first

Author: NGBigField

codes/quantum/oscillators/uncategorized/squeezed_vacuum.yml

@@ -0,0 +1,115 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+
+
+code_id: 'squeezed_vacuum'
+
+name: 'Squeezed-vacuum codes'
+
+short_name: 'Squeezed-vacuum'
+
+introduced: '\cite{arxiv:2511.06108}'
+
+description: |-
+  
+  A family of rotation-symmetric bosonic quantum error-correcting codes constructed from a coherent superposition of $m$ squeezed vacuum states, each squeezed along evenly-spaced axes in phase space. For an even integer $m > 0$ (the number of ``legs'') and squeezing strength $r$, the two logical codewords are defined as
+  \begin{align}
+    |0_L\rangle & \propto \sum_{j=0}^{m-1} S\left(r, \frac{\pi j}{m}\right) \ket{\vac}, \\
+    |1_L\rangle & \propto \sum_{j=0}^{m-1} (-1)^{j} S\left(r, \frac{\pi j}{m}\right) \ket{\vac},
+  \end{align}
+  where $S(r,\theta) \equiv S(r e^{i\phi(\theta)})$ is the squeezing operator with $\phi(\theta) = 2\theta + \pi \pmod{2\pi}$, defined as
+  \begin{equation}
+  S(\zeta) = \exp\!\left[\frac{1}{2}\left(\zeta^{*} a^{2}-\zeta\, a^{\dagger 2}\right)\right],
+  \end{equation}
+  where $\zeta = r e^{i\phi}$ and $r$ is the squeezing strength. This operator elongates the vacuum state along direction $\theta$ in phase space.
+
+  In Fock space, the logical states occupy photon numbers $n \equiv 2k \pmod{2m}$ for $k \in \{0, m/2\}$, yielding natural number distributions that are interleaved by $\Delta n = m$. The code provides protection against both photon loss and dephasing noise, with a fundamental trade-off: increasing $m$ improves loss tolerance at the cost of higher dephasing sensitivity.
+
+  The squeezed-vacuum codes approach the ideal number-phase code in the limit $r \to \infty$. They generalize the single-primitive squeezed Fock states ($m=1$) and the two-legged case ($m=2$) studied independently.
+
+alternative_names:
+  - 'Multi-legged squeezed codes'
+
+  - 'Squeezed vacuum bosonic codes'
+
+physical: 'Quantum harmonic oscillators'
+
+logical: 'qubits'
+
+protection: |2-
+    The code distance against single-photon loss is \(d = m\), where \(m\) is the number of legs (squeezed vacuum states in superposition). The code provides approximate protection against photon loss and dephasing channels, with performance determined by the parameters \(m\) and \(r\). 
+    
+    As \(m\) increases, the code exhibits improved loss tolerance (lower Knill-Laflamme violation) but becomes more susceptible to dephasing noise.
+
+features:
+  
+  encoders:
+    - |-
+      \textbf{Probabilistic preparation (\(m=2\)):} 
+            The simplest circuit uses a Hadamard-Controlled-Squeezing-Hadamard (\(H\)-\(CS\)-\(H\)) sequence on a single ancilla qubit coupled to a bosonic mode initially in vacuum. The conditional squeezing gate is defined as
+            \begin{equation}
+            CS(r;\theta_0,\theta_1) = \ket{0}\!\bra{0}\otimes S(r,\theta_0) + \ket{1}\!\bra{1}\otimes S(r,\theta_1).
+            \end{equation}
+            After applying \(H\)-\(CS(r;0,\pi/2)\)-\(H\) and measuring the ancilla in the \(Z\) basis, the bosonic mode collapses to either \(\ket{0_L}\) or \(\ket{1_L}\) with probabilities
+            \begin{equation}
+            \text{prob}(L \mid r) = \frac{1}{2} + \frac{(-1)^L}{2 \cosh r \sqrt{\tanh^2 r + 1}},
+            \end{equation}
+            where \(L \in \{0, 1\}\). Post-selection on the measurement outcome yields the desired logical state.
+
+    - |-
+      \textbf{Deterministic preparation (general \(m\)):}
+            For \(m > 2\), the codes can be prepared using sequences of conditional rotations \(CR(\theta)\) that rotate the bosonic mode in phase space by angle \(\theta\) conditioned on the qubit state, combined with logical-\(X\) gates that flip between the computational basis states. The circuit involves creating superpositions with single-qubit gates and applying conditional operations in a recursive manner. With full single-qubit control and controlled-squeezing operations, these circuits provide universal control over the joint qubit-oscillator system.
+
+    - |-
+      \textbf{Recursive construction:}
