qsy

A quantum computer state vector/stabilizer circuit simulator and assembly language.

Table of Contents

• Installation
• qsy
  • Example
• qsyASM
  • Usage
  • Example
  • Syntax
    • Operations
      • Adjoint Operation
      • List of Operations
    • Registers
    • Measurement
  • Efficient simulation of stabilizer circuits
• License

Installation

$ pip install qsy

This will install the Python library qsy and command-line tool qsyasm.

qsy

qsy is a Python library for simulating quantum circuits.

Example

The following code creates an entangled state and prints its state vector in Dirac notation.

from qsy import QuantumRegister, gates

qr = QuantumRegister(2)
qr.apply_gate(gates.H, 0)
qr.apply_gate(gates.CX, 0, 1)

print(qr.to_dirac())

The output will be:

+0.70711|00> +0.70711|11>

qsyASM

qsyASM is a quantum assembly language acting as front-end for qsy. It allows you to quickly write and debug quantum programs. It also allows for efficient simulation of stabilizer circuits using the chp back-end.

Usage

usage: qsyasm [-h] [-V] [-v] [-t] [-b B] [-s SHOTS] [--ignore-print-warning]
              [--skip-zero-amplitudes]
              filename

qsyasm assembly runner

positional arguments:
  filename              qsyasm file to execute

optional arguments:
  -h, --help            show this help message and exit
  -V, --version         show program's version number and exit
  -v, --verbose         verbose output
  -t, --time            time program execution
  -b B, --backend B     simulator back-end to use: chp or statevector
                        (default: statevector)
  -s SHOTS, --shots SHOTS
                        amount of shots to run
  --ignore-print-warning
                        ignore register too large to print warning
  --skip-zero-amplitudes
                        don't print states with an amplitude of 0

Example

The following qsyASM program creates an entangled state and measures to a classical register:

qreg[2] q
creg[2] c

h q[0]
cx q[0], q[1]

meas q, c

Running it:

$ qsyasm examples/qsyasm/bell.qs
q[2]: +1|11>
      +0 | 00
      +0 | 01
      +0 | 10
      +1 | 11
c[2]: 11

Or running it a number of times:

$ qsyasm examples/qsyasm/bell.qs --shots=1024
q[2]: +1|00>
      +1 | 00
      +0 | 01
      +0 | 10
      +0 | 11
c[2]: {'11': 550, '00': 474}

More examples such as the quantum phase estimation algorithm can be found in the examples/qsyasm folder.

Syntax

The structure of a qsyASM program consists of a list of instructions. An instruction is defined as an operation followed by its arguments.

Operations

The instruction

cx q[0], q[1]

applies a CNOT operation with control qubit q[0] and target qubit q[1]. Some operations take an angle (in radians) as argument. The parameterized operation

rz(pi/2) q[0]

rotates q[0] π/2 radians around the Z axis. Expressions are allowed in parameterized operations. Expression operators supported are +, -, *, / and ** (power). The variable pi is available for convenience.

Adjoint Operation

To apply the adjoint of a gate, the adj keyword is available. For example, to apply the adjoint of S (S dagger):

adj s q[0]

List of Operations

Gate	qsyASM operation
Pauli I	i target
Pauli X	x target
Pauli Y	y target
Pauli Z	z target
Hadamard	h target
S	s target
T	t target
Rx	rx(angle) target
Ry	ry(angle) target
Rz	rz(angle) target
CNOT	cx control, target
CZ	cz control, target
CRx	crx(angle) control, target
CRy	cry(angle) control, target
CRz	crz(angle) control, target
Toffoli	ccx controlA, controlB, target

Registers

Defining a quantum register is done with the qreg operation. The instruction

qreg[5] q

defines a 5 qubit quantum register named q. Likewise, a classical register (useful for measuring) can be defined as

creg[5] c

Qubits in a quantum register are initiated to |0⟩, and bits in a classical register to 0.

Measurement

Measurement can be done on individual qubits, or a complete quantum state. The program

qreg[5] q
creg[1] c

h q[0]

meas q[0], c[0]

measures q[0] to c[0], collapsing the state and storing the result in c[0]. The measurement result can be ignored by only passing one argument to meas:

meas q[0]

To measure a complete quantum state you can pass the whole quantum and classical register:

qreg[3] q
creg[3] c

; 3 qubit GHZ state
h q[0]
cx q[0], q[1]
cx q[0], q[2]

meas q, c

collapsing the quantum register q and storing the measurement result in c. This only works when the quantum register and classical register are equal in size.

Efficient simulation of stabilizer circuits

Circuits consisting only of CNOT, H, S, X, Y, Z and CZ gates can be efficiently simulated with the CHP back-end. Using any other operations with the CHP back-end will result in an error.

For example, we can simulate a partially entangled 750 qubit state:

$ qsyasm examples/qsyasm/750_qubits.qs --backend=chp
c[750]: 000000000000000000000000000000000000000000000000001111111111100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

This back-end is an implementation of the CHP simulator described by Scott Aaronson and Daniel Gottesman in their paper "Improved Simulation of Stabilizer Circuits" (arXiv:quant-ph/0406196).

License

This project is licensed under the MIT License. See the LICENSE file for the full license.