QUANTUM COMPUTER VERIFICATION APPARATUS AND METHOD
A quantum computer verification apparatus includes: a division unit 1 that divides n qubits on which a quantum circuit U acts into m qubits and (n−m) qubits such that the number of CZ gates across the qubits becomes D=O(log n); a stabilizer operator calculation unit 2 that calculates a stabilizer operator {circumflex over ( )}s k for each k; an estimation unit 3 that randomly selects (i, j, i′, j′) T 2 times for each k and calculates estimates of a real part of a value of the following expression to obtain T 2 estimates; ( - 1 ) i · j + i ′ · j ′ T r [ ρ out [ Q i , j † ( ∏ i = 1 n Z i k i ) Q i ′ , j ′ ] ] an average calculation unit 4 that obtains an average of the T 2 estimate for each k and sets the obtained average as an estimate of Tr[ρ out {circumflex over ( )}s k ] corresponding to each k, and a fidelity estimation value calculation unit 5 that obtains an average of estimates of Tr[ρ out {circumflex over ( )}s k ] corresponding to each k.
1 . A quantum computer verification apparatus comprising processing circuitry configured to:
divide n qubits on which a quantum circuit U acts into m qubits and (n−m) qubits such that a number of CZ gates across the qubits becomes D=O(log n), the quantum circuit U being assumed to be able to be expressed by the following expression using an m-qubit gate V i and an (n−m) qubit gate W j ;
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24
]
randomly select a value of k∈{0, 1} n T 1 times, and calculate a stabilizer operator {circumflex over ( )}s k defined by the following expression for each k, where Q i,j † =V i (×)W j , k i is an i-th bit of k, Z i is a Pauli Z gate acting on an i-th qubit, i L and j L are L-th bits of i and j, i·j=(+) L=1 D i L j L , and T 1 is a predetermined positive integer;
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randomly select (i, j, i′, j′) T 2 times for each k and calculate estimates of a real part of a value of the following equation to obtain T 2 estimates, where ρ out is a state output by the quantum circuit U;
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obtain an average of the T 2 estimates for each k and set the obtained average as an estimate of Tr[ρ out {circumflex over ( )}s k ] corresponding to each k; and
obtain an average of estimates of Tr[ρ out {circumflex over ( )}s k ] corresponding to each k and set the average as an estimate F est of fidelity F of the quantum circuit U.
2 . A quantum computer verification method comprising:
a division step in which a division unit divides n qubits on which a quantum circuit U acts into m qubits and (n−m) qubits such that a number of CZ gates across the qubits becomes D=O(log n), the quantum circuit U being assumed to be able to be expressed by the following expression using an m-qubit gate V i and an (n−m) qubit gate W j by a stabilizer operator calculation unit;
U
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[
Math
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27
]
a stabilizer operator calculation step in which the stabilizer operator calculation unit randomly selects a value of k∈{0, 1} n T 1 times, and calculates a stabilizer operator {circumflex over ( )}s k defined by the following equation for each k, where Q i,j † =V i (×)W j , k i is an i-th bit of k, Z i is a Pauli Z gate acting on an i-th qubit, i L and j L are L-th bits of i and j, i·j=(+) L=1 D i L j L , and T 1 is a predetermined positive integer;
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an estimation step in which an estimation unit randomly selects (i, j, i′, j′) T 2 times for each k and calculate estimates of a real part of a value of the following equation to obtain T 2 estimates, ρ out being a state output by the quantum circuit U;
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an average calculation step in which an average calculation unit obtains an average of the T 2 estimates for each k and sets the obtained average as an estimate of Tr[ρ out {circumflex over ( )}s k ] corresponding to each k; and
a fidelity estimate calculation step in which a fidelity estimate calculation unit obtains an average of estimates of Tr[ρ out {circumflex over ( )}s k ] corresponding to each k and sets the average as an estimate F est of fidelity F of the quantum circuit U.