Characterization of quantum logic gates via dynamical decoupling
One example aspect of the present disclosure is directed to a method for characterizing a multi-qubit logic gate operating on a pair of qubits. The method includes iteratively performing, via a multi-qubit quantum circuit, a set of serial operations on the pair of qubits. The multi-qubit quantum circuit includes the multi-qubit logic gate, a first single-qubit logic gate operating on the first qubit, and a second single-qubit logic gate operating on the second qubit. After iteratively performing the set of serial operations on the pair of qubits, a first quantum state of the first qubit and a second quantum state of the second qubit are measured. A first set of expectation values for the first qubit and a second set of expectation values for the second qubit are determined. A value for a first parameter of a set of parameters of the multi-qubit logic gate is determined.
1 . A method for characterizing a multi-qubit logic gate that is enabled to operate on a pair of qubits including a first qubit and a second qubit, the method comprising:
iteratively performing a set of serial operations, by a multi-qubit quantum circuit included in a quantum computing system, on the pair of qubits, wherein the multi-qubit quantum circuit includes at least the multi-qubit logic gate, a first single-qubit logic gate that is a first Pauli gate and is enabled to operate on the first qubit, and a second single-qubit logic gate that is a second Pauli gate and is enabled to operate on the second qubit, and wherein the set of serial operations includes a first operation comprising the multi-qubit logic gate operating on the pair of qubits and a second operation comprising the first single-qubit logic gate operating on the first qubit in parallel to the second single-qubit logic gate operating on the second qubit;
after iteratively performing the set of serial operations on the pair of qubits, measuring, at the quantum computing system, a first quantum state of the first qubit;
after iteratively performing the set of serial operations on the pair of qubits, measuring, at the quantum computing system, a second quantum state of the second qubit;
determining, at the quantum computing system, a first set of expectation values for the first qubit based on the first quantum state of the first qubit;
determining, at the quantum computing system, a second set of expectation values for the second qubit based on the second quantum state of the second qubit; and
determining, at the quantum computing system, a value for at least a first parameter of a set of parameters of the multi-qubit logic gate based on the first set of expectation values for the first qubit and the second set of expectation values for the second qubit.
2 . The method of claim 1 , wherein the multi-qubit logic gate is a Fermionic Simulation (fSim) gate and the first parameter corresponds to a controlled phase of the fSim gate.
3 . The method of claim 1 , wherein the multi-qubit logic gate is a Fermionic Simulation (fSim) gate and the first parameter corresponds to a swap angle of the fSim gate.
4 . The method of claim 1 , wherein the first parameter corresponds to a controlled phase of the multi-qubit logic gate and the method further comprises:
prior to iteratively performing the set of serial operations on the pair of qubits, preparing, at the quantum computing system, an initial quantum state of the first qubit in a vacuum state; and
prior to iteratively performing the set of serial operations on the pair of qubits, preparing, at the quantum computing system, an initial quantum state of the second qubit in a first Hadamard state.
5 . The method of claim 1 , wherein the first parameter corresponds to a swap angle of the multi-qubit logic gate and the method further comprises:
prior to iteratively performing the set of serial operations on the pair of qubits, preparing, at the quantum computing system, an initial quantum state of the first qubit in a vacuum state; and
prior to iteratively performing the set of serial operations on the pair of qubits, preparing, at the quantum computing system, an initial quantum state of the second qubit in a first excited state.
6 . The method of claim 1 , wherein the first parameter corresponds to a controlled phase of the multi-qubit logic gate, the first single-qubit logic gate is a first instantiation of a Pauli-X gate, and the second single-qubit logic gate is a second instantiation of the Pauli-X gate.
7 . The method of claim 1 , wherein the first parameter corresponds to a swap angle of the multi-qubit logic gate, the first single-qubit logic gate is a first instantiation of a Pauli-X gate, and the second single-qubit logic gate is a first instantiation of the Pauli-Y gate.
8 . The method of claim 1 , wherein the first quantum state of the first qubit corresponds to an eigenstate of an X-observable of the first qubit and the second quantum state of the second qubit corresponds to an eigenstate of an X-observable of the second qubit.
