Doubly controlled iX circuit
A quantum computing device including a doubly controlled iX (CCiX) circuit. The CCiX circuit may be configured to, in a preparation stage, prepare a plurality of magic states. The CCiX circuit may be further configured to receive a plurality of input qubit states including a first control qubit state, a second control qubit state, and a target qubit state. In an execution stage, the CCiX circuit may be further configured to perform a CCiX operation on the target qubit state at least in part by performing a plurality of local joint measurements. At least a subset of the plurality of local joint measurements may be performed between the plurality of magic states and a plurality of auxiliary qubits. Performing the CCiX operation may further include performing a plurality of remote joint measurements of the input qubit states and a plurality of interface qubits included among the plurality of auxiliary qubits.
1 . A quantum computing device comprising:
a doubly controlled iX (CCiX) circuit configured to:
in a preparation stage, prepare a plurality of magic states;
receive a plurality of input qubit states including a first control qubit state, a second control qubit state, and a target qubit state; and
in an execution stage, perform a CCiX operation on the target qubit state at least in part by:
performing a plurality of local joint measurements, wherein at least a subset of the plurality of local joint measurements are performed between the plurality of magic states and a plurality of auxiliary qubits; and
performing a plurality of remote joint measurements of the input qubit states and a plurality of interface qubits included among the plurality of auxiliary qubits.
2 . The quantum computing device of claim 1 , wherein the plurality of magic states prepared in the preparation stage includes a plurality of |S x states and a plurality of |T states.
3 . The quantum computing device of claim 2 , wherein the preparation stage includes:
a first preparation sub-stage in which the CCiX circuit is configured to prepare a first |S x state, a second |S x state, a first |T state, and a second |T state in parallel; and
a second preparation sub-stage subsequent to the first preparation sub-stage in which the CCiX circuit is configured to prepare a third |S x , a fourth |S x state, a third |T state, and a fourth |T state in parallel.
4 . The quantum computing device of claim 1 , wherein performing the plurality of remote joint measurements includes, in each of a first execution sub-stage and a second execution sub-stage, performing two remote ZZ measurements and a remote XZ measurement.
5 . The quantum computing device of claim 1 , wherein, in the execution stage, the CCiX circuit is configured to apply a plurality of exponential gates in parallel to the plurality of input qubit states when performing the CCiX operation.
6 . The quantum computing device of claim 5 , wherein the CCiX circuit is further configured to:
in the preparation stage, prepare a plurality of |GHZ n Z states and a plurality of |GHZ n X states; and
in the execution stage, apply the plurality of exponential gates at least in part by performing a plurality of local joint measurements on the plurality of |GHZ n Z states and the plurality of |GHZ n X states.
7 . The quantum computing device of claim 6 , wherein the CCiX circuit is configured to prepare the plurality of |GHZ n Z states and the plurality of |GHZ n X states at least in part by performing a plurality of quantum fanout operations.
8 . The quantum computing device of claim 7 , wherein the CCiX circuit is configured to prepare the plurality of |GHZ n Z states and the plurality of |GHZ n X states such that one or more of the |GHZ n Z states and one or more of the |GHZ n X states are formed along respective paths that have respective holes.
9 . The quantum computing device of claim 6 , wherein the execution stage includes:
a first execution sub-stage in which the CCiX circuit is configured to perform a plurality of local joint ZZ measurements of respective first subsets of the magic states and the auxiliary qubits; and
a second execution sub-stage in which the CCiX circuit is configured to perform a plurality of local joint XZ measurements of respective second subsets of the magic states and the auxiliary qubits.
10 . The quantum computing device of claim 5 , wherein the plurality of exponential gates includes an
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11 . The quantum computing device of claim 1 , wherein the CCiX circuit is further configured to perform a plurality of X corrections and a plurality of Z corrections subsequently to the execution stage.
12 . The quantum computing device of claim 1 , wherein the CCiX circuit is included in a rectangular grid of logical qubits.
13 . A method for use with a quantum computing device that includes a doubtly controlled iX (CCiX) circuit and a measuremnet device, the method comprising:
at the (CCiX) circuit:
in a preparation stage, preparing a plurality of magic states;
receiving a plurality of input qubit states including a first control qubit state, a second control qubit state, and a target qubit state; and
in an execution stage, performing a CCiX operation on the target qubit state at least in part by:
with the measurement device, performing a plurality of local joint measurements, wherein at least a subset of the plurality of local joint measurements are performed between the plurality of magic states and a plurality of auxiliary qubits; and
with the measurement device, performing a plurality of remote joint measurements of the input qubit states and a plurality of interface qubits included among the plurality of auxiliary qubits.
14 . The method of claim 13 , wherein:
the plurality of magic states prepared in the preparation stage includes a plurality of |S x states and a plurality of |T states; and
the preparation stage includes:
in a first preparation sub-stage, preparing a first |S x state, a second |S x state, a first |T state, and a second |T state in parallel; and
in a second preparation sub-stage subsequent to the first preparation sub-stage, preparing a third |S x , a fourth |S x state, a third |T state, and a fourth |T state in parallel.
15 . The method of claim 13 , wherein performing the plurality of remote joint measurements includes, in each of a first execution sub-stage and a second execution sub-stage, performing two remote ZZ measurements and a remote XZ measurement.
16 . The method of claim 13 , further comprising, in the execution stage, applying a plurality of exponential gates in parallel to the plurality of input qubit states when performing the CCiX operation, wherein the plurality of exponential gates includes an
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17 . The method of claim 16 , further comprising:
in the preparation stage, preparing a plurality of |GHZ n Z states and a plurality of |GHZ n X states at least in part by performing a plurality of quantum fanout operations; and
in the execution stage, applying the plurality of exponential gates at least in part by performing a plurality of local joint measurements on the plurality of |GHZ n Z states and the plurality of |GHZ n X states.
18 . The method of claim 17 , wherein the execution stage includes:
in a first execution sub-stage, performing a plurality of local joint ZZ measurements of respective first subsets of the magic states and the auxiliary qubits; and
in a second execution sub-stage, performing a plurality of local joint XZ measurements of respective second subsets of the magic states and the auxiliary qubits.
19 . The method of claim 13 , further comprising performing a plurality of X corrections and a plurality of Z corrections subsequently to the execution stage.
20 . A quantum computing device comprising:
a doubly controlled iX (CCiX) circuit configured to:
in a preparation stage, prepare a plurality of |S x states and a plurality of |T states at least in part by:
in a first preparation sub-stage, preparing a first |S x state, a second |S x state, a first |T state, and a second |T state in parallel; and
in a second preparation sub-stage subsequent to the first preparation sub-stage, preparing a third |S x , a fourth |S x state, a third |T state, and a fourth |T state in parallel; and
in an execution stage, perform a CCiX operation on the target qubit state at least in part by:
in a first execution sub-stage, performing a plurality of local joint ZZ measurements of respective first subsets of the |S x states, the |T states, and the auxiliary qubits;
in a second execution sub-stage, performing a plurality of local joint XZ measurements of respective second subsets of the |S x states, the |T states, and the auxiliary qubits; and
during each of the first execution sub-stage and the second execution sub-stage, performing a plurality of remote joint measurements of the input qubit states and a plurality of interface qubits included among the plurality of auxiliary qubits.