Classical computer, information processing method, and computer readable medium
A result confirmation unit ( 204 ) computes a state space probability that is a probability that a verification target device ( 300 ) has not correctly prepared a state space having a quantum state stored therein, a Pauli measurement probability that is a probability that the verification target device ( 300 ) has not correctly performed Pauli Z measurement and Pauli X measurement, and a magic state probability that is a probability that the verification target device ( 300 ) has not generated a magic state of CCZ. Then, using the state space probability, the Pauli measurement probability, and the magic state probability, the result confirmation unit ( 204 ) computes a degree of approximation between a quantum state and the magic state of CCZ at the verification target device ( 300 ) and measurement accuracies of the Pauli Z measurement and the Pauli X measurement on the quantum state at the verification target device ( 300 ).
1. A classical computer comprising:
processing circuitry:
to, using a first measurement result and a second measurement result, compute a state space probability that is a probability that a quantum computer has not correctly prepared a state space having a first quantum state stored therein, the first quantum state being a quantum state generated by the quantum computer, wherein the first measurement result is a result of measuring the first quantum state by the quantum computer, and the second measurement result is a result of measuring a second quantum state by the quantum computer, the second quantum state being a quantum state after change of the first quantum state caused by the measurement of the first quantum state;
to, using a third measurement result, a fourth measurement result, and the first measurement result, compute a Pauli measurement probability that is a probability that the quantum computer has not correctly performed Pauli Z measurement and Pauli X measurement on a fourth quantum state, wherein the third measurement result is a result of measuring a third quantum state by the quantum computer, the third quantum state being a quantum state after change of the first quantum state caused by the measurement of the first quantum state and different from the second quantum state, and the fourth measurement result is a result of measuring the fourth quantum state by the quantum computer, the fourth quantum state being a quantum state after change of the third quantum state caused by the measurement of the third quantum state;
to, using the first measurement result, the third measurement result, and the fourth measurement result, compute a magic state probability that is a probability that the quantum computer has not generated a magic state of CCZ (Controlled Controlled-Z); and
to, using the state space probability, the Pauli measurement probability, and the magic state probability, compute a degree of approximation between the fourth quantum state and the magic state of CCZ, and measurement accuracies of the Pauli Z measurement and the Pauli X measurement on the fourth quantum state, wherein
the processing circuitry generates a public key and a trapdoor from initial data,
the quantum computer generates the first quantum state based on the public key,
the processing circuitry computes the state space probability, using the first measurement result, the second measurement result, and the public key,
the processing circuitry computes the Pauli measurement probability, using the first measurement result, the third measurement result, the fourth measurement result, the public key, and the trapdoor, and
the processing circuitry computes the magic state probability, using the first measurement result, the third measurement result, the fourth measurement result, the public key, and the trapdoor.
2. The classical computer according to claim 1 , wherein
the processing circuitry computes the Pauli measurement probability by performing
a Z basis check process to, using the first measurement result and the public key, generate a Z basis check bit for checking whether the quantum computer has correctly prepared a state in Z basis for the fourth quantum state and has correctly performed the Pauli Z measurement or not, and to determine whether the Z basis check bit agrees with the fourth measurement result or not, and
an X basis check process to, using the first measurement result, the third measurement result, the public key, and the trapdoor, generate an X basis check bit for checking whether the quantum computer has correctly prepared a state in X basis in the fourth quantum state and has correctly performed the Pauli X measurement or not, and to determine whether the X basis check bit agrees with the fourth measurement result or not.
3. The classical computer according to claim 1 , wherein
the processing circuitry computes the magic state probability by: computing a generalized stabilizer measurement result, using the fourth measurement result and Kronecker delta; generating a generalized stabilizer measurement result check bit for checking validity of the generalized stabilizer measurement result, using the first measurement result, the third measurement result, the public key, and the trapdoor; and determining whether the generalized stabilizer measurement result agrees with the generalized stabilizer measurement result check bit or not.
4. The classical computer according to claim 1 , wherein
the processing circuitry generates a probability computation random number that is a random number for determining which of computation of the state space probability, computation of the Pauli measurement probability, and computation of the magic state probability is to be performed,
depending on a value of the probability computation random number, the processing circuitry performs any one of computation of the state space probability, computation of the Pauli measurement probability, and computation of the magic state probability.
5. The classical computer according to claim 1 , wherein
the quantum computer executes a quantum state generation and measurement sequence multiple times, the quantum state generation and measurement sequence consisting of generation of the first quantum state and measurement of the first quantum state, and measurement of the second quantum state or measurement of the third quantum state and measurement of the fourth quantum state,
the processing circuitry computes the state space probability using the first measurement result and the second measurement result for each of the quantum state generation and measurement sequence,
the processing circuitry computes the Pauli measurement probability, using the first measurement result, the third measurement result, and the fourth measurement result for each of the quantum state generation and measurement sequence, and
the processing circuitry computes the magic state probability, using the first measurement result, the third measurement result, and the fourth measurement result for each of the quantum state generation and measurement sequence.