+            Higher-\(m\) codes can be generated by feeding back the output of lower-\(m\) code preparation circuits, applying additional conditional rotations, and selecting appropriate measurement outcomes. This allows systematic construction of the entire code family.
+
+  general_gates:
+    - 'Universal quantum computation with squeezed-vacuum codes requires multiple bosonic modes and entangling gates between them, such as a controllable cross-Kerr interaction $a^\dagger a \otimes a^\dagger a$ that enables generation of the entangling $CZ$ gate.'
+
+    - 'Logical operations within a single mode can be performed using Gaussian operations (displacement, rotation, squeezing) combined with conditional control from an ancilla qubit.'
+
+  decoders:
+    - 'The interleaved photon-number structure ($n \equiv 2k \pmod{2m}$) enables photon-number-resolving measurements to identify single-photon loss events, which can then be corrected.'
+
+realizations:
+  - 'Circuit QED: Recent proposals demonstrate controlled-squeezing gates using driven multiphoton qubit-resonator interactions \cite{doi:10.1103/PhysRevA.110.053711}, Rabi-driven qubits dispersively coupled to high-$Q$ oscillators \cite{arxiv:2507.22641}, and SQUID-terminated resonators \cite{doi:10.1103/PhysRevA.111.042606}. Number-selective conditional rotations (SNAP gates) \cite{doi:10.1103/PhysRevLett.115.137002} and high-fidelity single-mode squeezing \cite{doi:10.1038/s41567-022-01708-1} also provide the necessary ingredients for implementation.'
+
+  - '\paragraph{Trapped ions:} Optimal-control techniques for conditional Gaussian operations \cite{arxiv:2505.20844} make trapped-ion platforms viable for implementing squeezed-vacuum codes.'
+
+notes:
+  - 'The conditional-squeezing gate required for code preparation has been proposed and is under active development across multiple platforms, including circuit QED \cite{doi:10.1103/PhysRevA.110.053711,arxiv:2507.22641,doi:10.1103/PhysRevA.111.042606} and trapped ions \cite{arxiv:2505.20844}.'
+
+  - 'Squeezed-vacuum codes are approximate number-phase codes, approaching the ideal number-phase code limit as $r \to \infty$. They represent a sub-family of rotation-symmetric bosonic codes with the characteristic trade-off between loss and dephasing protection.'
+
+relations:
+  
+  parents:
+    - code_id: 'single-mode'
+      detail: 'Squeezed-vacuum codes encode logical qubits into a single bosonic mode.'
+    - code_id: 'bosonic_rotation'
+      detail: 'Squeezed-vacuum codes are rotation-symmetric bosonic codes with $m$-fold rotational symmetry in phase space, constructed from $m$ primitive squeezed vacuum states arranged at evenly-spaced angles \cite{doi:10.1103/PhysRevX.10.011058}.'
+
+  cousins:
+    - code_id: 'cat'
+      detail: 'Both cat codes and squeezed-vacuum codes are rotation-symmetric bosonic codes constructed from superpositions of Gaussian states. Cat codes use coherent states (displacements) while squeezed-vacuum codes use squeezed states. Both exhibit the trade-off between loss and dephasing protection as the number of legs $m$ increases \cite{arxiv:2511.06108}.'
+
+    - code_id: 'binomial'
+      detail: 'Binomial codes and squeezed-vacuum codes both provide protection against photon loss and have finite mean energy. Both can be prepared using conditional operations on an ancilla qubit.'
+
+    - code_id: 'squeezed_fock_state'
+      detail: 'The $m=1$ case of squeezed-vacuum codewords reduces to a single squeezed Fock state~$S(\pm r)\ket{0}$.'
+
+    - code_id: 'number_phase'
+      detail: 'Squeezed-vacuum codes are approximate number-phase codes with Fock-space support $n \equiv 2k \pmod{2m}$, approaching ideal number-phase codes as squeezing strength $r \to \infty$~\cite{arxiv:2511.06108}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: NirGutman
+      date: '2025-11-17'

users/users_db.yml

@@ -599,6 +599,12 @@
   gscholaruser: 'cfFbFYUAAAAJ'
   githubusername: MarcSerraPeralta
 
+- user_id: NirGutman
+  name: 'Nir Gutman'
+  gscholaruser: 'azmlG_EAAAAJ'
+  githubusername: NGBigField
+
+
 #
 # Core members -- add 'zooteam: core' and 'zoorole: <role>' to each entry.
 #