Statevectors

The statevector is the complete quantum state: 2ⁿ complex amplitudes.

Requesting one

import numpy as np
from qiskit import QuantumCircuit

from menos.qiskit import MENOSBackend

qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)

result = MENOSBackend().run(qc, shots=0, want_statevector=True).result()
state = np.asarray(result.get_statevector())
print(state)
assert state.shape == (4,)
assert np.allclose(state, [2**-0.5, 0, 0, 2**-0.5])

A circuit with no measurements and shots=0 is the usual form. A statevector can also be requested alongside counts.

Conventions

• Index order. Amplitude index i has qubit j equal to bit j of i (little-endian). Index 1 is qubit 0 set; index 2 is qubit 1 set.
• Global phase. Included, exactly as Qiskit's Statevector does. The circuit's global_phase multiplies the whole state.
• Exactness. Computed in double precision without approximation.

See Conventions.

Agreement with Qiskit

The statevector example checks the result against Qiskit's own Statevector to about 1e-16.

Which engine produces it

Only the dense engine can produce a statevector, on CPU or on a GPU. The other engines do not materialize the state, by design. Consequently:

• a statevector request is refused for circuits too large for a dense state, with an error stating the bytes required and the budget;
• for circuits that split into independent groups, MENOS simulates each group densely and forms the full state as an exact tensor product.

Size

qubits   bytes
   20    16 MiB
   25    512 MiB
   30    16 GiB

The default memory budget is 50% of physical memory. See Memory Constraints.

import numpy as np
from qiskit import QuantumCircuit

from menos.qiskit import MENOSBackend

# 16 qubits: 1 MiB of amplitudes.
qc = QuantumCircuit(16)
for q in range(16):
    qc.ry(0.1 * (q + 1), q)
state = np.asarray(MENOSBackend().run(qc, shots=0, want_statevector=True).result().get_statevector())
assert state.size == 2**16
assert abs(np.linalg.norm(state) - 1.0) < 1e-12