6. The classical computer according to claim 2 , wherein
the processing circuitry generates a measurement random number that is a random number for use in measurement of the fourth quantum state by the quantum computer,
the quantum computer measures the fourth quantum state, using the measurement random number, and
the processing circuitry
in the Z basis check process, determines whether the Z basis check bit agrees with the fourth measurement result or not, and determines whether the measurement random number is of a prescribed value or not, and
in the X basis check process, determines whether the X basis check bit agrees with the fourth measurement result or not, and determines whether the measurement random number is of a value other than the prescribed value or not.
7. The classical computer according to claim 3 , wherein
the processing circuitry generates a measurement random number that is a random number for use in measurement of the fourth quantum state by the quantum computer,
the quantum computer measures the fourth quantum state, using the measurement random number, and
the processing circuitry determines whether the generalized stabilizer measurement result agrees with the generalized stabilizer measurement result check bit or not, determines whether the measurement random number is of a prescribed value or not, and computes the magic state probability.
8. An information processing method, wherein
using a first measurement result and a second measurement result, a classical computer computes a state space probability that is a probability that a quantum computer has not correctly prepared a state space having a first quantum state stored therein, the first quantum state being a quantum state generated by the quantum computer, wherein the first measurement result is a result of measuring the first quantum state by the quantum computer, and the second measurement result is a result of measuring a second quantum state by the quantum computer, the second quantum state being a quantum state after change of the first quantum state caused by the measurement of the first quantum state;
using a third measurement result, a fourth measurement result, and the first measurement result, the classical computer computes a Pauli measurement probability that is a probability that the quantum computer has not correctly performed Pauli Z measurement and Pauli X measurement on a fourth quantum state, wherein the third measurement result is a result of measuring a third quantum state by the quantum computer, the third quantum state being a quantum state after change of the first quantum state caused by the measurement of the first quantum state and different from the second quantum state, and the fourth measurement result is a result of measuring the fourth quantum state by the quantum computer, the fourth quantum state being a quantum state after change of the third quantum state caused by the measurement of the third quantum state;
using the first measurement result, the third measurement result, and the fourth measurement result, the classical computer computes a magic state probability that is a probability that the quantum computer has not generated a magic state of CCZ (Controlled Controlled-Z); and
using the state space probability, the Pauli measurement probability, and the magic state probability, the classical computer computes a degree of approximation between the fourth quantum state and the magic state of CCZ, and measurement accuracies of the Pauli Z measurement and the Pauli X measurement on the fourth quantum state, wherein
the information processing method further comprises:
generating, by the classical computer, a public key and a trapdoor from initial data,
generating, by the quantum computer, the first quantum state based on the public key,
computing, by the classical computer, the state space probability, using the first measurement result, the second measurement result, and the public key,
computing, by the classical computer, the Pauli measurement probability, using the first measurement result, the third measurement result, the fourth measurement result, the public key, and the trapdoor, and
computing, by the classical computer, the magic state probability, using the first measurement result, the third measurement result, the fourth measurement result, the public key, and the trapdoor.
9. A non-transitory computer readable medium storing an information processing program that causes a classical computer to execute:
a state space probability computation process to, using a first measurement result and a second measurement result, compute a state space probability that is a probability that a quantum computer has not correctly prepared a state space having a first quantum state stored therein, the first quantum state being a quantum state generated by the quantum computer, wherein the first measurement result is a result of measuring the first quantum state by the quantum computer, and the second measurement result is a result of measuring a second quantum state by the quantum computer, the second quantum state being a quantum state after change of the first quantum state caused by the measurement of the first quantum state;
a Pauli measurement probability computation process to, using a third measurement result, a fourth measurement result, and the first measurement result, compute a Pauli measurement probability that is a probability that the quantum computer has not correctly performed Pauli Z measurement and Pauli X measurement on a fourth quantum state, wherein the third measurement result is a result of measuring a third quantum state by the quantum computer, the third quantum state being a quantum state after change of the first quantum state caused by the measurement of the first quantum state and different from the second quantum state, and the fourth measurement result is a result of measuring the fourth quantum state by the quantum computer, the fourth quantum state being a quantum state after change of the third quantum state caused by the measurement of the third quantum state;
a magic state probability computation process to, using the first measurement result, the third measurement result, and the fourth measurement result, compute a magic state probability that is a probability that the quantum computer has not generated a magic state of CCZ (Controlled Controlled-Z); and
an approximation accuracy computation process to, using the state space probability, the Pauli measurement probability, and the magic state probability, compute a degree of approximation between the fourth quantum state and the magic state of CCZ, and measurement accuracies of the Pauli Z measurement and the Pauli X measurement on the fourth quantum state, wherein
the information processing program causes the classical computer to further execute:
a key information generation process to generate a public key and a trapdoor from initial data, to enable the quantum computer to generate the first quantum state based on the public key,
the state space probability computation process to compute the state space probability, using the first measurement result, the second measurement result, and the public key,
the Pauli measurement probability computation process to compute the Pauli measurement probability, using the first measurement result, the third measurement result, the fourth measurement result, the public key, and the trapdoor, and
the magic state probability computation process to compute the magic state probability, using the first measurement result, the third measurement result, the fourth measurement result, the public key, and the trapdoor.