposition where relative phase drives interference, e.g. inside -basis stabilizer measurements.
Takes1 qubitWhat joins here
Takes a 1-qubit register and states no assumption about what is on it. That is the whole condition: anything returning 1 qubits can feed it.
15 entries meet this end. Named below.
Returns1 qubitWhat joins here
Returns a 1-qubit register a next stage can take. This is the end that joins.
13 entries meet this end. Named below.
A unitary. The same register goes in and comes out, and this entry states no assumption about what is on it — which is what lets anything of the same width feed it. See all 29 →
- Qubits
- 1
- Depth
- 1 gate
- Outcomes
- 1 per input
- Matrix
- [[0, -i], [i, 0]]
- Rotation
- π around Y
- Square
- I
Yon q[0]
Quantum vs classical
Classical baseline
Use a classical state-vector or matrix simulation at the same width, precision, and measurement objective.
Quantum claim
The quantum record demonstrates a state or operator behavior; it does not make classical simulation or communication costs disappear.
How to compare
Compare fidelity, samples, gate depth, noise, memory, and the cost of preparing and reading the state.
Nobody has reviewed this record for gaps yet.
OPENQASM 3.0;
include "stdgates.inc";
qubit q;
y q;Related entries
- Pauli-X operator
Operators
- Pauli-Z gate
Gates
References
- Quantum Computation and Quantum Information: 10th Anniversary Edition
Michael A. Nielsen and Isaac L. Chuang · 2010
Standard graduate textbook covering the single- and two-qubit gate definitions, matrix identities, and circuit primitives this record states.