# The Quil Compiler¶

## Expectations for Program Contents¶

The QPUs have much more limited natural gate sets than the standard gate set offered by pyQuil: the gate operators are constrained to lie in RZ(θ), RX(kπ/2), and CZ; and the gates are required to act on physically available hardware (for single-qubit gates, this means acting only on live qubits, and for qubit-pair gates, this means acting on neighboring qubits). To ameliorate these limitations, the Rigetti software toolkit contains an optimizing compiler that translates arbitrary Quil to native Quil and native ProtoQuil to executables suitable for Rigetti hardware.

## Interacting with the Compiler¶

A QuantumComputer object supplied by the function pyquil.api.get_qc() comes equipped with a connection to a Rigetti quantum compiler. If the object is called qc, then this can be accessed using the instance method .compile(), as in the following:

from pyquil.quil import Pragma, Program
from pyquil.api import get_qc
from pyquil.gates import CNOT, H

qc = get_qc("9q-square-qvm")

ep = qc.compile(Program(H(0), CNOT(0,1), CNOT(1,2)))

print(ep.program) # here ep is of type PyquilExecutableResponse, which is not always inspectable


with output

PRAGMA EXPECTED_REWIRING "#(7 8 5 0 1 2 3 4 6)"
RZ(pi/2) 7
RX(pi/2) 7
RZ(-pi/2) 8
RX(pi/2) 8
CZ 8 7
RZ(-pi/2) 5
RX(pi/2) 5
RX(-pi/2) 8
CZ 5 8
RX(-pi/2) 5
RZ(pi/2) 5
RZ(-pi/2) 7
RZ(-pi/2) 8
PRAGMA CURRENT_REWIRING "#(7 8 5 0 1 2 3 4 6)"
PRAGMA EXPECTED_REWIRING "#(7 8 5 0 1 2 3 4 6)"
PRAGMA CURRENT_REWIRING "#(7 8 5 0 1 2 3 4 6)"


The compiler connection is also available directly via the property qc.compiler. The precise class of this object changes based on context (e.g., QPUCompiler, QVMCompiler, or LocalQVMCompiler), but it always conforms to the interface laid out by pyquil.api._qac:

• compiler.quil_to_native_quil(program): This method converts a Quil program into native Quil, according to the ISA that the compiler is initialized with. The input parameter is specified as a Program object, and the output is given as a new Program object, equipped with a .metadata property that gives extraneous information about the compilation output (e.g., gate depth, as well as many others). This call blocks until Quil compilation finishes.
• compiler.native_quil_to_executable(nq_program): This method converts a ProtoQuil program, which is promised to consist only of native gates for a given ISA, into an executable suitable for submission to one of a QVM or a QPU. This call blocks until the executable is generated.

The instance method qc.compile described above is a combination of these two methods: first the incoming Quil is nativized, and then that is immediately turned into an executable. Accordingly, the previous example snippet is identical to the following:

from pyquil.quil import Pragma, Program
from pyquil.api import get_qc
from pyquil.gates import CNOT, H

qc = get_qc("9q-square-qvm")

p = Program(H(0), CNOT(0,1), CNOT(1,2))
np = qc.compiler.quil_to_native_quil(p)
ep = qc.compiler.native_quil_to_executable(np)

print(ep.program) # here ep is of type PyquilExecutableResponse, which is not always inspectable


## Region-specific compiler features through PRAGMA¶

The Quil compiler can also be communicated with through PRAGMA commands embedded in the Quil program.

Note

The pyQuil compiler interface is under construction, and some of the PRAGMA directives will soon be replaced by finer-grained method calls.

### Preserved regions¶

The compiler can be circumvented in user-specified regions. The start of such a region is denoted by PRAGMA PRESERVE_BLOCK, and the end is denoted by PRAGMA END_PRESERVE_BLOCK. The Quil compiler promises not to modify any instructions contained in such a region.

The following is an example of a program that prepares a Bell state on qubits 0 and 1, then performs a time delay to invite noisy system interaction before measuring the qubits. The time delay region is marked by PRAGMA PRESERVE_BLOCK and PRAGMA END_PRESERVE_BLOCK; without these delimiters, the compiler will remove the identity gates that serve to provide the time delay. However, the regions outside of the PRAGMA region will still be compiled, converting the Bell state preparation to the native gate set.