9 . The method of claim 1 , wherein the first quantum state of the first qubit corresponds to an eigenstate of a Y-observable of the first qubit and the second quantum state of the second qubit corresponds to an eigenstate of a Y-observable of the second qubit.
10 . The method of claim 1 , wherein the first quantum state of the first qubit corresponds to an eigenstate of an X-observable of the first qubit and the second quantum state of the second qubit corresponds to an eigenstate of an Y-observable of the second qubit.
11 . The method of claim 1 , wherein the first parameter corresponds to a swap angle of the multi-qubit logic gate and the multi-qubit logic gate is operated as a controlled Z gate (CZ gate).
12 . A quantum computing system, comprising:
a pair of qubits that includes a first qubit and a second qubit;
a multi-qubit quantum circuit that includes a multi-qubit gate, a first single qubit logic gate that is a first Pauli gate, and a second single qubit logic gate that is a second Pauli gate, wherein the multi-qubit logic gate is enabled to operate on the pair of qubits, the first single-qubit logic gate is enabled to operate on the first qubit, and the second single-qubit logic gate is enabled to operate on the second qubit;
one or more processors;
one or more memory devices, the one or more memory devices storing computer-readable instructions that when executed by the one or more processors cause the one or more processors to perform operations for characterizing the multi-qubit logic gate, the operations comprising:
iteratively performing a set of serial operations, by the multi-qubit quantum circuit, on the pair of qubits, wherein the multi-qubit quantum circuit includes at least the multi-qubit logic gate, a first single-qubit logic gate enabled to operate on the first qubit, and a second single-qubit logic gate that is enabled to operate on the second qubit, and wherein the set of serial operations includes a first operation comprising the multi-qubit logic gate operating on the pair of qubits and a second operation comprising the first single-qubit logic gate operating on the first qubit in parallel to the second single-qubit logic gate operating on the second qubit;
after iteratively performing the set of serial operations on the pair of qubits, measuring a first quantum state of the first qubit;
after iteratively performing the set of serial operations on the pair of qubits, measuring a second quantum state of the second qubit;
determining a first set of expectation values for the first qubit based on the first quantum state of the first qubit;
determining a second set of expectation values for the second qubit based on the second quantum state of the second qubit; and
determining a value for at least a first parameter of a set of parameters of the multi-qubit logic gate based on the first set of expectation values for the first qubit and the second set of expectation values for the second qubit.
13 . The system of claim 12 , wherein the multi-qubit logic gate is a Fermionic Simulation (fSim) gate and the first parameter corresponds to a controlled phase of the fSim gate.
14 . The system of claim 12 , wherein the multi-qubit logic gate is a Fermionic Simulation (fSim) gate and the first parameter corresponds to a swap angle of the fSim gate.
15 . The system of claim 12 , wherein the first parameter corresponds to a controlled phase of the multi-qubit logic gate and the method further comprises:
prior to iteratively performing the set of serial operations on the pair of qubits, preparing an initial quantum state of the first qubit in a vacuum state; and
prior to iteratively performing the set of serial operations on the pair of qubits, preparing an initial quantum state of the second qubit in a first Hadamard state.
16 . The system of claim 12 , wherein the first parameter corresponds to a swap angle of the multi-qubit logic gate and the method further comprises:
prior to iteratively performing the set of serial operations on the pair of qubits, preparing an initial quantum state of the first qubit in a vacuum state; and
prior to iteratively performing the set of serial operations on the pair of qubits, preparing an initial quantum state of the second qubit in a first excited state.
17 . The system of claim 12 , wherein the first parameter corresponds to a controlled phase of the multi-qubit logic gate, the first single-qubit logic gate is a first instantiation of a Pauli-X gate, and the second single-qubit logic gate is a second instantiation of the Pauli-X gate.
18 . The system of claim 12 , wherein the first parameter corresponds to a swap angle of the multi-qubit logic gate, the first single-qubit logic gate is a first instantiation of a Pauli-X gate, and the second single-qubit logic gate is a first instantiation of the Pauli-Y gate.