DECLARE ro BIT[2]

#   prepare a Bell state
H 0
CNOT 0 1

#   wait a while
PRAGMA PRESERVE_BLOCK
I 0
I 1
I 0
I 1
# ...
I 0
I 1
PRAGMA END_PRESERVE_BLOCK

#   and read out the results
MEASURE 0 ro[0]
MEASURE 1 ro[1]


### Parallelizable regions¶

The compiler can sometimes arrange gate sequences more cleverly if the user gives it hints about sequences of gates that commute. A region containing commuting sequences is bookended by PRAGMA COMMUTING_BLOCKS and PRAGMA END_COMMUTING_BLOCKS; within such a region, a given commuting sequence is bookended by PRAGMA BLOCK and PRAGMA END_BLOCK.

The following snippet demonstrates this hinting syntax in a context typical of VQE-type algorithms: after a first stage of performing some state preparation on individual qubits, there is a second stage of “mixing operations” that both re-use qubit resources and mutually commute, followed by a final rotation and measurement. The following program is naturally laid out on a ring with vertices (read either clockwise or counterclockwise) as 0, 1, 2, 3. After scheduling the first round of preparation gates, the compiler will use the hinting to schedule the first and third blocks (which utilize qubit pairs 0-1 and 2-3) before the second and fourth blocks (which utilize qubit pairs 1-2 and 0-3), resulting in a reduction in circuit depth by one half. Without hinting, the compiler will instead execute the blocks in their written order.

DECLARE ro BIT[4]

# Stage one
H 0
H 1
H 2
H 3

# Stage two
PRAGMA COMMUTING_BLOCKS
PRAGMA BLOCK
CNOT 0 1
RZ(0.4) 1
CNOT 0 1
PRAGMA END_BLOCK
PRAGMA BLOCK
CNOT 1 2
RZ(0.6) 2
CNOT 1 2
PRAGMA END_BLOCK
PRAGMA BLOCK
CNOT 2 3
RZ(0.8) 3
CNOT 2 3
PRAGMA END_BLOCK
PRAGMA BLOCK
CNOT 0 3
RZ(0.9) 3
CNOT 0 3
PRAGMA END_BLOCK
PRAGMA END_COMMUTING_BLOCKS

# Stage three
H 0
H 1
H 2
H 3

MEASURE 0 ro[0]
MEASURE 1 ro[1]
MEASURE 2 ro[2]
MEASURE 3 ro[3]


### Rewirings¶

When a Quil program contains multi-qubit instructions that do not name qubit-qubit links present on a target device, the compiler will rearrange the qubits so that execution becomes possible. In order to help the user understand what rearrangement may have been done, the compiler emits two forms of PRAGMA: PRAGMA EXPECTED_REWIRING and PRAGMA CURRENT_REWIRING. From the perspective of the user, both PRAGMA instructions serve the same purpose: PRAGMA ..._REWIRING "#(n0 n1 ... nk)" indicates that the logical qubit labeled j in the program has been assigned to lie on the physical qubit labeled nj on the device. This is strictly for human-readability: user-supplied instructions of the form PRAGMA [EXPECTED|CURRENT]_REWIRING are discarded and have no effect.

In addition, you have some control over how the compiler constructs its rewiring. If you include a PRAGMA INITIAL_REWIRING "[NAIVE|RANDOM|PARTIAL|GREEDY]" instruction before any non-pragmas, the compiler will alter its rewiring behavior.

• PARTIAL (default): The compiler will start with nothing assigned to each physical qubit. Then, it will fill in the logical-to-physical mapping as it encounters new qubits in the program, making its best guess for where they should be placed.
• NAIVE: The compiler will start with an identity mapping as the initial rewiring. In particular, qubits will not be rewired unless the program requests a qubit-qubit interaction not natively available on the QPU.
• ! ! ! Error: Matrices do not lie in the same projective class. The compiler attempted to decompose an operator as native Quil instructions, and the resulting instructions do not match the original operator. This can happen when the original operator is not a unitary matrix, and could indicate an invalid DEFGATE block.